OS*
REESE LIBRARY
OF THE
UNIVERSITY OF CALIFORNIA.
Received^. . _ . ^*&.&$L $dLt_ _ _ i88/_,
Shelf No.___ ^ /_-/--
' ' Tzi
HYDRAULIC ENGINEERING
AND
MAN UAL
FOR
WATER SUPPLY ENGINEERS.
PUBLIC FOUNTAIN, CINCINNATI.
PRACTICAL TREATISE
ON
WATER-SUPPLY ENGINEERING:
RELATING TO THE
HYDROLOGY, HYDRODYNAMICS, AND PRACTICAL
CONSTRUCTION OF WATER-WORKS, IN
NORTH AMERICA.
WITH NUMEROUS
TABLES AND ILLUSTRATIONS,
BT
J. T. FANNlM^ v C.Bf,/y^
MEMBER OF THE AMERICAN
SECOXD EDITIOIST.
NEW YORK:
D. VAN NOSTRAND, PUBLISHER,
23 MURRAY STREET & 27 WARREN STREET.
1878.
^
v
COPYKIGHT, 1877,
BY
J. T. FANNING.
//
Electrotyped by Printed by
SMITH & McDOTJGAL. H. J. HEWETT
PREFACE TO THE SECOND EDITION.
THE author having been informed by the Publisher of this
treatise that he has already had the sheets of a second
edition struck off, and is about to hand them to the binder, gladly
avails himself of the opportunity to thank his professional friends
in practice and in training for the honor they have conferred, by
taking up the first edition ere it is scarce six months out of the
press, and to thank the scientific press generally for their kind
criticisms and commendations; and he is especially glad to have
opportunity so early to call attention to some typographical errors
in the first edition, and to ask the purchasers to make the proper
corrections therein, viz. :
In 423, p. 423, equation 28, one h t was omitted. It should
read,
P l = $w 9 \Ji, sec <f> (7i, 3 tan 2 < + c 2 2 )* f 2 .
In the Appendix, p. 597, the decimal point in the weight per
cubic inch of metals is one place too far to the left; thus, the
weight of aluminum is printed .00972, but should read .0972.
No one can regret so much as the author that other duties have
prevented a thorough revision and improvement of the work, so
that it may be more worthy of so generous a reception.
J. T. F.
WATER SUPPLY ENGINEERING. ERRATA.
Page 225. In line 10 the equation should read
v
249. The eighth line from the bottom should read :
In which h" = the resistance head in feet.
" 266. In equation 19 insert the sign + before m in
each of the three equations of v.
" 273. In line 15, after the word equation, strike out
the words, " double the subdivisor 9," and sub-
stitute, to find the new value of v. Also, in line
20 strike out the word " zero," and substitute
the word unity.
" 289. In the foot note, after the word deduct, substi-
tute the following : from the total length, in feet,
'an amount equal to one-tenth the head upon
the weir, in feet. Reduce the total length a
like amount for each end contraction.
' 380. In table 80 the two equations of Q at heads of
columns, are to change places.
" 487. In equation 20 place a decimal point before the
divisor, thus : .33338. .
528. In table 108, in the four columns of cubic feet
per minute, on this page, remove the decimal
point one place further to the right.
PREFACE.
fT^HERE is at present no sanitary subject of more general
-- interest, or attracting more general attention, than that
relating to the abundance and wholesomeness of domestic water
supplies.
Each citizen of a densely populated municipality must of
necessity be personally interested in either its physiological or
its financial bearing, or in both. Each closely settled town and
city must give the subject earnest consideration early in its ex-
istence.
At the close of the year 1875, fifty of the chief cities of the
American Union had provided themselves with public water sup-
plies at an aggregate cost of not less than ninety-five million
dollars, and two hundred and fifty lesser cities and towns were
also provided with liberal public water supplies at an aggregate
cost of not less than fifty-five million dollars.
The amount of capital annually invested in newly inaugurated
water-works is already a large sum, and is increasing, yet the
entire American literature relating to water-supply engineering
exists, as yet, almost wholly in reports upon individual works,
usually in pamphlet form, and accessible each to but compara-
tively few of those especially interested in the subject
. Scores of municipal water commissions receive appointment
each year in the growing young cities of the Union, who have to
inform themselves, and pass judgment upon, sources and systems
vi PREFACE.
of water supply, which are to become helpful or burdensome to
the communities they are intended to encourage accordingly as
the works prove successful or partially failures.
The individual members of these "Boards of Water Commis-
sioners," resident in towns where water supplies upon an extended
scale are not in operation, have rarely had opportunity to observe
and become familiar with the varied practical details and appa-
ratus of a water supply, or to acquaint themselves with even the
elementary principles governing the design of the several different
systems of supply, or reasons why one system is most advanta-
geous under one set of local circumstances and another system
is superior and preferable under other circumstances.
A numerous band of engineering students are graduated each
year and enter the field, many of whom choose the specialty of
hydraulics, and soon discover that their chosen science is great
among the most noble of the sciences, and that its mastery, in
theory and practice, is a work of many years of studious acquire-
ment and labor. They discover also that the accessible literature
of their profession, in the English language, is intended for the
class-room rather than the field, and that its formulae are based
chiefly upon very limited philosophical experiments of a century
and more ago but partially applicable to the extended range of
modern practice.
Among the objects of the author in the compilation of the
following pioneer treatise upon American Water-works are, to
supply water-commissioners with a general review of the best
methods practised in supplying towns and cities with water, and
with facts and suggestions that will enable them to compare in-
telligently the merits and objectionable features of the different
potable water sources within their reach ; to present to junior and
assistant hydraulic engineers a condensed summary of those ele-
mentary theoretical principles and the involved formulas adapted
to modern practice, which they will have frequently to apply,
together with some useful practical observations ; to construct
and gather, for the convenience of the older busy practitioners,
PREFACE. vii
numerous tables and statistics that will facilitate their calcula-
tions, some of which would otherwise cost them, in the midst of
pressing labors, as they did the author, a great deal of laborious
research among rare and not easily procurable scientific treatises ;
and also to present to civil engineers generally a concise reference
manual, relating to the hydrology, hydrodynamics, and practical
construction of the water-supply branch of their profession.
This work is intended more especially for those who have
already had a task assigned them, and who, as commissioner,
engineer, or assistant, are to proceed at once upon their recon-
noissance and surveys, and the preparation of plans for a public
water supply. To them it is humbly submitted, with the hope
that it will prove in some degree useful. Its aim is to develop
the bases and principles of construction, rather than to trace the
origin of, or to describe individual works. It is, therefore, prac-
tical in text, illustration, and arrangement ; but it is hoped that
the earnest, active young workers will find it in sympathy with
their mood, and a practical introduction, as well, to more pro-
found and elegant treatises that unfold the highest delights of the
science.
Good design, which is invariably founded upon sound mathe-
matical and mechanical theory, is a first requisite for good and
judicious practical engineering construction. We present, there-
fore, the formulae, many of them new, which theory and practical
experiments suggest as aids to preliminary studies for designs,
and many tables based upon the formulas, which will facilitate the
labors of the designer, and be useful as checks against his own com-
putations, and we give in addition such discussions of the elemen-
tary principles upon which the theories are founded as will enable
the student to trace the origin of each formula ; for a formula is
often a treacherous guide unless each of its factors and experience*
coefficients are well understood. To this end, the theoretical dis-
cussions are in familiar language, and the formulas in simple ar-
rangement, so that a knowledge of elementary mathematics only
is necessary to read and use them.
viii PREFACE.
We do by no means intimate, however, that an acquaintance
with elementary theories alone suffices for an accomplished en-
gineer. It is sometimes said that genius spurns rules, and it is
true that untutored genius sometimes grapples with and accom-
plishes great and worthy deeds, but too often in a bungling
manner, not to be imitated.
In kindly spirit we urge the student to bear in mind that it is
the rigorously trained genius who oftenest achieves mighty works
by methods at once accurate, economical, artistic, and in every
respect successful and admirable.
J. T. F.
BOSTON, November, 1876.
CONTENTS.
SECTION I.
COLLECTION AND STORAGE OF WATER, AND ITS
IMPURITIES.
CHAPTER I.
INTRODUCTORY. PAGE 25.
Art. i, Necessity of Public Water Supplies. 2, Physiological Office of Water.
3, Sanitary Office of Water Supplies. 4, Helpful Influence of Public
Water Supplies. 5, Municipal Control of Public Water Supplies. 6,
Value as an Investment. 7, Incidental Advantages.
CHAPTER II.
QUANTITY OF WATER REQUIRED. PAGE 31.
Art. 8, Statistics of Water Supplied. 9, Census Statistics. 10, Approximate
Consumption of Water. n, Water Supplied to Ancient Cities. 12, Water
Supplied to European Cities. 13, Water Supplied to American Cities.
14, The Use of Water Steadily Increasing. 15, Increase in Various Cities.
16, Relation of Supply per Capita to Total Population. 17, Monthly
and Hourly Variations in the Draught. 18, Ratio of Monthly Consump-
tion. 19, Illustrations of Varying Consumption. 20, Reserve for Fire
Extinguishment.
CHAPTER III.
RAINFALL. PAGE 45.
Art. 21, The Vapory Elements of Water. 22, The Liquid and Gaseous Succes-
sions. 23, The Source of Showers. 24, General Rainfall. 25, Review of
Rainfall Statistics. 26, Climatic Effects. 27, Sections of Maximum Rain-
fall. 28, Western Rain System. 29, Central Rain System. 30, Eastern
Coast System. 31, Influence of Elevation upon Precipitation. 32, River
Basin Rains. 33, Grouped Rainfall Statistics. 34, Monthly Fluctuations
x CONTENTS.
in Rainfall. 35, Secular Fluctuations in Rainfall. 36, Local Physical
and Meteorological Influences. 37, Uniform Effects of Natural Laws.
38, Great Rain Storms. 39, Maximum Ratios of Floods to Rainfalls. 40^
Volume of Water from given Rainfalls. 41, Gauging Rainfalls.
CHAPTER IV.
FLOW OF STREAMS. PAGE 65.
Art. 42, FJtood Volumes Inversely as the Areas of Basins. 43, Formulas for
Flood Volumes. 44, Table of Flood Volumes. 45, Seasons of Floods.
46, Influence of Absorption and Evaporation upon Flow. 47, Flow in Sea-
sons of Minimum Rainfall. 48, Periodic Classification of available Flow.
49, Sub-surface Equalizers of Flow. 50, Flashy and Steady Streams.
51, Peculiar Watersheds. 52, Summaries of Monthly Flow Statistics.
53, Minimum, Mean, and Flood Flow of Streams. 54, Ratios of Monthly
Flow in Streams. 55, Mean Annual Flow of Streams. 56, Estimates of
Flow of Streams. 57, Ordinary Flow of Streams. 58, Tables of Flow,
Equivalent to given Depths of Rain.
CHAPTER V.
STORAGE AND EVAPORATION OF WATER. PAGE 84.
STORAGE. Art. 59, Artificial Storage. 60, Losses Incident to Storage. 61,
Sub-strata of the Storage Basin. 62, Percolation from Storage Basins.
63, Rights of Riparian Owners. 64, Periodical Classification of Riparian
Rights. 65, Compensations. EVAPORATION. 66, Loss from Reservoir
by Evaporation. 67, Evaporation Phenomena. 68, Evaporation from
Water. 69, Evaporation from Earth. 70, Examples of Evaporation. 71,
Ratios of Evaporation. 72, Resultant Effect of Rain and Evaporation.
73, Practical Effect upon Storage.
CHAPTER VI.
SUPPLYING CAPACITY OF WATER-SHEDS. PAGE 94.
Art. 74, Estimate of Available Annual Flow of Streams. 75, Estimate of
Monthly available Storage Required. 76, Additional Storage Required.
/7, Utilization of Flood Flows. 78, Qualification of Deduced Ratios. 79,
Influence of Storage upon a Continuous Supply. 80, Artificial Gathering
Areas. 81, Recapitulation of Rainfall Ratios.
CHAPTER VII.
SPRINGS AND WELLS. PAGE 102.
Art. 82, Subterranean Waters. 83, Their Source, the Atmosphere. 84, Po-
rosity of Earths and Rocks. 85, Percolations in the Upper Strata. 86,
The Courses of Percolation. 87, Deep Percolations. 88, Subterranean
CONTENTS.
Reservoirs. 89, The Uncertainties of Subterranean Searches. 90, Re-
nowned Application of Geological Science. 91, Conditions of Overflow-
ing Wells. 92, Influence of Wells upon each other. 93, American Ar-
tesian Wells. 94, Watersheds of Wells. 95, Evaporation from Soils.-^
96, Supplying Capacity of Wells and Springs.
CHAPTER VIII.
IMPURITIES OF WATER. PAGE 112.
Art. 97, The Composition of Water. 98, Solutions in Water. 99, Properties
of Water. zoo, Physiological Effects of the Impurities of Water. 101,
Mineral Impurities. 102, Organic Impurities. 103, Tables of Analyses
of Potable Waters. 104, Ratios of Standard Gallons. 105, Atmospheric
Impurities. 106, Sub-surface Impurities. 107, Deep-well Impurities.
108, Hardening Impurities. 109, Temperature of Deep Sub-surface
Waters. no, Decomposing Organic Impurities. in, Vegetal Organic
Impurities. 112, Vegetal Organisms in Water-pipes. 113, Animate Or-
ganic Impurities. 114, Propagation of Aquatic Organisms. 115, Purify-
ing Office of Aquatic Life. 116, Intimate Relation between Grade of
Organisms and Quality of Water. 117, Animate Organisms in Water-
pipes. 118, Abrasion Impurities in Water. 119, Agricultural Impuri-
ties. 120, Manufacturing Impurities. 121, Sewage Impurities. 122,
Impure Ice in Drinking- Water. 123, A Scientific Definition of Polluted
Water.
CHAPTER IX.
WELL, SPRING, LAKE, AND RIVER SUPPLIES. PAGE 139.
WELL WATERS. Art. 124, Locations for Wells. 125, Fouling of Old Wells.
SPRING WATERS. 126, Harmless Impregnations. 127, Mineral Springs.
LAKE WATERS. 128, Favorite Supplies. 129, Chief Requisites. 130,
Impounding. 131, Plant Growth. 132, Strata Conditions. 133, Plant
and Insect Agencies. 134, Preservation of Purity. 135, Natural Clarifi-
cation. 136, Great Lakes. 137, Dead Lakes. RIVER WATERS. 138,
Metropolitan Supplies. 139, Harmless and Beneficial Impregnations.
140, Pollutions. 141, Sanitary Discussions. 142, Inadmissible Polluting
Liquids, 143, Precautionary Views. 144, Speculative Condition of the
Pollution Question. 145, Spontaneous Purification. 146, Artificial Clari-
fication. 147, A Sugar Test of the Quality of Water.
xii CONTENTS.
SECTION II.
FLOW OF WATER THROUGH SLUICES, PIPES, AND
CHANNELS.
CHAPTER X.
WEIGHT, PRESSURE, AND MOTION OF WATER. PAGE 161.
Art. 148, Special Characteristics of Water. 149, Atomic Theory. 150, Molec-
ular Theory. 151, Influence of Caloric. 152, Relative Densities and
Volumes. WEIGHT OF WATER. 153, Weight of Constituents of Water.
154, Crystalline Forms of Water. 155, Formula for Volumes at Differ-
ent Temperatures. 156, Weight of Pond Water. 157, Compressibility
and Elasticity of Water. 158, Weights of Individual Molecules. 159, In-
dividual Molecular Actions. PRESSURE OF WATER. 160, Pressure Propor-
tional to Depth. 161, Individual Molecular Reactions. 162, Equilibrium
destroyed by an Orifice. 163, Pressures from Vertical, Inclined, and Bent
Columns of Water. 164, Artificial Pressure. 165, Pressure upon a Unit
of Surface. 166, Equivalent Forces. 167, Weight a Measure of Pressure.
168, A Line a Measure of Weight. 169, A Line a measure of Pressure
upon a Surface. 170, Diagonal Force of Combined Pressures Graphically
Represented. 171, Angular Resultant of a Force Graphically Repre-
sented. 172, Angular Effects of a Force Represented by the Sine and
Cosine of the Angle. 173, Total Pressure. 174, Direction of Maximum
Effect. 175. Herizontal and Vertical Effects. 176, Centres of Pressure
and of Gravity. 177, Pressure upon a Curved Surface, and Effect upon
its Projected Plane. 178, Centre of Pressure upon a Circular Area.
179, Combined Pressures. 180, Sustaining Pressure upon Floating and
Submerged Bodies. 181, Upward Pressure upon a Submerged Lintel.
182, Atmospheric Pressure. 183, Rise of Water into a Vacuum. 184,
Siphon. 185, Transmission of Pressure to a Distance. 186, Inverted
Syphon. 187, Pressure Convertible into Motion. MOTION OF WATER.
188, Flow of Water. 189, Action of Gravity upon Individual Molecules.
190, Frictionless Movement of Molecules. 191, Acceleration of Motion.
192, Equations of Motion. 193, Parabolic Path of Jet. 194, Velocity of
Efflux Proportional to the Head. 195, Conversion of the Force of Grav-
ity from Pressure into Motion. 196, Resultant Effects of Pressure and
Gravity upon the Motion of a Jet. 197, Equal Pressures give Equal
Velocities in all Directions. 198, Resistance of the Air. 199, Theoretical
Velocities.
CHAPTER XI.
FLOW OF WATER THROUGH ORIFICES. PAGE 194.
Art. 200, Motion of the Individual Particles. 201, Theoretical Volume of
Efflux. 202, Converging Path of Particles. 203, Classes of Orifices.
CONTENTS. xiii
204, Form of Submerged Orifice Jet. 205, Ratio of Minimum Section of
Jet. 206, Volume of Efflux. 207, Coefficient of Efflux. 208, Maximum
Velocity of the Jet. 209, Factors ol the Coefficient of Efflux. 210, Prac-
tical Use of a Coefficient. 211, Experimental Coefficients. (From Michel-
otti, Abbe Bosset, Rennie, Castel, Lespinasse, General Ellis.) 212, Co-
efficients Diagramed. 213, Effect of Varying the Head, or the Proportions
of the Orifice. 214, Peculiarities of Efflux from an Orifice. 215, Mean
Velocity of the Issuing Particles. 216, Coefficients of Velocity and
Contraction. 217, Velocity of Particles Dependent upon their Angular
Positions. 218, Equation of Volume of Efflux from a Submerged Orifice.
219, Effect of Outline of Geometrical Orifices upon Efflux. 220, Vari-
able Value of Coefficients. 221, Assumed Mean Value of Efflux. 222,
Circular Jets, Polygonal do., Complex do. 223, Cylindrical and Divergent
Orifices. 224, Converging Orifices.
CHAPTER XII.
FLOW OF WATER THROUGH SHORT TUBES. PAGE 213.
Art. 225, An Ajutage. 226, Increase of Coefficient. 227, Adjutage Vacuum,
and its Effect. 228, Increased Volume of Efflux. 229, Imperfect Va-
cuum. 230, Divergent Tube. 231, Convergent Tube. 232, Additional
Contraction. 233, Coefficients of Convergent Tubes. 234, Increase and
Decrease of Coefficient of Smaller Diameter. 235, Coefficient of Final
Velocity. 236, Inward Projecting Ajutage. 237, Compound Tube.
238, Coefficients of Compound Tubes. 239, Experiments with Cylindri-
cal and Compound Tubes. 240, Tendency to Vacuum. 241, Percussive
Force of Particles. 242, Range of Eytelwein's Table. 243, Cylindrical
Tubes to be Preferred.
CHAPTER XIII.
FLOW OF WATER THROUGH PIPES, UNDER PRESSURE.
PAGE 223.
Art. 244, Pipe and Conduit. 245, Short Pipes give Greatest Discharge. 246,
Theoretical Volume from Pipes. 247, Mean Efflux from Pipes. 248, Sub-
division of the Head. 249, Mechanical Effect of the Efflux. 250, Ratio
of Resistance at Entrance to the Pipe. RESISTANCE TO FLOW W*THIN
A PIPE. 251, Resistance of Pipe-Wall. 252, Conversion of Velocity into
Pressure. 253, Coefficients of Efflux from Pipes. 254, Reactions from the
Pipe-Wall. 255, Origin of Formulas of Flow. 256, Formula of Resist-
ance to Flow. 257, Coefficient of Flow. 258, Opposition of Gravity and
Reaction. 259, Conversion of Pressure into Mechanical Effect. 260,
Measure of Resistance to Flow 261, Resistance Inversely as the Square
of the Velocity. 262, Increase of Bursting Pressure. 263, Acceleration
and Resistance. 264, Equation of Head Required to Overcome the Re-
sistance. 265, Designation of h" and /. 266, Variable Value of m. 267,
Investigation of Values of m. 268, Definition of Symbols. 269, Experi-
xiv CONTENTS.
mental Values of the Coefficient of Flow. 270, Peculiarities of the Coeffi-
cient (m)of Flow. 271, Effects of Tubercles. 272, Classification of Pipes
and their Mean Coefficients. 273, Equation of the Velocity Neutralized
by Resistance to Flow. 274, Equation of Resistance Head. 275, Equation
of Total Head. 276, Equation of Volume. 277, Equation of Diameter.
278, Relative Value of Subdivisions of Total Head. 279, Many Popular
Formulas Incomplete. 280. Formula of M. Chezy. 281, Various Pop-
ular Formulas Compared. 282, Sub-heads Compared. 283, Investiga-
tions by Dubuat, and Coloumb, and Prony. 284, Prony's Analysis. 285,
Eytelwein's Equation of Resistance to Flow. 286, D'Abuisson's Equation
of Resistance to Flow. 287, Weisbach's Equation of Resistance to Flow.
288, Transpositions of an Original Formula. 289, Unintelligent Use of
Partial Formulas. 290, A Formula of more General Application. 291,
Values of v for Given Slopes. 292, Values of h and h! for Given Velocities.
293, Classified Equations for Velocity, Head, Volume, and Diameter.
294, Coefficients of Entrance of Jet. 295, Mean Coefficients for Smooth>
Rough, and Foul Pipes. 296, Mean Equations for Smooth, Rough, and
Foul Pipes. 297, Modification of a Fundamental Equation of Velocity.
298, Values of c 1 . 299, Bends. 300, Branches. 301, How to Economize
Head.
CHAPTER XIV.
MEASURING WEIRS, AND WEIR GAUGING. PAGE 277.
Art. 302, Gauged Volumes of Flow. 303, Form of Weir. 304, Dimensions.
305, Stability. 306, Varying Length. 307, End Contractions. 308,
Crest Contractions. 309, Theory of Flow over a Weir. 310, Formulas
for Flow, without and with Contractions. 311, Increase of Volume due
to Initial Velocity of Water. 312, Coefficients for Weir Formulas. 313,
Discharges for Given Depths. 314, Vacuum under the Crest. 315, Ex-
amples of Initial Velocity. 316, Wide-crested Weirs. 317, Triangular-
Notch Weirs. 318, Obstacles to Accurate Measures. 319, Hook Gauge.
320, Rule Gauge. 321, Tube and Scale Gauge.
CHAPTER XV.
FLOW OF WATER IN OPEN CHANNELS PAGE 299.
Art. 322, Gravity the Origin of Flow. 323, Resistance to Flow. 324, Equa-
tions of Resistance and Velocity. 325, Equation of Inclination. 326, Co-
efficients of Flow for Channels. 327, Observed Data of Flow in Channels.
328, Table of Coefficients for Channels. 329, Various Formulas of Flow
Compared. 330, Velocities of Given Films. 331, Surface Velocities.
332, Ratios of Surface to Mean Velocities. 333, Hydrometer Gaugings.
334, Tube Gauges. 335, Gauge Formulas. 336, Pitot Tube Gauge 337,
Woltmann's Tachometer. 338, Hydrometer Coefficients. 339, Henry's
Telegraphic Moulinet. 340, Earlier Hydrometers. 341, Double Floats.
342, Mid-depth Floats. 343, Maximum Velocity Floats. 344, Relative
Velocities and Volumes due to Different Depths.
CONTENTS.
SECTION III.
PRACTICAL CONSTRUCTION OF WATER-WORKS.
CHAPTER XVI.
RESERVOIR EMBANKMENTS AND CHAMBERS. PAGE 333.
Art. 345, Ultimate Economy of Skillful Construction. 346, Embankment Foun-
dations. 347, Springs under Foundations. 348, Surface Soils. 349, Con-
crete Cut-off Walls. 350, Treacherous Strata. 351, Embankment Core
Materials. 352, Peculiar Pressures. 353, Earthwork Slopes. 354, Re-
connaissance for Site. 355, Detailed Surveys. 356, Illustrative Case. .
357, Cut-off Wall. 358, Embankment Core. 359, Frost Covering. 360,
Slope Paving. 361, Puddle Wall. 362, Rubble Priming Wall. 363, A
Light Embankment. 364, Distribution Reservoirs. 365, Application of
Fine Sand. 366, Masonry Faced Embankment. 367, Concrete Paving.
368, Embankment Sluices and Pipes. 369, Gate Chambers. 370, Sluice
Valve Areas. 371, Stop-valve Indicator. 372, Power required to Open
a Valve, 373, Adjustable Effluent Pipe. 374, Fish Screens. 375, Gate
Chamber Foundations. 376, Foundation Concrete. 377, Chamber
Walls.
CHAPTER XVII.
OPEN CANALS.-PAGE 370.
Art. 378, Canal Banks. 379, Inclinations and Velocities in Practice. 380,
Ice Covering. 381, Table of Dimensions of Supply Canals. 382, Canal
Gates. 383, Miners' Canals.
CHAPTER XVII I.
WASTE WEIRS. PAGE 377.
Art. 384, The Office and Influence of a Waste-Weir. 385, Discharges over
Waste-Weirs. 386, Required Lengths of Waste- Weirs. 387. Forms of
Waste-Weirs. 388, Isolated Weirs. 389, Timber Weirs. 390, Ice-Thrust
upon Storage Reservoir Weirs. 391, Breadths of Weir-Caps. 392, Thick-
nesses of Waste-Weirs and Dams. 393, Force of Overflowing Water.
394, Heights of Waves.
CHAPTER XIX.
PARTITIONS AND RETAINING WALLS. PAGE 390.
Art. 395, Design. 396, Theory of Water-Pressure upon a Vertical Surface.
397, Water Pressure upon an Inclined Surface. 398, Frictional Stability
xvi CONTENTS.
of Masonry. 399, Coefficients of Masonry Friction. 400, Pressure Lever-
age of Water. 401, Leverage Stability of Masonry. 402, Moment of
Weight Leverage of Masonry. 403, Thickness of a Vertical Rectangular
Wall for Water Pressure. 404, Moments of Rectangular and Trapedoidal
Sections. 405, Graphical Method of Finding the Leverage Resistance.
406, Granular Stability. 407, Limiting Pressures. 408, Table of Walls for
Quiet Water. 409, Economic Profiles. 410, Theory of Earth Pressures.
411, Equation of Weight of Earth Wedge. 412, Equation of Pressure of
Earth Wedge. 413, Equation of Moment of Pressure Leverage. 414,
Thickness of a Vertical Rectangular Wall for Earth Pressure. 415, Sur-
charged Earth Wedge. 416, Pressure of a Surcharged Earth Wedge.
417, Moment of a Surcharged Pressure Leverage. 418, Pressure of an
Infinite Surcharge. 419, Resistance of Masonry Revetments. 420, Final
Resultants in Revetments. 421. Table of Trapezoidal Revetments. 422,
Curved-face Batter Equation. 423, Back Batters and their Equations.
424, Inclination of Foundation. 425, Front Batters and Steps. 426,
Top Breadth. 427, Wharf Walls. 428, Counterforted Walls. 429, Ele-
ments of Failure. 430, End Supports. 431, Faced and Concrete Revet-
ments.
CHAPTER XX.
MASONRY CONDUITS. PAGE 431.
Art. 432, Protection of Channels for Domestic Water Supplies. 433, Examples
of Conduits. 434, Foundations of Conduits. 435, Conduit Shells. 436,
Ventilation of Conduits. 437, Conduits under Pressure. 438, Protection
from Frost. 439, Masonry to be Self-sustaining. 440, A Concrete Con-
duit. 441, Example of a Conduit under Heavy Pressure. 442, Mean
Radii of Conduits. 443, Formulas of Flow for Conduits. 444, Table of
Conduit Data.
CHAPTER XXI.
MAINS AND DISTRIBUTION PIPES. PAGE 446.
Art, 445, Static Pressures in Pipes. 446, Thickness of Shell resisting Static
Pressure. 447, Water-Ram. 448, Formulas of Thickness for Ductile
Pipes. 449, Strengths of Wrought Pipe Metals. 450, Moulding of Pipes.
451, Casting of Pipes. 452, Formulas of Thickness for Cast-iron Pipes.
453, Thicknesses found Graphically. 454, Table of Thicknesses of Cast-
iron Pipes. 455, Table of Equivalent Fractional Expressions. 456, Cast-
iron Pipe-Joints. 457, Dimensions of Pipe-Joints. 458, Templets for
Bolt Holes. 459, Flexible Pipe-Joint. 460, Thickness Formulas Com-
pared. 461, Formulas for Weights of Cast-iron Pipes. 462, Table of
Weights of Cast-iron Pipes. 463, Interchangeable Joints. 464, Charac-
teristics of Pipe Metals. 465, Tests of Pipe-Metals. 466, The Preserva-
tion of Pipe Surfaces. 467, Varnishes for Pipes and Iron Work. 468,
Hydraulic Proof of Pipes. 469, Special Pipes. 470, Cement-lined and
CONTENTS. xvii
Coated Pipes. 471, Methods of Lining. 472, Covering. 473, Cement
Joints. 474, Cast Hub Joint. 475, Composite Branches. 476, Thickness
of Shells for Cement Linings. 477, Gauge Thickness and Weights of
Rolled Iron. 478, Lining, Covering, and Joint Mortar. 479, Asphaltum-
Coated Wrought-iron Pipes. 480, Asphaltum Bath, for Pipes. 481,
Wrought Pipe Plates. 482, Bored Pipes. 483, Wyckoff's Patent
Pipe.
CHAPTER XXI I.
DISTRIBUTION SYSTEMS, AND APPENDAGES. PAGE 493.
Art. 484, Loss of Head by Friction. 485, Table of Frictional Heads in Pipes.
486, Relative Discharging Capacities of Pipes. 487, Table of Relative
Capacities of Pipes. 488, Depths of Pipes. 489, Elementary Dimensions
of Pipes. 490, Distribution Systems. 491, Rates of Consumption of
Water. 492, Rates of Fire Supplies. 493, Diameter of Supply Main.
494, Diameters of Sub-mains. 495, Maximum Velocities of Flow. 496,
Comparative Frictions. 497, Relative Rates of Flow for Domestic and
Fire Supplies. 498, Required Diameters for Fire Supplies. 499, Duplica-
tion Arrangement of Sub-Mains. 500, Stop-Valve Systems. 501, Stop-
Valve Locations. 502, Blow-off and Waste Valves. 503, Stop-Valve De-
tails. 504, Valve Curbs. 505, Fire Hydrants. 506, Post Hydrants. 507,
Hydrant Details. 508, Flush Hydrants. 509, Gate Hydrants. 510, High
Pressures. 511, Air Valves. 512, Union of High and Low Services. 513,
Combined Reservoir and Direct Systems. 514, Stand Pipes. 515, Fric-
tional Heads in Service-Pipes.
CHAPTER XXII I.
CLARIFICATION OF WATER. PAGE 530.
Art. 516, Rarity of Clear Waters. 517, Floating Debris. 518, Mineral Sedi-
ments. 519, Organic Sediments. 520, Organic Solutions. 521, Natural
Processes of Clarification. 522, Chemical Processes of Clarification. 523,
Charcoal Process. 524, Infiltration. 525, Infiltration Basins. 526, Ex-
amples of Infiltration. 527, Practical Considerations. 528, Examples
of European Infiltration. 529, Example of Intercepting Well. 530,
Filter Beds. 531, Settling and Clear-Water Basins. 532, Introduction
of Filter-Bed System. 533. Capacity of Filter Beds. 534, Cleaning of
Filter Beds. 535, Renewal of Sand Surface. 536, Basin Coverings.
CHAPTER XXIV.
PUMPING OF WATER. PAGE 557.
Art. 537, Types of Pumps. 538, Prime Movers. 539, Expense of Variable
Delivery of Water 540, Variable Motions of a Piston. 541, Ratios of
Variable Delivery of Water. 542, Office of Stand-Pipe and Air- Vessel.
xviii CONTENTS.
543, Capacities of Air -Vessels. 544, Valves. 545, Motions of Water
through Pumps. 546, Double-Acting Pumping Engines. 547, Geared
Pumping Engines. 548, Costs of Pumping Water. 549, Duty of
Pumping Engines. 550, Special Trial Duties. 551, Economy of a High
Duty.
CHAPTER XXV.
SYSTEMS OF WATER SUPPLY. PAGE 585.
Art. 552, Permanence of Supply Essential. 553, Methods of Gathering and
Delivering Water. 554, Gravitation. 555, Choice ot Water. 556,
Pumping with Reservoir Reserve 557, Pumping with Direct Pres-
sure.
LIST OF TABLES.
Table No. Page
1. Population, Families, and Dwellings in Fifty American Cities. ....... 32
2. Water Supplied, and Piping in several Cities 38
3. Water Supplied in years 1870 and 1874 39
4. Average Gallons of Water Supplied to each Inhabitant 40
5. Ratios of Monthly Consumption of Water in 1874 43
6. Mean Rainfall in different River Basins 51
7. Rainfall in the United States 53
8. Volumes of Rainfall per minute for given inches of Rain per twenty-
four hours 62
9. Flood Volumes from given Watershed Areas 67
10. Summary of Rainfall upon the Cochituate Basin 72
11. Summary of Rainfall upon the Croton Basin 72
12. Summary of Rainfall upon the Croton West-Branch Basin 73
13. Summary of Percentage of Rain Flowing from the Cochituate Basin. . . 73
14. Summary of Percentage of Rain Flowing from the Croton Basin 73
15. Summary of Percentage of Rain Flowing from the Croton West-Branch
Basin 74
16. Summary of Volume of Flow from the Cochituate Basin 74
17. Summary of Volume of Flow from the Croton Basin 74
18. Summary of Volume of Flow from the Croton West- Branch Basin 75
19. Estimates of Minimum, Mean, and Maximum Flow of Streams 75
20. Monthly Ratios of Flow of Streams 76
21. Ratios of Mean Monthly Rain and Inches of Rain Flowing each Month 77
22. Equivalent Volumes of Flow for given Depths of Rain in One Month. 82
23. Equivalent Volumes of Flow for given Depths of Rain in One Year. . . 83
24. Evaporation from Water 89
25. Mean Evaporation from Earth 89
26. Monthly Ratios of Evaporation from Reservoirs 92
27. Multipliers for Equivalent Inches of Rain Evaporated 92
28. Monthly Supply to and Draft from a Reservoir (with Compensation). . 96
29. Monthly Supply to and Draft from a Reservoir (without Compensation) 97
30. Ratios of Monthly Rain, Flow, Evaporation, and Consumption 101
31. Percolation of Rain into One Square Mile of Porous Soil m
32. Analyses of Various Lake, Spring, and Well Waters 117
33. Analyses of Various River and Brook Waters 118
34. Analyses of Various Streams in Massachusetts 120
35. Analyses of Various Water Supplies from Domestic Wells 121
xx LIST OF TABLES.
Table No. p age
36. Artesian Well Temperatures 1 1 1 1 4 , , , 4 4 127
37. Analyses of Various Mineral Spring Waters 143
38. Weights and Volumes of Water at Different Temperatures 166
39. Pressures of Water at Stated Depths 172
40. Correspondent Heights, Velocities, and Times of Falling Bodies 190
41. Coefficients from Michelotti's Experiments with Orifices 198
42. Coefficients from Bossut's Experiments with Orifices 199
43. Coefficients from Rennie's Experiments with Orifices 199
44. Coefficients from Lespinasse's Experiments with Orifices 201
45. Coefficients from General Ellis's Experiments with Orifices 203
46. Coefficients for Rectangular Orifices (vertical) 205
47. Coefficients for Rectangular Orifices (horizontal) 206
48. Castel's Experiments with Convergent Tubes 217
49. Venturi's Experiments with Divergent Tubes 219
50. Eytelwein's Experiments with Compound Tubes 220
51. Coefficients of Efflux (c) for Short Pipes 227
52. Experimental Coefficients of Flow (m) by Darcy 237
53. Experimental Coefficients of Flow (m) by Fanning 238
54. Experimental Coefficients of Flow (m) by Du Buat 238
55. Experimental Coefficients of Flow (m) by Bossut 238
56. Experimental Coefficients of Flow (m) by Couplet 239
57. Experimental Coefficients of Flow (m) by Provis 239
58. Experimental Coefficients of Flow (m) by Rennie 239
59. Experimental Coefficients of Flow (m) by Darcy 240
60. Experimental Coefficients of Flow (m) by General Greene and others. . 240
61. Tabulated Series of Coefficients of Flow (m) 242
62. Coefficients for Clean, Slightly Tuberculated, and Foul Pipes 248
63. Various Formulas for Flow of Water in Pipes 254
64. Velocities (v) for given Slopes and Diameters 259
65. Tables of h and K due to given Velocities 264
66. Values of c v and c for Tubes 267
66a. Sub-coefficients of Flow (*:') in Pipes. 271
67. Coefficients of Resistance in Bends 274
68. Experimental Weir Coefficients 288
69. Coefficients for given Depths upon Weirs 289
70. Discharge for given Depths upon Weirs 290
71. Weir Coefficients by Castel , 291
72. Series of Weir Coefficients by Smeaton and others 291
73. Coefficients for Wide Weir-crests 294
74. Observed and Computed Flows in Canals and Rivers 307
75. Coefficients (m) for Open Channels 308
76. Various Formulas for Flow in Open Channels 310
77. Weights of Embankment Materials 341
78. Angles of Repose, and Frictions of Embankment Materials 345
79. Dimensions of Water Supply and Irrigation Canals 373
80. Waste-Weir Volumes for given Depths 380
81. Lengths and Discharges of Waste-Weirs 381
f ' '"
LIST OF TABLES , xxi
Table No. Page
82. Thicknesses of Masonry Weirs and Dams 387
83. Heights of Reservoir and Lake Waves 388
84. Coefficients of Masonry Frictions 396
85. Computed Pressures in Masonry 403
86. Limiting Pressures upon Masonry 404
87. Dimension of Walls to Retain Water 406
88. Dimension of Walls to Sustain Earth 420
89. Thicknesses of a Curved-face Wall 422
90. Hydraulic Mean Radii for Circular Conduits 442
900. Coefficients (m) for Smooth Conduits 444
91. Conduit Data 445
92. Tenacities of Wrought Pipe Metals 451
93. Thicknesses of Cast-iron Pipes 455
930;. Thicknesses of Cast-iron Pipes as used in several Cities 456
94. Parts of an Inch and Foot expressed Decimally 457
95. Dimensions of Cast-iron Water-pipes 461
96. Flange Data of Flanged Cast-iron Pipes 462
97. Various Formulas for Thicknesses of Cast-iron Pipes 466
98. Weights of Cast-iron Pipes 468
980;. Weights of Cast-iron Pipes as used in several Cities 469
99. Thicknesses of Wrought-iron Pipe Shells 486
100. Thicknesses and Weights of Iron Plates 488
101. Frictional Head in Pipes 495
102. Relative Discharging Capacities of Pipes ; 5
103. Depths to lay Water-pipes in different Latitudes 502
104. Elementary Dimensions of Pipes 54
105. Maximum Advisable Velocity of Flow in Pipes 508
106. Diameters of Pipes to supply given Numbers of Hose Streams 510
107. Experimental Volumes of Fire Hydrant Streams. 520
108. Frictional Head in Service Pipes 528
109. Dimensions of Filter-beds for given Volumes 554
no. Piston Spaces for given Arcs of Crank Motion ... 562
in. Ratios of Piston Motions for given Crank Arcs 5 6 4
112. Costs of Pumping in Various Cities 575
113. Special Trial Duties of Various Pumping Engines 580
114. Comparative Consumptions of Coal at Different Duties 581
115. Fuel Expenses for Pumping compared on Duty Bases 581
116. Comparison of Values of Pumping-Engines on Fuel Bases 583
LIST OF FULL PAGE ILLUSTRATIONS.
PAGE
Public Fountain, Cincinnati 2
Gateway, Chestnut Hill Reservoir, Boston 24
Pumping Station, Toledo 31
Diagram of Pumping, Annual 43
Pumping Station, Millwaukee 45
Diagrams of Rainfall 55
Diagrams of Rainfall 57
Diagrams of Secular Rainfall 59
Section and Plan of Pump-House 65
Reservoir Embankment, Norwich 84
Intercepting Well, Prospect Park, Brooklyn 102
Pumping Station, New Bedford 139
Stand-Pipe, Boston 160
Pumping Station, Manchester. 213
Compound Duplex Pumping Engine 223
Measuring Weir, for Turbine Test 277
Fairmount Turbines and Pumps, Philadelphia 332
Distributing Reservoir. 333
Compound Inverted Pumping-Engine 377
Conduit Sections 431
Cylindrical Penstock 440
Forms of Pipe-Sockets and Spigots 446
Branch, Reducer and Bend 478
Double-Faced Stop-Valves 493
Plan of a Pipe System 505
Flush Fire Hydrants 521
Pumping-Engine, No. 3, Brooklyn 557
Cornish Plunge-Pump 563
Compound Beam Pumping-Engine, Lynn 567
Geared Pumping-Engine, Providence 573
Hydraulic Power Pumping Machinery, Manchester 585
Jonval Turbine 593
WHOLE NUMBER OF ILLUSTRATIONS 180
APPENDIX.
Page
Metric Weights and Measures 593
Table of French Measures and United States Equivalents 594
Cubic Inch, and Equivalents 595
Gallon, and Equivalents 595
Cubic Foot, and Equivalents 595
Imperial Gallon, and Equivalents 596
Cubic Yard, and Equivalents 596
Table of Units of Heads and Pressures of Water, and Equivalents 596
Table of Average Weights, Strengths, and Elasticities of Materials 597
Formulas for Diameters and Strengths of Shafts 599
Trigonometrical Expressions 599
Trigonometrical Equivalents 600
Table of Sines, Tangents, &c 601
What Constitutes a Car Load 602
Lubricating Compounds for Gears 602
Compound for Cleaning Brass 602
Iron Cement, for Repairing Cracks in Castings 602
Alloys, Table of 603
Velocities of Flow in Channels, that Move Sediments 604
Tensile Strengths of Cements and Mortars 605
Dimensions of Bolts and Nuts 606
Weights of Lead and Tin-lined Service-Pipes 607
Meters and Meter Rates - 608
Resuscitation from Death by Drowning 609
if LIBRA RY X
1 UNIVERSITY OF jj
I CALIFORNIA.
./'
SECTION I.
COLLECTION AND STORAGE OF WATER, AND ITS IMPURITIES,
CHAPTER I.
INTRODUCTORY.
1. Necessity of Public Water Supplies. A new or
an additional water supply is an inevitable necessity when-
ever and wherever a new settlement establishes itself in an
isolated position ; again whenever the settlement receives
any considerable increase ; and again when it becomes a
great metropolis or manufacturing centre.
In all the wonderful and complex transformations in
Nature, in the sustenance of all organized beings, and in
the convenience and delight of man, water is appointed to
perform an important and essential part.
Life cannot long exist in either plant or animal, unless
water, in some of its forms, is provided in due quantity.
Wholesome water is indispensable in the preparation of
all our foods ; clear and soft water is essential for promot-
ing the cleanliness and health of our bodies; and pure
water is demanded for a great variety of the operations of
the useful and mechanic arts.
2. Physiological Office of Water. Of the three
essentials to human life, air, water, and food, the one now
26 INTRODUCTORY.
to be specially considered, water ^ has for its physiological
office to maintain all the tissues of the body in healthy
action.
If the water received into the system is unfit for such
special duty, all the animal functions suffer and are weak-
ened, air then but partially clarifies the blood, food then is
imperfectly assimilated, and the body degenerates.
Vigor is essential to the uniform success and happiness
of every individual, and strength and happiness of the
people are essential to good public morals, good public
government, and sound public prosperity.
Sanitary improvements are, therefore, among the first
and chief duties of public officers and guardians, and have
ever been the objects of the most earnest thought and labor
of great public philanthropists.
3. Sanitary Office of Public Water Supplies.
Water has thus far proved the most effectual and econom-
ical agent, as sanitary scavenger, in the removal from our
habitations of waste slops and sewage, and also the most
effectual * and economical agency in the protection of life
and property from destruction by fire.
The necessity of a judiciously executed system of public
water-supply increases as the population of a town increases;
as the mass of buildings thickens ; as the lands upon which
the town is built become saturated with sewage, and the
individual sources within the town are polluted; as the
atmosphere over and within the town is fouled by gases
* We need refer to but one of many experiences, viz. : At Columbus,
Ohio, the average loss by fire for the four years preceding the completion of
the public water- works was -f 3 ^ of one per cent, of the valuation. The average
loss during the first four years after the completion of the works was y 1 ^, and
during the fifth year, from April 1, 1875, to April 1, 1876, was yW of the valu-
ation. These statistics show a probable saving in the first four years of upward
of one-half million dollars, and in five years of more than the entire cost of the
water-works.
f ' '
HELPFUL INFLUENCE OF PUBLIC WATER SUPPLIES. 27
arising therefrom ; and as the dangers of epidemics, fevers,
and contagious diseases increase.
4. Helpful Influence of Public Water Supplies.
No town or city can submit to a continued want of an
adequate supply of pure and wholesome water without a
serious check in its prosperity.
Capital is always wary of investment where the elements
of safety and health are lacking, and industry dreads fre-
quent failures and objectionable quality in its water supply.
It is true that considerations of profit sometimes induce
the assembling of a town where potable waters are procur-
able with difficulty, but in such cases the lack is sure to
prove a growing hindrance to its prosperity, and before the
town arrives at considerable magnitude, its remedy will
present one of the most difficult problems with which its
municipal authorities are obliged to cope.
In the experience of all large and thriving cities, there
has come a time when an additional or new and abundant
water supply was a necessity, terribly real, that would not
be talked down, or resolved out of existence by public
meetings, or wait for a more convenient season; a time
when it was not possible for every citizen to supply his
household or his place of business independently, or even
for a majority of the citizens to do so, and when prompt,
united, and systematic action must be taken to ensure the
health, prosperity, and safety of the people. Such stern
necessity often appears to present difficulties almost insur-
mountable by the available mechanical and financial re-
sources of the citizens.
Out of such simple but positive necessities have grown
the grandest illustrations, in our great public water sup-
plies, of the benefits of co-operative action, recorded in the
annals of political economy. Out of such simple necessi-
28 INTRODUCTORY.
ties grew some of the most magnificent and enduring con-
structions of the powerful empires of the Middle Ages, the
architectural grandeur of which the moderns have not
attempted to surpass.
5. Municipal Control of Public Water Supplies.
The magnitude of the labors to be performed and the
amount of capital required to be invested in the construc-
tion of a system of water supplies invariably brings into
prominence the question, Shall the construction, operation,
and control of these works be entrusted to private capital,
or shall they be executed under the patronage of the muni-
cipal authorities and under the direction of a commission
delegated by the people? The conclusion reached in a
majority of the American cities has been that the works
ought to be conducted as public enterprises. They have
been believed to be so intimately connected with the public
interests and welfare as to be peculiarly subjects for pub-
lic promotion ; and that, under the direction of a commis-
sion appointed by the people to study and comprehend all
their needs, to consider, with the aid of expert advice, and
to suggest plans, the works would be projected on such a
liberal and comprehensive scale as would best fulfil the
objects desired to be attained, and that the true interests of
the people would not be subordinated to mere considera-
tions of profit.
Further, that if the works when complete were operated
under municipal care, their standard and effectiveness would
more certainly be maintained; their extension into new
territory might keep pace with and encourage the growth
of the city ; they might not, by excessive rates, be made to
oppress important industries ; their advantages might more
surely be kept within the reach of the poorer classes ; they
might more economically be applied to the adornment of
INCIDENTAL ADVANTAGES. 29
the public buildings and grounds ; and that they might,
when judiciously planned, constructed, and managed, be-
come a source of public revenue.
Nearly all the objects desirable to be attained in a pub-
lic water supply have, however, been accomplished, in
numerous instances that might be cited, under the auspices
of private enterprise.
6. Value as an Investment. The necessary capital
honestly applied to the construction of an intelligently and
judiciously planned effective public water supply has
almost invariably proved, both directly and indirectly, a
remunerative investment.
Many, though not all, of our American Water-supply
Reports, show annual incomes from water-rates in excess
of the combined annual operating expenses and interest on
the capital expended. In addition to this cash return, there
are in all cases benefits accruing to the public, usually
exceeding in real value that of the more generally recog-
nized money income.
7. Incidental Advantages. The construction of water-
works is almost sure to enhance the value of property along
its lines, under its protection, and availing of its conve-
niences. There is, also, a perpetual reduction* in the
* In a recently adopted schedule of the National Board of Underwriters,
there are additions to a minimum standard rate in a standard city, which is
provided with good water supply, fire alarm, police, etc., as follows, termed
deficiency charges :
Minimum standard rate of insurance of a standard building. . 25 cents.
If no water supply add 15
If only cisterns, or equivalent " 10
If system is other than gravity " 05
If no fire department " 25
If no police organization " 05
If no building law in force " 05
The financial value of the enhanced fire risk, as deduced by the Board from
an immense mass of statistics, and the additional premium charged on the
30 INTRODUCTORY.
yearly rates of insurance. The substitution of soft water
for hard water, as almost all waters are, results in a mate-
rial reduction in the daily waste accompanying the prepa-
ration of foods, in laundry and cleansing operations, in the
production of steam power, and in many of the processes
employed in the useful arts.
There are many industries, the introduction of which are
of value to a community, that cannot be prosecuted with-
out the use of tolerably pure and soft water. To save the
annual aggregate of labor required to convey water from
wells into and to the upper floors of city tenements or resi-
dences, is a matter of no inconsiderable importance ; but
paramount to all these is the value of the sanitary results
growing out of the maintenance of health, and the induce-
ment to cleanliness of person and habitation, by the con-
venience of an abundance of water delivered constantly in
the household, and the enhanced safety to human life and
to property from destroying flames, accompanying a liberal
distribution of public fire hydrants under adequate pressure
throughout the populous districts.
most favorable buildings, is 60 per cent, without good water- works, and 40 per
cent, if only fire cisterns are provided.
?;:;:)
f I, I B R A R Y
UNIVKUS1TY OF
CHAPTER II.
QUANTITY OF WATER REQUIRED.
8. Statistics of Water Supplied. One of the first
duties of a Commission to whom has been assigned the
task of examining into and reporting upon a proposed
supply of water for a community, is to determine not only
what is a wholesome water, but what quantity of such
wholesome water will be required, and adequate for its
present and prospective uses.
In many cases, this problem is parallel with the deter-
mination of a product from two factors, one of which only
is a known quantity. Oftea all factors must be assumed.
The total number of inhabitants, the total number of
dwellings, and the total number of manufacturing and
commercial firms can be obtained without great difficulty,
and it can safely be assumed that eighty per cent, of all
these within reach of a new and improved water supply
will be among its patrons within a few years after the intro-
duction of the new supply ; but how much water will be
required for actual use, or will be wasted, per person, per
dwelling, or per firm, is always quite uncertain.
Rarely can any data worthy of confidence respecting
these quantities be obtained. The practice, therefore, gen-
erally is, to obtain statistics from towns and cities already
supplied, and to attempt to reduce these to some general
average that will apply to the case in hand.
9. Census Statistics. In a small portion of the water-
supply reports there is given, in addition to the total quan-
32
QUANTITY OF WATER REQUIRED.
tity of water supplied, the number of families supplied ; in
other reports, the number of dwellings, or the number of
fixtures of the several classes supplied, and occasionally
the population supplied, or the total population of the
municipality.
In the investigations for facts applicable to a new sup-
ply, when information must necessarily be culled from
various water reports, it is often desirable to know the
populations of the places from which the reports are re-
ceived, their number of families, persons to a family, num-
ber of dwellings and persons to a dwelling, so as to be able
to reduce their water-supply data to a uniform classifica-
tion. We therefore present an abstract from the United
States Census for the year 1870, giving such information
respecting fifty prominent American cities :
TABLE No- 1 .
POPULATION, FAMILIES, AND DWELLINGS IN FIFTY AMERICAN CITIES,
IN THE YEAR 1 870.
CITIES.
SIZE.*
POPULATION.
FAMILIES.
DWELLINGS.
Number.
Persons
to a
family.
Number.
Persons
to a
dwelling
Albany N. Y
20
23
6
7
3
ii
33
26
47
69,422
53,180
267,354
250,526
396,099
117,714
39,634
48,956
28,323
298,977
216,239
14,105
10,147
49,929
48,188
80,066
22,325
7,897
9,098
6,i55
59,497
42,937
4.92
5-24
5-35
5.20
4-95
5-27
5.02
5.38
4.60
5-3
5-4
8,748
8,347
40,35
29,623
45,834
18,285
6,348
6,861
4,396
44,620
24,55
7-94
6.37
6.63
8.46
8.64
6-44
6.24
7.14
6.44
6.70
8.81
Allegheny, Penn
Baltimore, Md
Boston Mass
Brooklyn N. Y
Buffalo, N. Y
Cambridge, Mass
Charleston S C
Charlestown, Mass ....
Chicago 111
Cincinnati, Ohio
* This column expresses the order of size as numbered from largest to
smallest ; New York, the largest, being numbered 1.
STATISTICS OF FIFTY AMERICAN CITIES. 33
POPULATION, ETC., IN FIFTY AMERICAN CITIES (Continued).
CITIES.
SIZE.
POPULATION.
FAMILIES.
DWELLINGS.
Number.
Persons
to a
family.
Number.
Persons
to a
dwelling
Cleveland Ohio ....
15
42
44
18
5
34
27
17
38
45
14
3i
49
32
*9
39
13
2 5
9
i
37
2
16
41
21
36
24
22
10
48
35
4
29
40
28
46
12
43
30
92,829
3l>274
30,473
79*577
26,766
37,180
48,244
82,546
32,260
28,921
J oo,753
40,928
28,233
40,226
71,440
32,034
105,059
50,840
191,418
942,292
33*579
674,022
86,076
3i4 I 3
68,904
33*930
51,038
62,386
149*473
28,235
35' 92
310,864
43*05!
3i*5 8 4
46,465
28,804
109,199
30,841
41,105
18,411
5*790
6,109
I5* 6 36
5,216
7,427
9,200
16,687
5*585
5*287
J 9,!77
7,649
6,100
7,824
14,226
6,301
21,631
10,482
39*13^
185,789
7*048
127,746
16,182
6,632
J 4,775
6,932
9,792
12,213
30,553
5, OI 3
6,642
59,43i
8,677
6,457
9,302
5*793
2i,343
5*8o8
8,658
5.04
5-40
4-99
5.09
5.13
, 5.oi
' 5-24
4-95
5.78
5.47
5.25
5-35
4.63
5.H
5.02
5.o8
4.86
4.85
4.89
5.07
4.76
5.28
5.32
4.74
4.66
4.89
5.21
5-"
4.89
5.63
5.28
5.23
4.96
4.89,
5.00
4.97
5.12
5-31
4-74
16,692
5* 011
5,6n
14,688
2,687
6,688
7,820
9,867
5*424
3,443
14,670
6,362
4,625
6,408
13,048
5,738
14,350
8,100
33,656
64,044
4,653
112,366
14,224
4,836
9,227
6,294
8,033
11,649
25,905
4,56i
5,646
39*675
7,088
6,069
5,893
4,799
'9*545
5*398
4,922
5.56
6.24
5-43
5-42
9.96
5.56
6.17
8.37
5-95
8.40
6.87
6.43
6.10
6.28
5.48
5.58
7.32
6.28
5-69
14.72
7.22
6.01
6.05
6.50
746
5-39
6.35
5.36
5-77
6.19
6.21
7-84
6.07
5.20
7.88
6.00
5-59
5-7 1
8-35
Columbus Ohio
Dayton, Ohio
Detroit, Michigan
Fall River Mass
Hartford, Conn
Indianapolis Ind
Jersey City NT
Kansas City Mo
Lawrence, Mass
Louisville, Ky
Lowell, Mass
Lynn, Mass
Memphis, Tenn. . . .
Milwaukee, Wis
Mobile, Ala
Newark, N. J
New Haven, Conn
New Orleans, La. .
New York, N. Y
Paterson, N. J
Philadelphia, Pa
Pittsburg, Pa
Portland, Me
Providence, R. I
Reading, Pa. .
Richmond Va
Rochester, N Y
San Francisco, Cal ....
Savannah, Ga
Scranton, Pa
St. Louis, Mo
Syracuse, N. Y
Toledo, Ohio
Troy, N. Y
Utica NY ....
Washington, D. C
Wilmington Del . .
Worcester Mass
34 QUANTITY OF WATER REQUIRED.
1O. Approximate Consumption of Water. In
American cities, having well arranged and maintained sys-
tems of water supply, and furnishing good wholesome
water for domestic use, and clear soft water adapted to the
uses of the arts and for mechanical purposes, the average
consumption is found to be approximately as follows, in
United States gallons :
(a.) For ordinary domestic use, not including hose use,
20 gallons per capita per day.
(b.) For private stables, including carriage washing,
when reckoned on the basis of inhabitants, 3 gallons per
capita per day.
(c.) For commercial and manufacturing purposes, 5 to
15 gallons per capita per day.
(d.) For fountains, drinking and ornamental, 3 to 10
gallons per capita per day.
(e.) For fire purposes, -f$ gallon per capita per day.
(/.) For private hose, sprinkling streets and yards,
10 gallons per capita per day, during the four dryest
months of the year.
(g.) Waste to prevent freezing of water in service-pipes
and house-fixtures, in Northern cities, 10 gallons per capita
per day, during the three coldest months of the year.
(h.) Waste by leakage of fixtures and pipes, and use
for flushing purposes, from 5 gallons per capita per day
upward.
The above estimates are on the basis of the total popu-
lations of the municipalities.
There will be variations from the above approximate
general average, with increased or decreased consumption
for each individual town or city, according to its social and
business peculiarities.
WATER SUPPLIED TO ANCIENT CITIES. 35
The domestic use is greatest in the towns and cities, and
in the portions of the towns and cities having the greatest
wealth and refinement, where water is appreciated as a
luxury as well as a necessity, and this is true of the yard
sprinkling and ornamental fountain use, and the private
stable use.
The greatest drinking-fountain use, and fire use, and
general waste, will ordinarily be in the most densely-
populated portions, while the commercial and manufactur-
ing use will be in excess where the steam-engines are most
numerous, where the hydraulic elevators and motors are, on
the steamer docks, and where the brewing and chemical
arts are practiced.
The ?atio of length of piping to the population is greater
in wealthy suburban towns than in commercial and manu-
facturing towns.
Some of these peculiarities are brought out in a follow-
ing table of the quantity of water supplied and of piping in
several cities, which is based upon the census table hereto-
fore given and upon various water-works reports for the
year 1870.
The general introduction of public water- works, on the
constant-supply system, with liberal pressures in the mains
and house-services, throughout the American towns and
cities, has encouraged its liberal use in the households, so
that it is believed that the legitimate and economical domes-
tic use of water is of greater average in the American cities
than in the cities of any other country, at the present time,
and its general use is steadily increasing.
11. Water Supplied to Ancient Cities. The sup-
plies to ancient Jerusalem, imperial Rome, Byzantium, and
Alexandria, were formerly equal to three hundred gallons
per individual daily ; and, later, the supplies to Nismes,
36
QUANTITY OF WATER REQUIRED.
Metz, and Lyons, in France, and Lisbon, Segovia, and
Seville, in Spain, were most liberal, but a small proportion
only of the water supplied from these magnificent public
works was applied to domestic use, except in the palaces
of those attached to the royal courts.
12. Water Supplied to European Cities. In the
year 1870, the average daily supply to some of the leading
European cities was approximately as follows :
CITIES.
IMP. GALLONS.
London, England
2Q
Manchester " .......
*7
2/1
Sheffield "
2Q
Liverpool, "
^y .
27
Leeds, "
21
Edinburgh Scotland . .
?o
Glasgow " .
o w
4.O
7Q
40
30
Geneva Switzerland
16
16
18
* r-
In the year 1866, public water supplies * were, in vol-
ume, as follows, in the cities named :
CITIES.
POPULATION.
SUPPLY PER CAPITA.
Hamburg Prussia .
2OO,OOO
34. sfals.
Altona "
C2,OOO
20 "
Tours France
42.OOO
22 "
Ansrers. "
Toulouse, "
IOO,OOO
13-5 "
Nantes "
II2,OOO
13.6 "
Lyons, "
^OO.OOO
22 "
///Ji.6
* Vide Kirkwood's " Filtration of River Waters." Van Nostranfl, N. Y., 1869.
WATER SUPPLIED TO AMERICAN CITIES.
37
Prof. Rankine gives,* as a fair estimate of the real daily
demand for water, per inhabitant, amongst inhabitants of
different habits as to the quantity of water they consume,
the following, based upon British water supply and con-
sumption :
RANKINE'S ESTIMATE FOR ENGLAND.
IMP.
GALLONS PER
DAY.
Least.
Average.
Greatest.
Used for domestic purposes
7
I O
Washing streets, extinguishing fires, sup-
plying fountains, etc
Trade and manufactures
Waste under careful regulations, say ....
Total demand
2
2
22
!*
2 7?
13. Water Supplied to American Cities. The lim-
ited use of water for domestic purposes in many of the
European cities during the last half century, led the engi-
neers who constructed the pioneer water-works of some of
the American States to believe that 30 gallons of water per
capita daily would be an ample allowance here ; and in
their day there was scarce a precedent to lead them to
anticipate the present large consumption of water for lawn
and street sprinkling by hand-hose, or for waste to prevent
freezing in our Northern cities.
The following tables will show that this early estimated
demand for water has been doubled, trebled, and in some
instances even quadrupled ; and this considerable excess,
to which there are few exceptions, has been the cause of
much annoyance and anxiety.
* " Civil Engineering," London, 1872, p. 731.
38
QUANTITY OF WATER REQUIRED.
In the year 1870, the average daily supply to some of
the American cities was as follows, in United States gallons :
TAB LE No. 2.
WATER SUPPLIED AND PIPING IN SEVERAL CITIES, IN THE YEAR 1870.
CITIES.
POPULA-
TION
IN 1870.
SUPPLY
PER
PERSON,
DAILY
AVERAGE
SUPPLY
PER
FAMILY,
DAILY
AVERAGE.
SUPPLY
PER
DWELLING,
DAILY
AVERAGE.
TOTAL
DAILY SUPPLY,
AVERAGE.
TOTAL MILES
OF PIPE MAINS.
MILES OF PIPE
PER 1,000
INHABITANTS.
Baltimore
Boston
267,354
2 CO C 26
Gallons.
52.81
60 T C
Gatfons,
282.53
7 T 2 >rft
Gallons.
SS^S
co8 87
Gattons.
14,122,032
T C O7O AOO
Miles.
214
IOA
Miles.
0.80
7&
Brooklyn ....
Buffalo
^G U ,0^ IJ
396,099
117 7 I A.
JU. l^j
47.16
c.8 08
3 1 ^-7
233-44
206 08
5 uo -7
407.46
2*7/1 QA
A 0> U / U ,T- UU
18,682,219
6 8^8 7O7
1 y4
*s8
c6
0.65
o 48
Cambridge . . .
Charlestown. .
Chicago .
1 A /,/ x ^f
39,634
28,323
208 0.7*7
43-90
43-90
62 "^2
220.38
201.94
2 T -2 A T
O/ T-^T-
273-94
282.72
A -1 *J A
U J O <J JO W O
J ,739869
1,243,380
T R ()% ? r>oo
o u
60
25
24.0
1.64.
0.90
o 81
Cincinnati . . .
Cleveland
Detroit
^yjy//
216,239
92,829
7Q C77
40.OO
33- 2 4
f\A 2/1
o 1 o-47
201.60
167.53
2^6 08
4 i /-54
352.40
184.81
-jxig 18
10,812,609
3,085,559
51 T 2 A.Q "?
132
5
I 2Q
0.6 1
o-54
i 61
Hartford
/ yo / /
27 180
**H*^
6c 81
32Q 71
26 C QO
, j. j.^,q.y^
2 Ad.7 OOO
^y
4.8
T SO
Jersey City. . .
Louisville ....
Montreal, Can.
O/> i<JW
82,546
^,753
117, coo
83.66
28.95
4.Q.OO
o^y-/ i
414.12
I 5 I -99
o^o-y
700.23
198.89
i ,^-'4-/5 l -"-' w
6,906,056
2,817,300
572O ^?o6
^.J
70
58
06
J..^<-
0.85
o.5&
0.8 1
Newark
New Haven . .
New Orleans .
New York . . .
Philadelphia .
Salem
105,059
50,840
191,418
942,292
674,022
2A. 1 17
*Vy***
2O.20
59.00
30.19
9O.20
55-n
4.1 4.6
98.17
286.15
147-63
457.31
290.98
147.86
370-52
171.78
i,327-74
33L2I
2,121,842
3,000,000
5,779,317
85,000,000
37^45,385
I OOO OOO
52
53
5
346
488
-2C.
0.50
1.04
0.30
o-37
0.71
i 04.
St. Louis
Washington . .
Worcester. . . .
310,864
109,199
41,105
35.38
I27.0O
48.65
185.04
650.24
230.60
277.38
709.93
406.23
11,000,000
13,868,273
2,000,000
OO
I0 5
1 02
45
0.34
o-93
1.09
/.
The average quantity of water supplied to some of the
same cities in 1874 is indicated in the following table, show-
ing also the extensions of the pipe systems, and the increase
in the average daily consumption of water per capita, from
year to year :
INCREASE IN VARIOUS CITIES.
TAB LE No. 3.
WATER SUPPLIED IN YEARS 1870 AND 1874.
CITIES.
AVERAGE
DAILY SUPPLY
PER CAPITA.
TOTAL AVERAGE DAILY SUPPLY.
TOTAL
MILES OF PIPES.
1870.
I874 .
i8 7 a
i8 74 .
1870.
1874.
Boston
60
47
58
44
44
64
40
32
64
84
29
20
55
41
127
49
49
60
f
60
54
62
84
45
45
87
86
24
38
58
55
138
80
66
15,070,400
18,682,219
6,838,303
1,739,869
1,243,380
18,633,000
10,812,609
3,085,559
5, II2 ,493
6,906,056
2,817,300
2,121,842
37^45,385
1,000,000
13,868,273
2,000,000
5,720,306
18,000,000
24,772,467
8,509,481
2,300,000
7,643,017
38,090,952
13,600,596
5,625,150
9, OI 3,35
10,421,001
3,598,730
4,73 2 ,7 l8
42,111,730
1,380,000
18,000,000
3,000,000
8,395,8io
194
258
I 6
60
25
240
I 3 2
5
129
70
58
52
488
35
102
45
96
262
323
87
76
132
386
156
81
177
in
9 1
112
625
40
141
63
114
Brooklyn
Buffalo
Cambridge. .
Charlestown . . .
Chicago .
Cincinnati
Cleveland
Detroit
jersey City ...
Louisville
Newark
Philadelphia . . .
Salem ....
Washington ....
Worcester
Montreal
14. The Use of Water Steadily Increasing. The
legitimate use of water is steadily being popularized, calling
for an increased average in the amount of household appa-
ratus, increased facilities for garden irrigation and jets
d'eau, increased street areas moistened in dusty seasons,
and increased appliances for its mechanical use ; from all
which follows increased waste of water.
15. Increase in Various Cities. The following table
is introduced to show the average daily supply in various
cities through a succession of years :
40
QUANTITY OF WATER REQUIRED.
TABLE No. 4.
AVERAGE GALLONS WATER SUPPLIED TO EACH INHABITANT DAILY IN
YEAR.
|
Buffalo.
d
>>
Cleveland.
Cincinnati.
Chicago.
Detroit.
Jersey City.
Louisville.
Montreal.
Jsj
o
>H
te
4)
Philadelphia.
1
1856
i8c7
8
55
4.6
1858 . .
8
22
16
71;
1859
1860 ....
1861 .
ii
14
16
OO
40
43
4."?
48
52
r-2
/ D
77
1862 ....
17
IQ
?Q
T-O
4.4.
JO
r8
14.
186*
A /
22
^y
2 I
oy
AJ
D^
r8
12
1864
i86c
26
2Q
22
22
TO
41
4.2
57
c c
77
14
17
62
1866 . . .
ee
*y
3?
22
4.-?
a
60
/ /
A /
17
1867
1868
1869
1870
1871
Oo
59
62
62
60
4.
58
ci
oo
36
43
46
47
^6
24
25
27
33
76
40
TO
5
f
62
63
73
64
6 7
61
64
7^
84
A /
J 5
16
18
29
IQ
49
cc
62
68
84
90
8";
4 6
5 1
5 1
55
cc
127
I^O
1872 . .
ce
61
so
4.O
60
75
8?
QQ
22
ce
88
CA
174.
i873
1874
DO
58
60
60
60
55
r8
43
A r
dC
/
75
81
90
87
86
22
24.
t
60
66
104
56
r8
138
T-?,8
*Y/*r'
TO
T-D
"/
16. Relation of Supply per Capita to Total Pop-
ulation. In the larger cities there are generally the great-
est variety of purposes for which water is required, and
consequently a greater average daily consumption per cap-
ita. Exceptions to this general rule may be found in a few
suburban towns largely engaged in the growth of garden
truck, and plants, and shrubs for the urban markets, in
which there is a large demand for water for purposes of
irrigation.
In the New England towns and cities the average daily
consumption and waste of water according to population is
approximately as follows :
MONTHLY AND HOURLY VARIATIONS. 41
Places of 10,000 population, 35 to 45 gallons per capita.
" " 20,000 " 40 to 50 "
" " 30,000 " 45 to 65 "
" " 50,000 " 55 to 75
Places of 75,000 population and upward, 60 to 100 gal-
lons per capita.
1 7. Monthly and Hourly Variations in the Draught.
The data heretofore given relating to the daily average
consumption of water have referred to annual quantities
reduced to their daily average. The daily draught is not,
however, uniform throughout the year, but at times is
greatly in excess of the average for the year, and at other
times falls below.
It may be twenty to thirty per cent, in excess during
several consecutive weeks, fifty per cent, during several
consecutive days, and not infrequently one hundred per
cent, in excess during several consecutive hours, independ-
ently of the occasional heavy drafts for fires. Diagrams of
this daily consumption of water in the cities usually show
two principal maxima and two principal minima. The
earliest maximum in the year occurs, in the Eastern and
Middle States, about the time the frost is deepest in the
ground and the weather is coldest, that is, between the
middle of January and the first of March, and in New
England cities this period sometimes gives the maximum of
the year. The second maximum occurs usually during the
hottest and dryest portion of the year, or between the mid-
dle of July and the first of September. The two principal
minima occur in the spring and autumn, about midway
between the maxima. Between these four periods the pro-
file shows irregular wavy lines, and a profile diagram
continued for a series of years shows a very jagged line.
To illustrate the irregular consumption of water, we
FIG. 1.
Chicago.
Brooklyn.
Cincinnati. Montreal
-uiaip lad suo^S uoiitiui jo 'o NJ
RATIO OF MONTHLY CONSUMPTION. 43
have prepared the diagrams, Fig. 1, of the operations of the
pumps at Chicago, Brooklyn, Cincinnati, and Montreal,
during the years 1871, 1872, 1873, and 1874.
18. Ratio of Monthly Consumption. The varia-
tions in draught, as by monthly classification, in several
prominent cities, in the year 1874, have been reduced to
ratios of mean monthly draughts for convenience of compar-
ison, and are here presented ; unity representing the mean
monthly draught for the year :
TABLE No. 5.
RATIOS OF MONTHLY CONSUMPTION OF WATER IN 1874.
CITIES.
c
4J
6
fe
1
I
I
jj
>>
"3
i >
bi>
P
<
&
$
>
o
%
1
Brooklyn. . .
1.029
I.I32
971
.892
.941
1.008
1.069
1.034
1.044
.987
.919
974
Buffalo. . .
1.008
I.OO7
.0.60
.941
983
9 6 3
996
1.020 ,1.044
I.OII
1.040
1. 000
Cleveland. .
.883
.901
.850
.871
.992
1.180
1.181
.206
1.058
I.OOI
.942
915
Detroit
.856
.80 7
90S
.844
1.029
1.065
1.051
.I6 7
1.171
1.115
.987
1.003
Philadelphia
.850
.844
834
.898
1.056
1,199
1.289
145
1.091
.990
952
.853
Chicago . . .
.862
.844
.904
.904
.942
.942
1.171
193
1.162
1.039
.966
1.029
Cincinnati..
.792
.762
.778
.80
I.OII
1.217
1.207
.257
1.302
1.058
.960
799
Louisville. .
.842
.819
.848
.841
.960
1.192
1.207
.223
1.202
1.138
940
.876
Montreal. . .
.864
959
943
1.025
.916
.907
I.IOI
151
1.096
1.043
.971
1.023
Mean. . .
.887
.897
.888
.897
.960
1-075
1.144
I.I55
I.I30
1.042
.964
.941
There is also a very perceptible daily variation in each
week, and hourly variation in each day, in the domestic
consumption of water.
The Brooklyn diagram shows that the average draught
in the month of maximum consumption was in 1872, fifteen
per cent, in excess of the average annual draught ; in 1873,
seventeen per cent, in excess ; in 1874, thirteen per cent, in
excess.
A Boston Highlands direct pumping diagram lying "be-
fore the writer shows that the average draught at nine
o'clock in the forenoon was thirty-seven per cent, in excess
44
QUANTITY OF WATER REQUIRED.
of the average draught for the three months, and that at
eight o'clock A.M. on the Mondays the draught was sixty
per cent, in excess of the average hourly draught for the
three months.
The maximum hourly draught indicated by the two
diagrams taken together is nearly seventy -five per cent, in
excess of the average throughout the year.
19. Illustrations of Varying Consumption. In
illustration, we will assume a case of a suburban town re-
quiring, say, an average daily consumption for the year of
1,000,000 United States gallons of water, and compute the
maximum rate of draught on the bases shown by the above-
named diagrams, thus:
GALLONS
PER DAY.
GALLONS
PER MlN.
CUBIC FEET
PER MlN.
Average draught per year
I OOO OOO
6o4 A.
02 8
Add 17 per cent, for max. monthly average
draught making
I,OI7,OOO
7O6 2
Q-7 I
Add to the last quantity 10 per cent, for the
max weekly average draught making. .
I O27 I7O
7iq 2
QC q
Add to the last quantity 37 per cent, for the
max hourly average draught making
I <1O7 222
Q72 2
I2O O
Add to the last quantity 23 per cent, for the
max. hourly av. draught on Mondays, making
1,730,883
1,202.0
i*yy
160.7
The experience of nearly every water-supply shows that
the maximum draught, aside from fire-service, is at times
more than double the average draught.
2O. Reserve for Fire Extinguishment. In addi-
tion to the above, there should be an ample reserve of water
for fire service, and extra conduit and distribution capacity
for its delivery. There is a possibility of two or three fires
being in progress at the same time, in even the smaller
cities, requiring at least twelve hydrant streams, or say 300
cubic feet of water per minute, for each fire.
PUMPING STATION, MILWAUKEE.
CHAPTER III.
RAINFALL.
21. The Vapory Elements. The elements of water
fill the ethereal blue above and the earth crust beneath.
They, with unceasing activity, permeate the air, the rocks,
the sand, the fruits we eat, and the muscles that aid our
motion.
Since first "there went up a mist from the earth," the
struggle between the ethereal elements and earth's internal
fire, between the intense cold of space and direct and
radiated heat enveloping the face of the earth, has gone
on unceasingly.
22. The Liquid and Gaseous Successions. If we
hold a drop of water in the clear sunshine and watch it
intently, soon it is gone and we could not see it depart ; if
we expose a dish of water to the heat of fire, silently it
disappears, and we know not how it gathered in its activity ;
if we leave a tank of water uncovered to the sun and wind,
it gradually disappears, and is replenished by many showers
of summer, still it departs and is replenished by snows of
winter. Under certain extreme conditions it may never be
full, it may never be exhausted, the rising vapor may equal
the falling liquid, as where " the rivers flow into the sea, yet
the sea is not full."
23. The Source of Showers. Physical laws whose
origin we cannot comprehend but whose steady effects we
observe, lift from the saline ocean, the fouled river, the moist
earth, a stream of vapor broad as the circuit of the globe,
46 RAINFALL.
but their solid impurities remain, and the flow goes up with
ethereal clearness.
From hence are the sources of water supply replenished.
From hence comes the showers upon the face of the earth.
24. General Rainfall. But there is irregularity in
the physical features of the earth, and unevenness in the
temperature about it, and the showers are not called down
alike upon all its surface. Upon the temperate zone in
America enough water falls in the form of rain and snow
to cover the surface of the ground to an average depth of
about 40 inches, in the frigid zone a lesser quantity, and in
the torrid zone full 90 inches, and in certain localities to
depths of 100 and 150, and at times to even 200 inches.
We recognize in the rain an ultimate source of water
supply, but the immediate sources of local domestic water
supply are, shallow or deep wells, springs, lakes, and rivers.
The amplitude of their supply is dependent upon the avail-
able amount of the rainfall that replenishes them. In
cases of large rivers, and lakes like the American inland
seas, there can be no question as to their answering all
demands, as respects quantity, that can be made upon them,
but often upon watersheds of limited extent, margins of
doubt demand special investigations of their volumes of
rainfall, and the portions of them that can be utilized.
25. Review of Rainfall Statistics. Looking broadly
over some of the principal river valleys of the United States
we find their average annual rainfalls to be approxi-
mately as follows : Penobscot, 45 inches ; Merrimack, 43 ;
Connecticut, 44 ; Hudson, 39 ; Susquehanna, 37 ; Koanoke,
40; Savannah, 48; Appalachicola, 48; Mobile, 60; Mis-
sissippi, 46 ; Rio Grande, 19 ; Arizonian Colorado, 12 ; Sac-
ramento, 28 ; and Columbia, 33 inches ; but the amount
of rainfall at the various points from source to mouth of
WESTERN RAIN SYSTEM. 47
river is by no means uniform ; as, for instance, upon
the Susquehanna it ranges from 26 to 44 inches ; on the
Eio Grande, from 8 to 37 inches ; and on the Columbia,
from 12 to 86 inches.
26. Climatic Effects. The North American Continent
presents, in consequence of its varied features and reach
from near extreme torrid to extreme polar regions, almost
all the special rainfall characteristics to be found upon the
face of the globe ; and even the United States of America
includes within its limits the most varied classes of climato-
logical and meteorological effects, in consequence of its range
of elevation, from the Florida Keys to the Rocky Mountain
summits, and its range of humidity from the sage-bush
plains between the Sierras and Wahsatch Mountains, and
the moist atmosphere of the lower Mississippi valley, and
from the rainless Yuma and Gila deserts of southern Cali-
fornia to the rainy slopes of north-western California and of
Oregon, where almost daily showers maintain eternal verdure.
27. Sections of Maximum Rainfall. The maxi-
mum recorded rainfall, an annual mean of 86 inches, occurs
in the region bordering upon the mouth of the Columbia
River and Puget Sound. A narrow belt of excessive hu-
midity extends along the Pacific coast from Vancouver's
Island southerly past the borders of Washington Territory,
Oregon and California, to latitude 40.
Next in order of humidity is the region bordering upon
the Delta of the Mississippi River and the embouchure of
the Mobile, whose annual mean of rain reaches 64 inches.
Next in order is a section in the heart of Florida of
about one-half the breadth of the State, whose mean annual
rain reaches 60 inches.
28. Western Rain System. The great northerly
ocean current of the Pacific moves up past the coast of
RAINFALL.
China and the Aleutian Islands and impinges upon the
North American shore, then sweeps down along the coast
of Washington Territory, Oregon and California ; and from
its saturated atmosphere, flowing up their bold western
slopes, is drawn the excessive aqueous precipitations that
water these regions.
Their moist winds temper the climate and their condensed
vapors irrigate the land, so that the southerly portion of the
favored region referred to is often termed the garden of
America.
Fig. 2 is a profile, showing a general contour across the
Worth American Continent, along the thirty-ninth parallel
of latitude.
FIG. 2.
A. Pacific Ocean.
B. Coast Ran'ge.
C. Sierra Nevada.
D. Wahsatch Mountains.
E. Rocky Mountains.
F. Mississippi River.
G. Alleghany Mountains.
H. Blue Ridge.
I. Atlantic Ocean.
ELEVATION.
feet.
a. Sacramento City 82
b. Carson City 4,629
c. Salt Lake Region 4,382
d. Colorado River
e. Colorado City 6,000
f. St. Louis 481
g. Cincinnati 582
h. Washington 70
The California coast range and the western slope of the
Sierra Nevadas are the condensers that gather from the
prevailing westerly ocean breezes their moisture. From
thence the winds pass easterly over the Sierra summit
almost entirely deprived of moisture, and yield but rarely
any rain upon the broad interior basin stretching between
the bases of the Sierra and Wahsatch Mountains. Upon the
CENTRAL RAIN SYSTEM. 49
arid plains of this region, above the Gulf of California,
whose average annual rainfall reaches scarce 4 inches, the
winds roll down like a thirsty sponge.
Further to the east, the western slopes of the Wahsatch
and Eocky Mountains lift up and condense again the west-
ern winds, and gather in their storms of rain and snow.
In the lesser valley "between these mountains, 12 to 20
inches of rain falls annually, and the tributaries of the
Colorado Eiver gathers its scanty surplus of waters and
leads them from thence around the southerly end of the
Wahsatch Mountains past the Yuma Desert to the Gulf.
Over the summit of the Eocky Mountains onward moves
the westerly wind, again deprived of its vapor, and down it
rolls with thirsty swoop upon the Great American Desert,
skirting the eastern base of the mountains. Farther on, it
is again charged with moisture by the saturated wind-eddy
from the Caribbean Sea and Gulf of Mexico.
The great Pacific currents of water and wind, and the
extended ridges and furrows of the westerly half of our
Continent lend their combined influence, in a marked man-
ner, to develop its special local and its peculiar general
climatic and meteorological systems.
29. Central Rain System. A second system of anti-
trade winds bears the saturated atmosphere of the Gulf of
Mexico up along the great plain of the Mississippi. Its
moisture is precipitated in greatest abundance about the
delta, and more sparingly in the more elevated valleys of
the Eed and Arkansas rivers upon the left, and the Tennes-
see and Ohio rivers upon the right. Its influence is per-
ceptible along the plain from the Gulf to the southern bor-
der of Lake Michigan, and easterly along the lower lakes
and across New England, where the chills of the Arctic
polar current sweeping through the Gulf of St. Lawrence
4
50 RAINFALL.
and down the Nova Scotia coast into Massachusetts Bay,
throws down abundantly its remaining moisture.
30. Eastern Coast System. A third system en-
velops Florida, Georgia, and the eastern Carolinas, espe-
cially in summer, with an abundance of rain.
A fourth subordinate system shows the contending
thermic and electric influences of the warm and moist
atmosphere from the Gulf Stream, flowing northerly past,
and of the cooler atmosphere from the polar current flowing
southerly upon the New England coast, where an abundant
rain is distributed more evenly throughout the seasons than
elsewhere upon the Continent.
31. Influence of Elevation upon Precipitation.
The influence of elevation above the sea-le/el is far less
active in producing excessive rain uponao
ranges and high river sources than upon other continents
and some of the mountainous islands, being quite subordi-
nate to general wind currents.
Upon the mountainous island of Guadaloupe, in latitude
16, for instance, a rainfall of 292 inches per annum at an
elevation of 4500 feet is recorded.
Upon the Western Ghauts of Bombay, at an elevation
of 4,500 feet, an average rainfall for fifteen years is given as
254 inches.
On the southerly slope of the Himalayas, northerly of
the Bay of Bengal, at an elevation of 4,500 feet, the rainfall
of 1851 was 610 inches. These localities all face prevailing
saturated wind currents.
32. River-basin Rains. A study of some of our
principal river valleys independently, reveals the fact that
their rainfall gradually decreases from their outlets to their
more elevated sources.
RIVER-BASIN RAINS.
51
In illustration of this fact, we present the following river-
valley statistics relating to the principal basins along the
Atlantic, Gulf, and Pacific coasts.
TABLE No. 6.
MEAN RAINFALL ALONG RIVER COURSES, SHOWING THE DECREASE
IN PRECIPITATION OF RAIN AND MELTED SNOW FROM THE
RIVER MOUTHS, UPWARD.
ST. JOHN'S RIVER.
NAME OF STATION.
SUMMER.
WINTER.
YEAR.
DISTANCE FROM MOUTH.
St. Johns
Inches.
IO
Inches.
14
Inches.
ci
Miles (approximate).
c ) Distances from
Average ra.in
Fort Kent..
12
10
16
* the Atlantic
A.I inches.
MERRIMACK RIVER.
Newburyport .
Lawrence
Manchester . ,
Concord . .
12
19
II
II*
12
II
II
9
41
45
45
41
25 I ^/^P* Average rain,
43 inches.
CONNECTICUT RIVER.
i-i
iq
4Q
4~)
Middletown. ......
ii
12
46
oe
Hartford
IO
II
44
4O
Hanover
i i
4O
1 80
II
8
16
21*
Sound.
44 inches.
HUDSON RIVER.
New York City
Poughkeepsie
Hudson
Albany
12
12
10
9
10
9
8
44
40
35
36
81
re Distances from
_' J > the Atlantic
"5 I Ocean.
145 J
Average rain,
39 inches.
SUSQUEHANNA RIVER.
Havre de Grace ....
Harrisburg
13
12
10
g
44
AQ
5
7O
Lewi sb u rg
II
8
e vy
7Q
William sport
IO
7
1Q
I4O
Owego
8
6
24.
2OO
Elmira. .
7
4
26
200
ram,
37 inches.
RAINFALL.
MEAN RAINFALL ALONG RIVER COURSES (Continued).
MISSISSIPPI RIVER.
NAME OF STATION.
SUMMER.
WINTER.
YEAR.
DISTANCE FROM MOUTH.
Delta
Inches.
20
20
18
14
II
8
ii
13
14
ii
ii
Inches.
18
16
15
16
15
15
12
8
5
3
T
Inches.
60
60
60
56
55
42
42
42
38
30
25
Miles
IO^
95
190
240
350
560
700
850
1 100
1200
IW>
approximate).
Distances from
- the Gulf of
Mexico.
Average rain,
46 inches.
Baton Rouge
June, of Red River . .
Vicksburg
Memphis
Cairo
St Louis
Dubuque
Lacrosse
St. Paul's . .
Brownsville
June. Peeos River
El Paso
Albuquerque
Astoria
Walla-Walla
Boise City . .
Fort Hall ....
RIO GRANDE.
37
18
12
3
Distances from
Mexico.
Average rain,
19 inches.
COLUMBIA RIVER.
86
44
5
6
20
13
12
275 I Distances from Average rain,
600
Pacific Ocean.
33 inches.
Reference to the above, from among the principal river
valleys, is sufficient to show that the oft-made statement,
that "rain falls most abundantly on the high land," is
applicable, in the United States, to subordinate watersheds
only, and in rare instances.
33. Grouped Rainfall Statistics. The following
table gives the minimum, maximum, and mean rainfalls,
according to the most extended series of observations, at
various stations in the United States. They are grouped by
territorial divisions, having uniformity of meteorological
characteristics.
RAINFALL IN THE UNITED STATES.
TABLE No. 7.
RAINFALL IN THE UNITED STATES.
(Front Records to 1866 inclusive.)
GROUP 1. Atlantic Sea-coast from Portland to Washington.
STATION.
LAT.
LONG.
HEIGHT
ABOVE
SEA.
YEARS
OF
RECORD
MlN.
ANNUAL
RAIN.
MAX.
ANNUAL
RAIN.
MEAN
ANNUAL
RAIN.
Oardiner Me.
44.lo'
6O4</
76
Inches.
Inches.
Inches.
*A
26 38
5i-47
i!'S
Worcester, Mass
Cambridge "
43 54
42 ID
7i 49
52 7 8
26
34.60
75-64
61.83
44.00
46.92
Boston "
11
46-39
New Bedford " ....
ao 68
CO T ,
44-99
41.42
Flatbush, N. Y
Fort Hamilton, "
Fort Columbus, "
40 37
40 36
74 02
74 02
54
25
36
19
32.14
2 9'75
54-17
58.92
41-54
43-52
42-55
New York City, "
West Point, "
40 43
74 oo
1
l67
31
2O
34-79
62.87
6l -fl
43-24
43.00
Newark N. J.
47.65
Lambertville, "
tf
23
44-5
Philadelphia, Peon
Baltimore Md
39 57
75 ii
60
s
29-57
57-37
62.94
43-99
44-05
Fort McHenry, "
16
42-33
Washington, D. C
og C4.
28
37-S 2
43-44
GROUP 2. Atlantic Sea-coast, Virginia to Florida.
Fortress Monroe, Va.
oo /
76i8'
3
Charleston, S. C
32 47
Fort Moultrie, "
32 46
7Q CT
oe
Savannah Ga
8? 05
J
Fort Brooke, Fla
28 oo
82 28
42
2O
23
19.
35-93
47-04
53-63
47.63
GROUP 3. Hudson River Valley, Vermont, Northern and Western
New York.
Newburgh, N. Y
Poughkeepsie, "
Kingston, "
Hudson, "
Kinderhook, "
Albany, "
Watervliet Arsenal, " . ...
Lansingburg, "
Granville, "
Hanover, N. H
4i3i /
4i 4 1
4i 55
42 13
42 22
42 39
42 43
42 47
43 20
745 /
73 55
74 02
73 46
73 43
73 44
73 43
73 4
73 17
150
"188
150
125
130
50
30
250
20
IS
19
15
11
17
2O
15
25.04
31.92
27.50
55-63
50-97
44-93
cc'oS
36.61
40.36
35-iQ
34-52
36.48
40.52
34.65
33-31
3i-52
Burlington, Vt ....
530
Fairfield N Y
ii8e
34- J 5
Clinton, "
. . . .
*****
Utica "
22
c6 60
Lowville "
473
Gouverneur, "
22
Potsdam "
28 63
Cazenovia, " ....
394
20
*****
*****
Oxford, "
06 1
*
06 36
Pompey, "
75 3 2
16
45.08
Auburn "
76 28
*
Ithaca, "
34.71
f
Penn Yan " ...
IQ 66
28.42
Rochester, " .
43 08
5i6
24.97
43*03
32.56
Middlebury, " ....
78 10
800
30.44
Fredonia, "
16
36.55
34-99
RAINFALL.
RAINFALL IN THE UNITED STATES (Continued).
GROUP 4. Upper Mississippi, part of Iowa, Minnesota, and
Wisconsin.
STATION.
LAT.
LONG.
HEIGHT
ABOVE
SEA.
YEARS
OF
RECORD
MlN.
ANNUAL
RAIN.
MAX,
ANNUAL
RAIN.
MHAN
ANNUAL
RAIN.
Fort Ripley , Minn
46IQ /
04 I Q'
Inches.
Inches.
Inches.
Fort Snelling, " ....
820
Dubuque, Iowa
42 9.O
666
Milwaukee, Wis
8?
AA 86
41 20
9 1 5
sse
IQ
2*
27.66
42.88
Fort Madison, "
600
3
33.27
GROUP 8. Ohio River Valley, "Western Pennsylvania to Eastern
Missouri.
Marietta,
Cincinnati,
Portsmouth,
Athens, 111.
St. Louis Ar;
St. Louis,
irsenal, Penn
, Ohio
4o32'
4 2 5
8o02 /
80 41
704
070
23
37
25.62
28.02
47-79
57.28
35-23
41.48
39 2"?
wv ^
8l 2Q
580
48
32.46
53.54
42.70
u
oy *y
39 06
u ~y
84 2 1 ?
givv
582
QI
2 "5. 49
65.18
44.87
<(
38 42
04 ^3
82
468
le
*0'*ry
25.50
56.79
*rr*'-'/
38.33
OQ CO
80 56
5
800
16
2"5.I2
48.17
39.62
senal, Mo
jy o*
38 40
08 -17
oy ^v
90 10
oo 16
450
481
19
28
3M
24.08
27.OO
7 I -54
68.83
<
42.63
42.18
tracks, "
O J/
38 28
y\j AU
oo 15
472
21
*./.\^s
29.18
55.13
40.88
o w
yv- J-^
40.88
GROUP 6. Indian Territory and Western Arkansas.
95 3' 56o
Fort Gibson, Ind. Ten.
Fort Smith. Ark
Fort Washita, Ind. Ter.
3S48'
35 23
34 14
18.84
24-34
21.81
55-82
61.03
64.29
36.37
40.36
38.04
GROUP 7. Lower Mississippi and Red Rivers; part of Kentucky.
Springdale, Ken.
o807 /
85 24'
570
24
30.91
67.10
48.58
Washington Ark
O w ^/
00 A A
QO HI
660
22
41.40
70.40
54.50
Vicksburg, Miss. .
JO T-T-
32 2^
yj ^^
90 56
350
16
37.21
60.28
49.30
Natchez "
OT 1A
91 25
^9
264
18
31.09
78.73
53-55
O A JT 1
y A ^D
51.48
GROUP 8. Mississippi Delta, and Coast of Mississippi and Alabama.
New Orleans, La
Mt. Vernon Arsenal, Ala
Baton Rouge, La
295/
3 I 12
30 26
9002'
88 02
91 18
41.92
51-49
4L34
67.12
106.57
116.40
51.05
66.14
60. 16
59.12
GROUP 9. Pacific Coast, Bay of San Francisco to Alaska.
San Francisco, Cal
3748 /
I2226'
170
18
".73
36.03
21.69
Sacramento, " -
Fort Vancouver, W. Ter
38 35
45 4
121 28
122 30
82
50
18
16
11.15
25.91
27.44
56.09
19.56
38.84
Fort Steilacoom, "
47 I0
122 25
300
16
25-75
70.21
43-98
Sitka, Alaska
57 3
135 18
20
16
58.68
95.81
83-39
41.49
No. 2.
No. 1.
C-g
s
il,
J J A 80 N D J
.70
CURVES OF ANNUAL FLUCTUATIONS IN RAINFALL.
56 RAINFALL.
34. Monthly Fluctuations in Rainfall. Our gener-
alizations thus far have referred to the mean annual rainfall
over large sections. There is a large range of fluctuation in
the average amount of precipitation through the different
seasons of the year, in different sections of the United
States. It will be of interest to follow out this phase of the
question in diagrams 3 and 4, in which type curves * of
monthly means are drawn albout a line of annual mean
covering a series of years, in no case less than fifteen.
The letters J, F, M, &c., at the heads of the diagrams,
are the initials of the months. The heavy horizontal lines
represent means for the year, which are taken as unity.
Their true values may be found at the foot of their respect-
ive groups in the above table. About this line of annual
mean is drawn by free-hand the type curve of mean rain-
fall through the successive months, showing for each month
its percentage of the annual mean.
Each type curve relates to a section of country having
uniform characteristics in its annual distribution of rain.
Curve No. 1, for Group No. 1, includes the section of
country bordering upon the Atlantic sea-coast from Port-
land to Washington. The average fluctuation of the year
in this section is forty per cent. Its maximum rainfall
occurs oftenest in August, and its minimum oftenest in
January or February.
Curve No. #, for Group No. 2, includes the Atlantic
coast border from Virginia to Florida. The average fluc-
tuation of the year is one hundred and ninety-eight per
cent. Its maximum rainfall occurs oftenest about the first
of August, and nearly equal minima in April and October.
* Reduced from a diagram by Chas. Schott, C. E. , Smithsonian Contribu-
tion, Vol. XVIII, p. 16. The tables of American rainfall arranged by Mr.
Schott, and published in the same volume, are exceedingly valuable.
J F
N D J
V A M J J A SO
CURVES OF ANNUAL FLUCTUATIONS IN RAINFALL,
68 RAINFALL.
Curve No. 3, for Group No. 3, includes the upper Hud-
son River valley, and northern and western New York.
The average fluctuation of the year is sixty-six per cent.
Its maximum rainfall occurs oftenest near the first of July
and its minimum oftenest about the first of February.
Curve No. h for Group No. 4, includes a part of Iowa,
central Minnesota, and part of Wisconsin, in the upper
Mississippi valley. The average fluctuation of the year is
one hundred and nine per cent. Its maximum rainfall
occurs oftenest in the latter part of June and its minimum
oftenest about the first of February.
Curve No. 5, for Group No. 5, includes the Ohio River
valley, from western Pennsylvania to eastern Missouri.
The average fluctuation of the year, is seventy -three per
cent. Its maximum rainfall occurs oftenest about the first
of June and its minimum oftenest in the latter part of
January.
Curve No. 6, for Group No. 6, includes the Indian Ter-
ritory and Western Arkansas. The average fluctuation of
the year is ninety-one per cent. Its maximum rainfall
occurs oftenest about the first of May and its minimum
oftenest at the opening of the year.
Curve No. 8, for Group No. 8, includes the Mississippi
Delta and Gulf coast of Alabama and Mississippi. The
average fluctuation of the year is seventy -five per cent. Its
maximum rainfall occurs oftenest in the latter part of July
and its minimum oftenest early in October.
A similar type curve for Group No. 9, the region border-
ing upon the Pacific coast from the Bay of San Francisco
to Puget's Sound, would show an average annual fluctua-
tion through the seasons of two hundred and thirty-two
per cent. The fluctuations here have nothing in common
with the Mississippi and Atlantic types. The maximum
FIG. 5.
ail 2 V
l>
1864
1860
1856
1852
1848
1844
1840
1832
1824
1820
1816
1812
;
CURVES OF SECULAR FLUCTUATIONS IN RAINFALL.
60 RAINFALL.
rainfall here occurs oftenest in December and the minimum
oftenest in July.
35. Secular Fluctuations in Rainfall. Diagram 5
illustrates the secular fluctuations in the rainfall through a
long series of years in the Atlantic system and in the central
Mississippi system. It presents the successions of wet and
dry periods as they vibrate back and forth about the mean
of the whole period.
The extreme fluctuation is in the first case twenty-eight
per cent., and in the second case thirty per cent.
36. Local, Physical, and Meteorological Influ-
ences. The above statistics give sufficient data for deter-
mining approximately the general average rainfall in any
one of the principal river-basins of the States.
There are local influences operating in most of the main
physical divisions, analogous to those governing rainfall in
the grand atmospheric systems.
Referring to any local watershed, and the detailed study
of such is oftenest that of a limited gathering ground tribu-
tary to some river, we have to note especially the mean
temperature and capacity of the atmosphere to bear vapor,
the source from which the chief saturation of the atmos-
phere is derived, the prevailing winds at the different sea-
sons, whether in harmony with or opposition to the direction
of this source, and if any high lands that will act as con-
densers of the moisture lie in its path and filch its vapors,
or if guiding ridges converge the summer showers in more
than due proportion in a favored valley. A careful study
of the local, physical, and meteorological influences will
usually indicate quite unmistakably if the mean rainfall of
a subordinate watershed is greater or less than that of the
main basin to which its streams are tributary. There is
rarely a sudden change of mean precipitation, except at the
GREAT RAIN STORMS. 61
crest of an elevated ridge or the brink of a deep and narrow
ravine.
37. Uniform Effects of Natural Laws. When
studies of local rainfalls are confined to mean results,
neglecting the occasional wide departures from the influence
of the general controlling atmospheric laws, the actions of
nature seem precise and regular in their successions, and in
fact we find that the governing forces hold results with a
firm bearing close upon their appointed line.
But occasionally they break out from their accustomed
course as with a convulsive leap, and a storm rages as
though the windows of heaven had burst, and floods sweep
down the water-courses, almost irresistible in their fury.
If hydraulic constructions are not built as firm as the ever-
lasting hills, their ruins will on such occasions be borne
along on the flood toward the ocean.
38. Great Rain Storms. In October, 1869, a great
storm moved up along the Atlantic coast from Virginia to
New York, and passed through the heart of New England,
with disastrous effect along nearly its whole course. Its
rainfall at many points along its central path was from
eight to nine inches, and its duration in New England was
from forty to fifty-nine hours.
In August, 1874, a short, heavy storm passed over east-
ern Connecticut, when there fell at New London and at
Norwich twelve inches * of rain within forty-eight hours,
five inches of which fell in four hours. Such storms are
rare upon the Atlantic coast and in the Middle and West-
ern States.
Short storms of equal force, lasting one or^two hours,
are more common, and the flood effects from them, on hilly
* From data supplied by H. B. Winship, Supt. of Norwich Water-works.
62
RAINFALL.
watersheds, not exceeding one or two square miles area,
may be equally disastrous, and waterspouts sometimes
burst in the valleys and flood their streams.
39. Maximum Ratios of Floods to Rainfalls.
When the surface of a small watershed is generally rocky,
or impervious, or, for instance, when the ground is frozen
and uncovered by snow, the maximum rate of volume of
flow through the outlet channel may reach two-thirds of the
average rate of volume of rain falling upon the gathering-
ground.
40. Volume of Water from given Rainfalls. The
rates of volume of water falling per minute, for the rates of
rainfall per twenty-four hours, indicated, are given in cubic
feet per minute, per acre and per square mile, in the follow-
ing table :
TABLE No, 8.
VOLUME OF RAINFALL PER MINUTE, FOR GIVEN INCHES PER TWENTY-
FOUR HOURS.
RAINFALL PER
24 HOURS.
VOLUME PER
MINUTE ON
ONE ACRE.
VOLUME PER
MINUTE ON
ONE SQ. MILE.
RAINFALL
PER
24 HOURS.
VOLUME PER
MINUTE ON
ONE ACRE.
VOLUME PER
MINUTE ON
ONE SQ. MILE.
Inches.
Cu.feet.
Cu.feet.
Inches.
Cu. feet.
Cu.feet.
O.I
.252
l6l.33
I
2.521
1613.33
.2
-54
322.67
2
5.042
3226.67
3
.756
484.01.
3
7-563
4840.00
-4
1.008
645-33
4
10.084
6453-33
5
1.264
806.67
12.605
8066.65
.6
I-5IS
968.00
6
15.126
9689.99
7
I-765
1122.73
7
17.647
II2 93-33
.8
2.IO7
1290.67
8
20.168
12906.66
9
2.269
I450.OO
9
22.689
14529.99
10
25.210
i6i33-33
41. Gauging Rainfall. A pluviometer, Fig. 6, is used
to measure the amount of rain that falls from the sky. It is
a deep, cylindrical, open-topped dish of brass. Its top
GAUGING RAINFALL.
63
FIG. 6.
edge is thin, so it will receive just the rain due to the sec-
tional area of the open top.
A convenient size is of two inches diameter at a, and at
b of such diameter that its sectional
area is exactly one-tenth the sec-
tional area at #, or a little more
than one-half inch.
When extreme accuracy is re-
quired, the diameter at a is made
ten inches and at b a little more
than three inches, still maintaining
the ratio of sectional areas ten to
one, the displacement of the meas-
uring-rod being allowed for.
This rain-gauge should be set
vertically in a smooth, open, level
ground, and the grass around be
kept smoothly trimmed in summer.
The top of a ten-inch gauge is set
at about one foot above the surface
of the ground, and of smaller
gauges, clear of the grass surface.
The gauge should be placed sufficiently apart from
buildings, fences, trees, and shrubs, so that the volume of
rain gathered shall not be augmented or reduced by wind-
eddies.
If such a situation, secure from interference by animals
or by mischievous persons, is not obtainable, the gauge
may be set upon the flat roof of a building, and the height
above the ground noted.
The measuring-rod for taking the depth of rain in b is
graduated in inches and tenths of inches, so that when the
sections of a and b are ten to one, ten inches upon the rod
64 RAINFALL.
corresponds with one inch of actual rainfall, and one inch
on the rod to one-tenth inch of rain, and one-tenth on the
rod to one-hundredth of rain.
Snow is caught in a cylindrical, vertical-sided dish, not
less than ten inches diameter, melted, and then measured as
rain. Memorandums of depths of snow "before melting,
with dates, are preserved also.
It has been observed at numerous places, that elevated
pluviometers indicated less rain than those placed in the
neighboring ground. When there is wind during a shower,
the path of the drops is parabolic, being much inclined in
the air above and nearly vertical at the surface of the
ground. A circular rain-gauge, held horizontally, presents
to inclined drops an elliptic section, and consequently less
effective area than to vertical drops.
The law due to height alone is not satisfactorily estab-
lished, though several formulae of correction have been
suggested, some of which were very evidently based upon
erroneous measures of rainfall.
The observed rainfall at Greenwich Observatory, Eng-
land, in the year 1855, is reported, at ground level, 23.8
inches depth ; at 22 feet higher, .807 of that quantity, and
at 50 feet higher, .42 of that quantity.
The observed rainfall at the Yorkshire Museum, Eng-
land, in the years 1832, 1833, and 1834, is reported, for
yearly average, at ground level, 21.477 inches ; at 44 feet
higher, .81 as much, and at 213 feet higher, .605 as much.
Unless vigilantly watched during storms, the gauges are
liable to overflow, when an accurate record becomes impos-
sible. Overflow cups are sometimes joined to rain-gauges,
near their tops, to catch the surplus water of great storms.
OHAPTEE IT.
FLOW OF STREAMS.
42. Flood Volume Inversely as the Area of the
Basin. A rain, falling at the rate of one inch in twenty-
four hours, delivers upon each acre of drainage area about
2.5 cubic feet of water each minute.
If upon one square mile area, with frozen or impervious
surface, there falls twelve inches of rain in twenty-four
hours, and two-thirds of this amount flows off in an equal
length of time, then the average rate of flow will be 215
cubic feet per second.
Any artificial channel cut for a stream, or any dam
built across it, must have ample flood-way, overfall, or
waste-sluice to pass the flood at its maximum rate.
The rate of flood flow at the outlet of a watershed is
usually much less from a large main basin than from its
tributary basins, because the proportion of plains, storage
ponds, and pervious soils is usually greater in large basins
than in small, and the flood flow is consequently distrib-
uted through a longer time.
In a small tributary shed of steep slope the period of
maximum flood flow may follow close after the maximum
rainfall ; but in the main channel of the main basin the
maximum flood effect may not follow for one, two, three, or
more days, or until the storm upon its upper valley has
entirely ceased.
43. Formulae for Flood Volumes. The recorded flood
measurements of American streams are few in number, but
5
66 FLOW OF STREAMS.
upon plotting such data as is obtained, we find their mean
curve to follow very closely that of the equation,
Q = 200 (M)*, (I)
in which M is the area of watershed in square miles and Q
the volume of discharge, in cubic feet per second, from the
whole area.
Thus the decrease of flood with increase of area is seen
to follow nearly the ratio of two hundred times the sixth
root of the fifth power of the area expressed in square
miles.
Among the Indian Professional Papers we find the fol-
lowing formula for volume, in cubic feet per second :
Q = cx27(M). (2)
in which c is a co-efficient, to which Colonel Dickens has
given a mean value of 8.25 for East Indian practice.
Testing this formula by our American curve, we find the
following values of c for given areas :
Area in sq. miles. . .
Value of c
i.
7.41
z.
9-33
3-
10.68
4-
11.76
6.
13.46
8.
14.83
10.
15.96
IS-
18.26
20.
20.11
30-
23.02
40.
25-33
5-
27.28
75-
31.26
100.
34.38
Mr. Dredge suggests, also in Indian Professional Papers,
the following formula :
Q ts 1300 ^| (3)
in which L is the length of the watershed, and M the area
in square miles.
Our formula, modified as follows, gives an approximate
flood volume per square mile, in cubic feet per second :
TABLE OF FLOOD VOLUMES.
67
in which M is the area of the given watershed in square
miles.
44. Table of Flood Volumes. Upon the average
New England and Middle State basins, maximum floods
may be anticipated with rates of flow, as per the following
table:
TABLE No. 9.
FLOOD VOLUMES FROM GIVEN WATERSHEDS.
AREA OF WATER-
SHED.
FLOOD DISCHARGE
FOR WHOLE AREA,
Q = 200 (M)*'
FLOOD DISCHARGE PER
SQUARE MILE,
200 (M)*
M.
FLOOD DISCHARGE
PER ACRE.
Sg. Miles.
Cu. Feet per Second. ' Cu. Feet per Second.
Cu. Feet per Minute.
0-5
112
225.00
21.15
i
2OO
2OO.OO
18.75
2
356
178.20
l6 -75
3
500
166.53
^.65
4
635
IS9-2S
14.96
6
890
148.37
J 3-94
8
II 3 I
141.42
13.29
10
I3 6 3
136.26
12.80
*5
IQIO
127-33
11.97
20
2428
I2I.4O
11.41
25
2925
Iiy.OO
II. OO
30
3404
H3-47
10.66
40
4326
108.15
10,16
5
5208
104.16
9.82
75
734
97-39
9- I 5
IOO
9282
92.82
8.72
200
16542
82.71
7-77
300
23190
77.30
7.26
400
29480
73.70
6.93
500
355
71.00
6.67
600
41320
68.87
6.46
800
5 2 5 20
65-65
6.16
IOOO
63260
63.26
5-94
1500
88680
59.12
5-55
2000
112600
56.30
5-29
3000
158000
52.67
4.94
400O
200800
50.20
4.72
5000
241800
48.36
4-54
68 FLOW OF STREAMS.
45. Seasons of Floods. Great floods occur only
when peculiar combinations of circumstances favor such,
result.
A knowledge of the magnitude of the floods upon any
river, and of their usual season, is invaluable to the director
of constructions upon that stream, to enable him to take such
precautionary measures as to be always prepared for them.
Such knowledge is also requisite to enable him to compute
the storage capacity required to save and utilize such flood,
or to calculate the sectional area of waste weir required
upon dams to safely pass the same.
Long rivers, having their sources upon northern moun-
tain slopes, have usually well-known seasons of flood, de-
pendent upon the melting of snows ; but small watersheds
in many sections of America are subject to flood, alike, at
all seasons.
46. Influence of Absorption and Evaporation
upon Flow. The rainfall upon the Atlantic coast and
upon the Mississippi valley appears comparatively uniform
when noted in its monthly classification, but the ability of
any one of their watersheds to supply, from flow of stream,
a domestic demand equal to its mean flow is by no means
as uniform.
We have seen that, according to the statistics quoted,
the consumption of water is not as uniform, when noted by
monthly classification, as is the monthly rainfall. When
lesser classifications of rainfall and consumption are com-
pared, there is scarce a trace of identity in their plotted
irregular profiles.
Evaporation, though comparatively uniform in its
monthly classification, is very irregular as observed in its
lesser periods.
In the spring and early summer, when vegetation is in
CLASSIFICATION OF RAINFALL AVAILABLE IN FLOW. 69
most thrifty growth, the innumerable rootlets of flowers,
grasses, shrubs, and forests, gather in a large proportion of
rainfall, and pass it through their arteries and back into
the atmosphere beyond reach for animal uses.
47. Flow in Seasons of Minimum Rainfall. In
gathering, basins having limited pondage or available
storage of rainfall, the flow from minimum annual, and
minimum periodic rainfall demands especial study. Occa-
sionally the annual rainfall continues less than the general
mean through cycles of three or four years, as is indicated
in the above diagram of curves of secular rainfall. The
mean rain of such cycles of low-rainfall is occasionally less
than eight-tenths of the general mean.
We have selected for data upon this point the rainfall
records of twenty-one stations, of longest observation in the
United States, at various points from Maine to Louisiana
and from California to Sitka. The computation gives the
annual rainfall of the least three-year cycle at any one of
these points as .67 of the general mean annual rain at the
same point, and annual rainfall of the greatest three-year
low cycle as .97 of the general mean at the same point. An
average of all these stations gives the three-year low cycle
rainfall as .81 of the average mean annual rainfall.
48. Periodic Classification of Rainfall Available
in Flow. Next, the rainfall and the portion of it that can
be made available, demands especial study in its monthly,
or less periodic classification. It is desirable to know the
ratio of each month' s average fall to the mean monthly fall
for the year, and the percentage of this fall that is exempted
from absorptions by vegetation and evaporations into the
atmosphere, and that flows from springs, and in the streams,
since it is ordained by Nature that the lily and the oak
with their seed, shall first be supplied and the atmospheric
70 FLOW OF STREAMS.
processes be maintained, and the surplus rain be dedicated
to the animal creation, as their necessities demand and
ingenuities permit them to make available.
49. Sub- surface Equalizers of Flow. The inter-
stices of the soils and the crevices of the rocks were filled
long ages ago, and now regularly aid in equalizing the flow
of the springs and streams without, to any considerable
extent, affecting the total annual flow, yet their influence is
observable in cycles of droughts when the sub-surface water
level is drawn slowly down.
The substructure of each given watershed has its indi-
vidual storage peculiarities which may increase or diminish
the monthly flow and degree of regularity of flow of its
streams to an important extent.
If a porous subsoil of great depth and storage capacity
is overlaid with a thin crust of soil through which water
percolates slowly, a great flood-rain may fall suddenly over
the nearly exhausted sub-reservoir and be run off to the
rivers without replenishing appreciably the waning springs,
or increasing their flow as would an ordinary slow rainfall.
On the other hand, if its surface soil is open and absorb-
ent, it may be able to receive nearly the whole flood and
distribute it gradually from its springs.
The early sealing over of the subsoil by winter frosts
before the usual subterranean storage has accumulated
from winter storms, or a shedding of the melting snows in
spring by a like frost-crust, may result in a diminished flow
of the deep springs in the following summer.
Subsoils that exhaust themselves in ordinary seasons
are comparatively valueless to sustain the flow in the second
and third years of cycle droughts.
Steep and impervious earths yield no springs, but gather
their waters rapidly in the draining streams.
SUMMARIES OF MONTHLY FLOW STATISTICS. 71
50. Flashy and Steady Streams. Upon the steep
and rocky watersheds of northern New Hampshire, we find
extreme examples of ''flashy" streams that are furious in
storm and vanish in droughts.
Upon the saturated sands of Hempstead Plains on Long
Island, N. Y., we find an opposite extreme of constant and
even flow, where a great underground reservoir co-extensive
with its supplying watershed, feeds its streams with remark-
able uniformity.
Almost all degrees of constancy and fickleness of flow
are to be found in the several sub-section streams of any
one of our great river basins.
51. Peculiar Watersheds. The extremes or results
from peculiar watersheds, are in all cases to be considered
as extremes when their individual merits and capacities of
supply are investigated, and the investigation may often
take the direction of determining the relations of its results
to results from a general mean, or ordinary watershed,
especially as respects its mean temperature, its mean hu-
midity of atmosphere, the direction from whence its storms
come, the frequency of its storm winds, the extent of its
storms in the different seasons, the imperviousness or the
porosity of its soils and rocks, the proportions of its steep,
gently undulating, and flat surfaces, and also it is to be
observed if it can be classed among those rare instances in
which one watershed is tributary as giver to or receiver
from another basin, involving an investigation of its geo-
logical substructure.
53. Summaries of Monthly Flow Statistics.
We have analyzed some valuable statistics of monthly
rainfalls, and measured flow of streams in Massachusetts
and New York State, which are too voluminous for repro-
duction here, and present the deduced results. The records
72 FLOW OF STREAMS.
are, first, from a report by Jos. P. Davis, C. E., relating to
the watershed of Cochituate Lake, which has. supplied the
city of Boston with water until supplemented in 1876 from
the Sudbury River watershed ; second, from a table com-
piled by Jas. P. Kirkwood, C. E., relating to the watershed
of Croton River above the Croton Dam ; and third, from a
paper read by J. J. R. Croes, C. E., before the American
Society of Civil Engineers, July, 1874, relating to the water-
shed of the West Branch of the Croton River.
The summaries are as follows :
TABLE No. 1O.
SUMMARY OF RAINFALL UPON THE COCHITUATE BASIN.
Average annual, 55.032 inches ; average monthly, 4.586 inches.
d
t
|
1
i
1 i
!>
H-
5
<
t
g
1
in
in
Mean
Minimum
3-69
4-03
.08
5-35
4.58
5.69
2 66
3-9
.58
5-23
I. O6
4.91
3.81
.64
5-86
5.26
2.6^
3-52
Maximum
7-85
Jo
8.44
"34
8.25
5.96
14.12
12.36
8.49
9-50
8,S4
5.98
Ratio of monthly
mean...
.806
.878
1.167
.008
I.24.I
.67*
1. 141
1.070
.8qi
I.^OO
1. 147
.768
TABLE No. 11.
SUMMARY OF RAINFALL UPON THE CROTON BASIN.
Average annual, 46.497 inches ; average monthly, 4.227 inches.
c
> >
1
VH
Pi
<
1
o
i ,
^>>
*3
i i
fci
3
<5
U
C/D
|j
>
o
fc '
1
Mean
Minimum..
in.
*'$
in.
3- J 5
in.
?%
in.
3.12
2 4.8
in.
6.40
A 78
in.
4.58
/.
4-31
/.
6.03
in.
5-30
in.
4.70
in.
3-83
r*.
3-60
i 86
Maximum
4 .?8
5-03
5.6?
4-32
TO. 18
2.51
6.19
8.12
.9.21
13.35
8.7!
5.36
6.86
Ratio of monthly
mean
.625
8<u
1 .
SUMMARIES OF MONTHLY FLOW STATISTICS.
73
TA B L E No. 12.
SUMMARY OF RAINFALL UPON CROTON WEST-BRANCH BASIN.
Average annual, 44.429 inches ; average monthly, 4.039 inches.
1
.0
4>
&
&
tj
Q,
<3
>,
i,
>,
3
!
1
a
i
fc
1
Mean
in.
-\ 16
/,
in.
in.
, 84
in.
c og
in.
in.
in.
in.
in.
*.
in.
o jg
Minimum
Maximum
1.44
4.5i
1.22
6.40
2.55
4.27
3.01
5-45
2.30
8.79
4-32
2.06
5-73
3-43
5-5 2
5-10
10.04
1.44
3.69
2.15
9.46
2-43
4-35
1.49
5.96
Ratio of monthly
mean
.733
.767
1.296
.718
1-633
1.136
1.070
1-257
951
.818
793
783
TAB L E No. 13.
SUMMARY OF PERCENTAGE OF RAINFALL FLOWING FROM THE COCHIT-
UATE BASIN.
Average percentage of average annual rainfall flowing off, 45.6.
I
1
S3
ij
a
<J
1
H- >
!>>
"3
i,
to
I
.1
1
1
y
Q
in.
in.
in.
in.
80 s
in.
*.
in.
in.
iV*.
in.
26 ;
in.
27 8
in.
64 i
Minimum
Maximum
33
79
%'
159
44
153
39
124
20
76
8?
9
39
14
27
J 3
39
10
80
20
42
^
Ratio of monthly
i =;6
,c8
.61
1.41
TABLE No. 14.
SUMMARY OF PERCENTAGE OF RAINFALL FLOWING FROM THE CROTON
BASIN.
Average percentage of average annual rainfall flowing off, 57.47-
i
Xi
i
J3
!M
OH
!
|
d
i
^,
"3
i
t#
!
1
>
o
K
o
Q
Mean
in.
70 68
in.
in,
86.72
.
80.60
in.
48. 4.5
in.
4S-O2
in.
21. 02
z.
19.45
in.
30.10
in.
81.13
in.
60.40
in.
62.12
Minimum
Maximum
49.0
123.4
62.1
lOJ.O
21.9
147.4
53-5
125.7
42.8
,S6.4
18.6
67.4
8-5
29.6
8.4
42.2
IO.2
92.0
7.6
366.5
36.3
94-i
39-o
94-5
Ratio of monthly
mean . .
i 386
.840
.783
.369
.338
5 2 4
1.412
1.051
1.081
74
FLOW OF STREAMS.
TABLE No. 15.
SUMMARY OF PERCENTAGE OF RAINFALL FLOWING FROM THE CROTON
WEST-BRANCH BASIN.
Average percentage of average annual rainfall flowing off, 70.98.
d
rt
H>
1
cj
Jv*
<
|
i
i >
>,
3
H- >
bb
3
<
1
ti
o
i
*
1
in
in
ir
Mean
102.8
71.1
158.9
II7.2
80.5
44-8
19.0
24.6
26.6
30.4
78.9
97.0
Minimum..,
Maximum
17.7
186.6
59-
103.9
103.0
209.1
93- 2
158.4
46.7
100.3
!}.6
71.2
7-3
3i-4
&
3-3
39-8
II. 2
56.3
4-5
1 10. 2
65-6
140.8
Ratio of monthly
mean
1.448
I.OOI
2.238
1.651
i.i34
.636
.267
347
375
. 42 8
1. 112
1.367
TABLE No. 16.
SUMMARY OF VOLUME OF FLOW OF RAINFALL FROM THE COCHITUATE
BASIN (in cubic feet per minute per square mile).
I
,Q
1
O
>,
a
c5
N-
j>>
3
1 >
bb
3
<
"cL
8
>
g
Q
Mean ....
cu.ft.
99.17
37-99
245.12
cu.ft.
150.42
58.29
301.90
cu.ft.
174.76
91.60
242.52
cu.ft.
169.80
70.44
369.40
cu.ft.
131.80
67.14
321.11
cu.ft.
44.27
18.28
85.49
cu.ft.
45.27
21.34
154-57
cu.ft.
49-15
21.34
109.29
cu.ft.
42.84
4-30
99.48
cu.ft.
62.45
36-43
123.34
cu.ft.
75-9
47-32
I0 5-39
,*.//.
78.94
40.07
164.98
Minimum
Maximum
Ratio of monthly
mean
1.058
1.605
1.865
1.812
1.406
.472
.483
524
457
.666
.809
.842
TABLE No. 17.
SUMMARY OF VOLUME OF FLOW OF RAINFALL FROM THE CROTON
BASIN (in cubic feet per minute per square mile).
d
i >
cu.ft.
91.48
48.08
127.71
1
cu.ft
147.69
40.65
293.01
1-317
1
<
1
cu.ft.
164.49
108.25
298.98
i
lj
cu.ft.
115.12
34-9
224-33
j>>
3
H->
cu.ft.
48.37
10.46
81.76
$
<J
I
g
g
Q
Mean
cu.ft.
177.02
79-05
25.709
cu.ft
132.63
87-43
188.95
cu.ft.
70.22
13.12
202.19
r.//.
85-99
12.91
275-95
CK../3?.
81.08
18.05
141.14
<:.//.
124.92
61.41
201.30
C */''
100.23
72.08
146-24
.948
Maximum
Ratio of monthly
mean
.816
i-579
1.183
1.467
1.027
431
.627
.767
.7=3
1.114
MINIMUM, MEAN, AND FLOOD FLOW OF STREAMS. 75
TABLE No. 18.
SUMMARY OF VOLUME OF FLOW OF RAINFALL FROM THE CROTON
WEST-BRANCH BASIN (in cubic feet per minute per square mile).
I
1
1
a
<
>,
A
8
i)
>,
s
fcJb
g
<
tl
&
o
>
o
fe
Q
Mean
cu.ft.
158.95
35.08
347-88
1.041
cu.ft\cu.ft. cu.ft.
185.191290.56 272.60
47.16 203.58 146.04
378.90 390.83 463.98
cu.ft.
161.60
26.19
394.92
cu.ft.
103.86
45.18
202.02
cu.ft.
40.02
19.26
_8*56
.262
cu.ft.
103.12
9.06
281.04
.676
cu.ft.
*47-59
5-i6
477-22
.967
cu.ft.
96.26
27-48
277.26
cu.ft.
107.85
5-92
203.28
c*.//.
164.07
50.88
299.16
1.075
Maximum . .
Ratio of monthly
mean
1.213
1.904
1.786
1.059
.680
.631
.707
53. Minimum, Mean, and Flood Flow of Streams.
An analysis of the published records of volumes of water
flowing in the streams in all the seasons has led to the fol-
lowing approximate estimate of volumes of flow in the aver-
age Atlantic coast "basins :
The minimum refers to a fifteen days' period of least
summer flow.
The mean refers to a one hundred and twenty days'
period, covering usually July, August, September, and
October, beginning sometimes earlier, in June, and ending
sometimes later, in November.
The maximum refers to flood volumes.
TABLE No. 19.
ESTIMATES OF MINIMUM, MEAN, AND MAXIMUM FLOW OF STREAMS.
Mm. in cu. ft. per
sec. per sq. mi.
Mean in cu. ft.'per
sec. per sq. mi.
Max. in cu ft. per
sec. per sq. mi.
Area of
watershed, i
sq. mi.
083.
I.OO
2OO
tt tt
10
ii
.1
99
I 3 6
tt it
2 5
tt
.11
.98
117
tt it
5o
n
.14
97
104
it n
100
"
.18
95
93
it it
" 250
ti
2 5
.90
80
if ii
500
it
30
.87
7 1
it ti
" IOOO
ii
35
.82
63
it it
" 1500
n
38
.80
59
it ii
" 2000
n
79 5 6
76
FLOW OF STREAMS.
This table refers to streams of average natural pondage
and retentiveness of soil, Ibut excludes effects of artificial
storage. The fluctuations of streams will be greater than
indicated by the table when prevailing slopes are steep and
rocks impervious, and less in rolling country with pervious
soils.
54. Ratios of Monthly Flow in Streams. A care-
ful analysis of the published records of monthly flow of the
average Atlantic coast streams leads to the following ap-
proximate estimate of the ratio of the monthly mean rain-
fall that flows down the streams in each given month of the
year, in which due consideration of the evaporation from
soils and foliage in very dry seasons has not been neglected.
TABLE No. 2O.
MONTHLY RATIOS OF FLOW OF STREAMS.
I
1
1
_j
I
<
i
i
h
s
bb
1
i
V)
i
i
si
Q
Ratio of flow .
1.65
1.50
1.65
i-45
.85
75
35
25
30
45
i. 20
1.60
Here unity equals the mean monthly flow, or one-twelfth
the mean annual flow.
To compute, approximately, the inches depth of rain
flowing in the streams each month, one-twelfth the mean
annual rain, at the given locality, may be multiplied by the
ratios in the following table. For illustration, a mean
annual rain of 40 inches depth, giving 3.333 inches mean
monthly depth, is assumed, and the available flow of stream
expressed in inches depth of rain is added after the ratios.
MEAN ANNUAL FLOW OF STREAMS.
77
TABLE No. 21.
RATIOS OF MEAN MONTHLY RAIN, AND INCHES OF RAIN FLOWING
EACH MONTH.
4
1
1
(X
ci
c
3
i >
*3
bb
3
ft
1
1
Ratios of mean
monthly rain
Inches of rain
.825
750
.825
725
425
375
.175
.125
ISO
.225
.600
.800
flowing
2.75
2.50
2-75
2.41
I.4I
1.25
0.59
0.41
0.50
0.75
2.OO
2.66
Eight - tenths
of same
2.20
2.00
2. 2O
i-93
...3
I.OO
0.47
0-33
0.40 O.6o
1. 60
2.13
For low-cycle years, use eight-tenths ( 47) the available
monthly depth of rain flowing.
tf 55. Mean Annual Flow of Streams. When month-
ly data of the flow of any given stream is not obtainable, it
may ordinarily be taken upon average drainage areas, for
an annual flow, as equal to fifty per cent, of the annual
rainfall.
Or, for different surfaces, its ratio of the annual rain,
including floods and flow of springs, is more approximately
as follows :
From mountain slopes, or steep rocky hills 80 to .90
Wooded, swampy lands 60 to .80
Undulating pasture and woodland 50 to .70
Flat cultivated lands and prairie 45 to .60
Since stations for meteorological observations are now
established in or near almost all the populous neighbor-
hoods, and some of the stations have already been estab-
lished more than a quarter of a century, it is easier to obtain
data relating to rainfall than to the flow of streams. In
fact, the required data relating to a given stream is rarely
obtainable, and the estimates relating to the capacity and
78 FLOW OF STREAMS.
reliability of the stream to furnish a given water-supply
must necessarily be quite speculative.
56. Estimates of Flow of Streams. In such case,
an estimate of the capacity of a stream to deliver into a
reservoir, conduit, or pump-well is computed according to
some scheme suggested by extended observations and study
of streams and their watersheds, and long experience in the
construction of water supplies.
The first reconnoissance of a given watershed by an ex-
pert in hydrology will ordinarily enable him to judge very
closely of its capacity to yield an available and suitable
water supply ; for his comprehension at once grasps its
geological structure, its physical features and its usual
meteorological phenomena, and his educated judgment
supplies the necessary data, as it were, instinctively.
If the estimate of flow of a stream must be worked up
from a survey of the watershed area and the mean annual
rainfall, as the principal data, then recourse may be had to
the data and estimates given above, relating to the question,
for average upland basins of one hundred or less square
miles area.
In illustration, let us assume a basin of one square mile
area, having a forty-inch average annual rainfall, and then
proceed with a computation. This is a convenient unit of
area upon which to base computations for larger areas.
The ratios of the three-year low rain cycles gives their
mean rainfall as about eight-tenths of the general mean
rainfall. We assume it to be eighty per cent. The mean
annual flow of the stream we assume to be fifty per cent, of
the annual rainfall. Eight-tenths of fifty per cent, gives
forty per cent, of the annual rainfall as the annual available
flow of the stream, and forty per cent, of the forty inches
rainfall gives an equivalent of sixteen inches of rainfall
ESTIMATES OF FLOW OF STREAMS.
79
flowing down the stream annually. The monthly average
flow is then taken as one-twelfth of sixteen, or one and one-
third inches. Our estimated monthly percentage of mean
flow, as given above ( 54), is sometimes much in excess
and sometimes less than the monthly average. Flows less
than the mean are to be compensated for by a proportion-
ate increase of storage above the mean storage required.
The monthly computations are as follows :
_ 40 inches x 50 percent, x .8
= 1.333
12 months
inches average available rain monthly. This average mul-
tiplied by the respective ratios of flow in each month gives
the inches depth of available rain flowing in the respective
months, thus:
MEAN MONTHLY
RAINFALL.
January.. 1.333
February
March
April
May
June
July
August
September
October ,..
November
December . .
INCHES DEPTH OF
AVAILABLE RAIN
FLOWING EACH
MONTH.
Again, uniting the constants, we have - ^ =.0333,
which, multiplied by the respective ratios of monthly flow,
thus : Jan., .0333 x 1.65 = ,055, etc., gives directly the mean
ratio of the low cycle annual rainfall that is available in the
stream each month.
80
FLOW OF STREAMS.
Jan
Feb. . .
March.
April .
May. . .
June..
July...
Aug...
Sept. . .
Oct....
Nov. . .
Dec..
40 nches
FLOW IN Cu. FT. PER
MINUTE PER SQ. Mi.
IN EACH MONTH.
055 =
2.20 inches depth =
116.60
.050 =
2.00
=
106.00
055 =
2.20
116.60
.0483 =
1-93
=
102.29
.0283 =
1.13
=
59-89
.025 -
1. 00
=
53-oo
.012 =
47
=
24.91
.0083 =
33
=
17.49
.OIO =
.40
21.20
.015 =
.60
=
31.80
.040
i. 60
=
84.80
0533 =
2.14
=
II342
Total,
16.00 inches. Mean,
70.67 cu. ft.
57. Ordinary Flow of Streams. Mr. Leslie has
proposed* an arbitrary rule for computing the "average
summer discharge" or " ordinary" flow of a stream, from
the daily gaugings, as follows :
" Range the discharges as observed daily in their order
of magnitude.
"Divide the list thus arranged into an upper quarter, a
middle half, and a lower quarter.
" The discharges in the upper quarter of the list are to be
considered as floods, and in the lower quarter as minimum
flows.
" For each of the gaugings exceeding the average of the
middle half, including flood gaugings, substitute the average
of the middle Jialf of the list, and take the mean of the
whole list, as thus modified, for the ordinary or average
discharge, exclusive of flood-waters"
This rule applied to a number of examples of actual
measurements of streams in hilly English districts gave
computed ordinary discharges ranging from one-fourth to
* Minutes of Proceedings of Institution of Civil Engineers, Vol. X, p. 327.
TABLES OF FLOW. 81
one-third of the measured mean discharge, including
floods.
The ordinary flow of New England streams is, at an
average, equivalent to about one million gallons per day
per square mile of drainage area, which expressed in cubic
feet, equals about ninety-two cubic feet per minute per
square mile.
The above computation for the average flow in low cycle
years gives a little less than eight-tenths of this amount, or
seventy-one cubic feet per minute per square mile as the
average flow throughout the year, and a little less than one-
fourth this amount as the minimum monthly flow.*
58. Tables of Flow Equivalent to Given Depths
of Rain. To facilitate calculations, tables giving the
equivalents of various depths of monthly and annual rain-
falls, in even continuous flow, in cubic feet per minute per
acre, and per square mile, are here inserted.
Greater or less numbers than those given in Tables 22
and 23 may be found by addition, or by moving the decimal
point ; thus, from Table 22, for 40.362 inches depth, take
Depth, 30 inches = 1590.204 cu. ft.
10 " = 530.068 "
.3 = 15.902
.06 " = 3.180 "
.002 " = .106 "
40.362 inches = 2139.460 cu. ft.
To reduce the flows in the two tables to equivalent vol-
umes of flow for like depths of rain in ONE DAY, divide the
flows in Table 22 by 30.4369 (log. = 1.483400), and divide
the flows in Table 23 by 365.2417 (log. = 2.562581).
* Some useful data relating to the flow of certain British and Continental
streams may be found in Beardmore's " Manual of Hydrology," p. 149 (Lon-
don, 1862).
FLOW OF STREAMS.
TABLE No. 22.
EQUIVALENT VOLUMES OF FLOW, FOR GIVEN DEPTHS OF RAIN IN
ONE MONTH.*
DEPTHS OF RAIN
IN ONE MONTH.
EQUIVALENT FLOW IN
CUBIC FEET PER
MINUTE PER ACRE.
EQUIVALENT FLOW IN CU-
BIC FEET PER MINUTE
PER SQUARE MILE.
EQUIVALENT FLOW IN CU-
BIC FEET PER MONTH PER
SQUARE MILE.
Inches.
.01
.00083
530
23,232
* .02
.O0l66
1. 060
#6,464
03
.00248
1.590
69,696
.04
.00331
2.I2O
92,928
5
.00414
2.650
Il6,l6o
.06
.00497
3.180
I39.392
.07
.00580
3.710
162,624
.08
.00662
4.240
185,856
.09
.00745
4.770
209,088
.1
.00828
5-3007
232,320
.2
.01656
IO.60I4
464,640
3
.02484
15.9020
696,960
4
.03312
21.2027
929,280
5
.04140
26.5034
I,l6l,6oo
.6
.04968
31.8041
i,393>9 20
7
.05796
37-I048
1,626,240
.8
.06624
42.4054
1,858,560
9
.07452
47.7061
2,090,880
1.0
.0828
53.0068
2,323,200
2
.1656
106.0136
4,646,400
3
.2484
159.0204
6,969,600
4
3312
212.0272
9,292,800
5
.4140
265.0340
11,616,000
6
.4868
318.0408
13,939.200
7
5796
371.0476
16,262,400
8
.6624
424.0544
18,585,600
9
7452
477.0612
20,908,800
10
.828
530.068
23,232,000
20
1.656
1060.136
46,464,000
3
2.484
I59O.204
69,696,000
* One month is taken equal to 30.4369 days.
TABLES OF FLOW.
83
TABLE No. 23.
EQUIVALENT VOLUME OF FLOW, FOR GIVEN DEPTHS OF RAIN IN
ONE YEAR.*
DEPTHS OF RAIN
IN ONE YEAR.
EQUIVALENT FLOW IN
CUBIC FEET PER
MINUTE PER ACRE.
EQUIVALENT FLOW IN CU-
BIC FEET PER MINUTE
PER SQUARE MILE.
EQUIVALENT FLOW IN CU-
BIC FEET PER YEAR PER
SQUARE MILE.
Inches.
.01
.000069
.0442
23,232
.02
.000138
.0883
46,464
03
.000207
1325
69,696
.04
.000276
.1767
92,928
5
.000345
.2209
Il6,l6o
.06
.000414
.2650
X 39>39 2
.07
.000483
.3092
162,624
.08
.000552
3534
185,856
.09
.OOO62I
3976
209,088
.1
.00069
.4417
232,320
.2
.00138
.8834
464,640
3
.002O7
1-3252
696,960
4
.00276
1.7669
929,280
5
00345
2.2086
1,161,600
.6
.00414
2.6503
I >393>9 2 <>
7
.00483
3.0921
1,626,240
.8
.00552
3.5338
1,858,560
9
.OO62I
3-9755
2,090,880
I.O
.0069
4.4172
2,323,200
2
.0138
8.8345
4,646,400
3
.0207
13-2517
6,969,600
4
.0276
17.6689
9,292,800
5
0345
22.0862
11,616,000
6
.0414
26.5034
1 3>939>2oo
7
.0483
30.9206
16,262,400
8
055 2
35-3379
18,585,600
9
.0621
39-755 1
20,908,800
10
.069
44.1723
23,232,000
20
.T 3 8
88.3447
46,464,000
30
.207
132.5170
69,696,000
40
.276
176.6894
92,928,000
50
345
220.8617
116,160,000
60
.414
265.0340
139,392,000
* One year is taken, equal to 365 days, 5 hours, 49 minutes.
CHAPTEE V.
STORAGE AND EVAPORATION OF WATER.
STORAGE.
59. Artificial Storage. The fluctuations of the rain-
fall, flow of streams, and consumption of water in the differ-
ent seasons of the year, require almost invariably that, for
gravitation and hydraulic power pumping supplies, there
shall be artificial storage of the surplus waters of the sea-
sons of maximum flow, to provide for the draught during
the seasons of minimum flow. A grand exception to this
general rule is that of the natural storage of the chain of
great lakes that equalizes the flow of the St. Lawrence
River, which furnishes the domestic water supply of the
City of Montreal and the hydraulic power to pump the same
to the reservoir on the mountain.
When the mean annual consumption, whether for do-
mestic use, or for power and domestic use combined is
nearly equal to the mean annual flow of the supplying
watershed, the question of ample storage becomes of su-
preme importance. The chief river basins of Maine present
remarkable examples of natural storage facilities, since
they have from six to thirteen per cent., respectively, of
their large watershed areas in pond and lake surfaces.
60. Losses Incident to Storage. There are losses
incident to artificial storage that must not be overlooked ;
for instance, the percolation into the earth and through the
embankment, evaporation from the reservoir surface and
from the saturated borders, and in some instances constant
draught of the share of riparian owners.
RIGHTS OF RIPARIAN OWNERS. 85
61. Sub- strata of the Storage Basin. The structure
of the impounding basin, especially when the water is to
fill it to great height above the old bed, is to be minutely
examined, as the water at its new level may cover the edges
of porous strata cropping out above the channel, or may
find access to fissured rocks, either of which may lead the
storage by subterranean paths along the valley and deliver
it, possibly, a long distance down the stream, or in a mul-
titude of springs beyond the impounding dam. If the
water carries but little sediment of a silting nature, this
trouble will be difficult to remedy, and liable to be serious-
ly chronic.
62. Percolation from Storage Basins. Percolation
through the retaining embankment is a result of slighted or
unintelligent construction, and will be discussed when con-
structive features are hereafter considered. (See Reservoir
Embankments.)
63. Rights of Riparian Owners. The rights of
riparian owners, ancient as the riparian settlements, to the
use of the water that flows, and its most favored piscatory
produce, is often as a thorn in the impounded s side. What
are those rights 1 The Courts and Legislatures of the man-
ufacturing States have wrestled with this question, their
judges have grown hoary while they pondered it, and their
attorneys have prospered, and yet who shall say what
riparian rights shall be, until the Court has considered all
anew.
Beloe mentions* that it is a "common (British) rule in
the manufacturing districts to deduct one-sixth the average
rainfall for loss by floods, in addition to the absorption and
evaporation, and then allow one-third of the remainder to
* Beloe on Reservoirs, p. 12. London, 1872.
86 , STORAGE AND EVAPORATION OF WATER.
the riparian owners, leaving two-thirds to the impounders.
In some instances this is varied to the proportion of one-
quarter to the former and three-quarters to the latter."
The question can only be settled equitably upon the
basis of daily gaugings of flow, through a long series of
years. A theoretical consideration involves a thorough
investigation of its geological, physical, and meteorological
features. There is no more constancy in natural flow at any
season than in the density of the thermometer's mercury.
The flow increases as the storms are gathered into the chan-
nel, it decreases when the bow has appeared in the heavens ;
it increases when the moist clouds sweep low in the valleys,
it decreases under the noonday sun ; it increases when the
shadows of evening fall across the banks, it decreases when
the sharp frosts congeal the streams among the hills.
64. Periodical Classification of Riparian Rights.
The riparian rights subject to curtailment by storage
might be classified by periods not greater than monthly,
though this is rarely desirable for either party in interest,
but they should be based upon the most reliable statistics
of monthly rainfall, evaporation, and flow, as analyzed and
applied with disciplined judgment to the particular locality
in question.
65. Compensations. In the absence of local statistics
of flow, it may become necessary, in settling questions of
riparian rights, or adjusting compensation therefor, to esti-
mate the periodic flow of a stream by some such method as
is suggested above in the general discussion upon the flow
of streams, after which it remains for the Court to fix the
proportion of the flow that the impounders may manipulate
for their own convenience in the successive seasons, and the
proportion that is to be passed down the stream regularly
or periodically.
EVAPORATION PHENOMENA. 87
EVAPORATION.
66. Loss from Reservoir by Evaporation. Losses
by evaporations from the surfaces of shallow storage reser-
voirs, lakes and ponds are, in many localities, so great in the
summer and autumn that their areas are omitted in compu-
tations of water derivable from their watersheds. This is a
safe practice in dry, warm climates, in which the evapora-
tions from shallow ponds may nearly or quite equal the
volume of rain that falls directly into the ponds. Marshy
margins of ponds are profligate dispensers of vapor to the
atmosphere, usually exceeding in this respect the water
surfaces themselves.
67. Evaporation Phenomena. Evaporation is the
most fickle of all the meteorological phenomena, and its
action is so subtle that we cannot observe its processes. Its
results demonstrate that the constituents of water are con-
stantly changing their state of existence from that of gas to
liquid, liquid to gas, liquid to solid, and solid to gas. The
action takes place as well upon polar ice fields or mountain
snows, as upon tropical lagoons, though less in degree.
The active vapors that form within the waters or porous ice,
silently emerge through their surfaces and proceed upon
their ethereal mission, and are not again recognizable until
they have been once more united into cloud and condensed
into rain.
The rapidity with which water, snow, and ice are con-
verted into vapor and pass off by evaporation is depend-
ent upon the temperature of the water and atmosphere, but
more especially upon their relative temperatures, and upon
the dryness and activity of the atmosphere. The formation
of vapor in a body of water is supposed to be at its mini-
mum when the atmosphere is moist and the atmosphere
88 STORAGE AND EVAPORATION OF WATER.
and water are quiet and of an equal low temperature, and
most active when the atmosphere is dryest and hottest and
the wind brisk and water warm.
M. Aime Drian observed that "when the temperature
of the dew point is higher than that of the evaporating sur-
face, water is deposited on that surface," which action he
styles negative evaporation.
Undoubtedly the cool surfaces of deep waters condense
moisture in summer from warm moist atmospheres wafted
across them, and thus at times are gaining in volume while
popularly supposed to be losing by evaporation. When
winds blow briskly across a water surface, large volumes
of unsaturated air are presented in rapid succession to
attract its vapors, and the wave motion increases the agita-
tion of the body and permits its vapors to escape freely.
The atmosphere has, however, its limit of power to ab-
sorb vapor for each given temperature, and when it is fully
saturated it can receive no more without depositing an equal
amount, or until its temperature is raised.
68.' Evaporation from Water. In an instructive
paper upon rainfall and evaporation, by Mr. A. Golding,
State Engineer at Copenhagen, quoted* by Beardmore, we
find some valuable measurements of evaporation in the
different seasons, from which the following, relating to
evaporation at Emdrup, is extracted.
* Vide Beardmore's Hydrology, p. 269 d. London, 1862.
EVAPORATION FROM EARTH.
89
TABLE No. 24.
EVAPORATION FROM WATER AT EMDRUP, DENMARK.
N. Lat. S54 I// ? E - Long i234 // from Greenwich.
YEAR.
d
ci
1
<
Ijl
!
bJD
P
i
g
o
1'
3
o
In.
In.
In.
In.
In. \ In.
In.
In
In.
In
In
In.
In
1849
1850
i.i
i.i
o-3
0-3
1.8
1.2
2.5
4.1 | 5-8
4-5 5-6
tl
4.0
4.8
2.6
2.4
i.i
1.6
0.9
0.9
0.6
O.2
29-5
29.1
1851
1852
o.S
0.7
0.4
o.S
0. 7
0.8
2.4
4.2 4.8
3-8 4.6
e
4-5
2-7
2-7
5
7
0.6
0.8
0-5
0-5
28.4
29.4
1853
1854
1855
1856
1857
o-5
I.O
o.S
0.7
O.I
0.9
i.i
0.6
0.7
0.9
0.5
1.2
0.6
I.O
3-2
1.2
2.1
4.1 6.2
3-3 4-5 ,
2.6 4.1
2.8 4.6
4.1 6.6
5.1
4.3
5-9
4-2
4-3
4.1
4.0
4-3
2.8
2.6
2.8
2.O
3.2
.1
.2
4
0.9
4
0.6
0.7
0.9
0.6
0.7
0.1
0.7
o-5
0.4
26.9
27.9
25-1
24.0
29.9
1858
0.4
0.7
1.2
3-i
5.1 6.1
4.9
5-6
2.8
.6
0.7
0.4
30.6
1859
o-5
0.7
4-3 5-8
5-3
3-8
1.8
I.O
0.7
o-3
26.4
Mean . .
0.7
o.5
0.9
2.0
3-7 5-4
5-2
4-4
2.6
1-3
0.7
0-5
27.9
Ratio . .
.301
.215
.387
.860
1.592 , 2.323
2-37
1.892
1.118
559
.301
.215
Mean..
Mean Evaporation from Short Grass, 1852 to 1859 inclusive.
0.7 | 0.8 | 1.2 1 2.6 | 4.1 | 5.5 | 5.2 | 4.7 | 2.8 | 1.3 | 0.7
0.5 | 30.1
Mean Evaporation from Long Grass, 1849 to 1856 inclusive.
Mean.. | 0.9 1 0.6 | 1.4 | 2.6 | 4.7 | 6.7 | 9.3 | 7.9 | 5.2 | 2.9 | 1.3
Mean Rainfall at same Station, 1848 to 1859 inclusive.
Mean.. | 1.5 | 1.7 ] i.o | 1.6 | 1.5 | 2.2 | 2.4 | 2.4 | 2.0 | 2.3 | 1.8
21.9
TABLE No. 25.
69. Evaporation from Earth. MEAN EVAPORATION FROM
EARTH, AT BOLTON LE MOORS,* LANCASHIRE, ENG., 1844 TO
1853, INCLUSIVE.
Lat. 533o" N. ; Height above the Sea, 320 Feet.
c
ci
h-
jd
<u
|
*
i
3
_>>
3
H- >
$
i
$
1.28
599
i
1
i
25.65
Mean . .
Ratio. . .
0.64
.299
0-95
.444
1-59
739
2.59
I.2I2
4.38
2.049
3.84
1.796
4.02
1.887
3.06
I-43I
2.02
945
0.81
379
0.47
.220
Mean Rainfall at same Station, 1844 to 1853 inclusive.
Mean..] 4.63 | 4.03 j 2.25 | 2.22 | 2.23 | 4 7 | 4-32 | 4-77 [ 3-79 [ S-o? | 4.64 | 3-94 | 45-96
* Beardmore's Hydrology, p. 325.
90
STORAGE AND EVAPORATION OF WATER.
MEAN EVAPORATION FROM EARTH, AT WHITEHAVEN, CUMBERLAND,
ENG., 1844 TO 1853 INCLUSIVE.
Lat. 54 30" N. ; Height above the Sea, 90 feet.
1
4
h
|
tgi
&
<
t>>
<u
a
3
H- >
_>,
3
H- >
<J
i
S
>
fe
8
Q
"3
5
Mean.
Ratio . .
0.95
39
I. 01
4 J 5
1.77
.727
2.71
1.113
4.11
1.689
4-25
1.746
4- I 3
1.697
3-29
1-352
2 . 9 6
i. 216
i. 7 6
723
1.25
513
1.02
.419
29.21
Mean Rainfall. at same Station, 1844 to 1853 inclusive.
Mean..] 5.1 [ 3.4 [ 2.5 ] 2.2 [ 1.9 | 3.1 | 4.3 | 4.3 | 3.! [ 5.3 | 4.5 [ 3.8 | 43 . 5
7O. Examples of Evaporation. Charles Greaves,
Esq., conducted a series of experiments upon percolation
and evaporation, at Lee Bridge, in England, .continuously
from 1860 to 1873, and has given the results * to the Insti-
tution of Civil Engineers. The experiments were on a large
scale, and the very complete record is apparently worthy
of full confidence.
The evaporation boxes were one yard square at the sur-
face and one yard deep. Those for earth were sunk nearly
flush in the ground, and that for water floated in the
river Lee. The mean annual rainfall during the time was
27.7 inches. The annual evaporations from soil were, mini-
mum 12.067 inches ; maximum 25.141 inches ; and mean
19.534 inches : from sand, minimum 1.425 inches ; maxi-
mum 9.102 inches; and mean 4.648 inches: from water,
minimum 17.332 inches ; maximum 26.933 inches ; and
mean 22.2 inches.
Some experimental evaporators were constructed at
Dijon on the Burgundy canal, and are described in Annales
des Fonts et CTiausses. They are masonry tanks lined
with zinc, eight feet square and one and one-third feet deep,
* Trans. Inst. Civil Engineers, 1876, Vol. XLV, p. 33,
RATIOS OF EVAPORATION. 91
and are sunk in the ground. From 1846 to 1852, there was
a mean annual evaporation of 26.1 inches from their water
surfaces against a rainfall of 26.9 inches. At the same time
a small evaporator, one foot square, placed near the larger,
gave results fifty per cent, greater.
Observations of evaporation from a water surface at the
receiving reservoir in New York indicated the mean annual
evaporation from 1864 to 1870 inclusive as 39.21 inches,
which equaled 81 per cent, of the rainfall.
On the West Branch of the Croton River, an apparatus*
was arranged for the purpose of measuring the evaporation
from water surface, consisting of a box four feet square and
three feet deep, sunk in the earth in an exposed situation
and filled with water. The mean annual evaporation was
found to be 24.15 inches, or about fifty per cent, of the
rainfall. The observations were made twice a day with
care. The maximum annual evaporation was 28 inches.
Evaporations from the surface of water in shaDow tanks
are variously reported as follows :
At Cambridge, Mass., one year, 56.00 inches depth.
" Salem, " " " 56.00 "
" Syracuse, N. Y., " " 50.20 "
* " Ogdensburgh, N. Y., " " 49.37 "
" Dorset, England, three " 25.92 "
" Oxford, " five " 31.04 "
" Demerara, three " 35.12 "
" Bombay, five " 82.28 "
71. Katios of Evaporation. In the eastern and mid-
dle United States, the evaporation from storage reservoirs,
having an average depth of at least ten feet, will rarely
exceed sixty per cent, of the rainfall upon their surface.
* Vide paper on " Flow of the West Branch of the Croton River," by J. Jas.
R. Croes. Traus. Am. Soc. Civ. Engrs., July, 1874, p. 83.
92 STORAGE AND EVAPORATION OF WATER.
The ratio of evaporation in each month to the monthly aver-
age evaporation, or one-twelfth the annual depth, is esti-
mated to be, for an average, approximately as follows :
TABLE No. 26.
MONTHLY RATIOS OF EVAPORATION FROM RESERVOIRS.
a
i
35
ctf
6
u
c
3
H- ,
jA
"3
> )
<
2.00
!
1
>
o
fe
cJ
Q
35
Mean ratio.. ..
3
50
.80
MS
I. 7
1.85
1.45
75
5
The following ratios of the annual evaporation from
water surfaces are equivalent to the above monthly ratios,
and may be used' as multipliers directly into the annual
evaporation to compute an equivalent depth of rain in
inches upon the given surface in action. Beneath the ratios
are given the equivalent depths for each month of 40 inches
annual rain, assuming the annual evaporation to equal
sixty per cent, of the rainfall, or 24 inches depth.
TABLE No. 27.
MULTIPLIERS FOR EQUIVALENT INCHES OF RAIN EVAPORATED.
,
i
ij
1
c
3
i ,
>>
3
t
be
I
1
$
i
*
1
H
Ratio of annual evapora-
tion
.0667
.1208
1667
1208
Equivalent depth of rain
6
1.0
i 6
2 AIM
I.O
12. Kesultant Effect of Kaiii and Evaporation.
For the purpose of comparing the effects upon a reservoir
replenished by rain only, let us assume the available rain-
fall to be eight-tenths of 40 inches per annum, and the
ratios of mean monthly rain, and the ratios of annual rain
in inches depth, to be as per the following table :
PRACTICAL EFFECT UPON STORAGE.
93
1
t
1
<
1
i
3
> i
t
<
!
g
>
o
fe
1
Ratio of aver.
monthly rain
75
.83
.00
I.IO
1.30
i. 08
1. 12
1.20
I. 00
95 j -93
.84
Ratio of .8 of
1
annual rain.
.0625
.0692
.0750
.0917
.1083
.0900
0933
.1000
.0833
.0792
.0775
.0700
Equiv. inches
of rain
2.00
2.21
2.40
2-93
3.47
2.88
2.99
3-20
2.67
.2.53
2.48
224
Comparing, in the two last tables, and their lowest
columns, the inches of gain by rainfall upon the reservoir,
supposing the sides of the reservoir to be perpendicular, and
the inches of loss from the same reservoir by evaporation,
we note that the gain preponderates until June, then the
loss preponderates until in November.
73. Practical Effect upon Storage. Since the prac-
tical value of storage is ordinarily realized between May
and November, the excess of loss during that term is,
practically considered, the annual deficiency from the reser-
voir chargeable to evaporation. We compute its maximum
in the following table, commencing the summation in June,
all the quantities being in inches depth of rain.
I
1
3*
i
I
>-
I
!
1
3
>
o
25
1
Gain by rain-
inches
2.00
2.21
240
2.93
347
2.88
2.99
3.20
2.67
2.53
2.48
2.24
Loss by evapo-
j
ration inches
Diff eren c e
.60
.70
1 .00
i. 60
2.90
3-40
3-70
4.00
2.90
1.50
1. 00
0.70
inches
Max. deficiency
-)-I.40
+ I.SI
+ 1.40
+ I-33
+0-57
0.62
0.71
0.80
-0.23
+0.97
+ 1.48
+ 1.54
after June
0.62
1-33
2.13
2.36
1.39
+ 0.09
....
If the classification is reduced to daily periods instead
of monthly, the maximum deficiency, according to the
above basis, will in a majority of years exceed three inches.
CHAPTEE VI.
SUPPLYING CAPACITY OF WATERSHEDS.
74. Estimate of Available Annual Flow of Streams.
Applying our calculations in the last chapter, of available
flow of water from the unit of watershed, one square mile,
and modifying it by the elements of compensation, storage,
evaporation, and percolation, we then estimate mean annual
quantities of low-cycle years, applicable to domestic con-
sumption, as follows :
Assumed mean annual rainfall 40 inches.
Flow of stream available for storage, 40 per cent, of mean rain = 16 inches of rain.
This available rain is applied to :
ist. Compensation to riparian owners, say 16.8 p. c. of mean rain = 6.72 in. of rain.
2d. Evaporation from surface of storage reservoir, u 2.4 " " " " = .96 " " "
3d. Percolation from storage reservoir, " 2.4 " " ' " = .96 " " "
4th. Balance available for consumption, 18.4 4t " " " = 7 . 3 6 u " u
Total 40 per cent. 16 inches.
The 7.36 inches of rain estimated as available from a
40-inch annual rain equals 17,098,762 cubic feet of water,
which is equivalent to a continuous supply of seven cubic
feet per day (= 52.36 gals.) each, to 6,692 persons.
By applying to the annual results the monthly ratios,
and thus developing the monthly surpluses or deficiencies
of flow, we shall have in the algebraic sum of the deficien-
cies the volume of storage necessary to make forty per cent,
of the rainfall available, and this storage must ordinarily
approximate one-third of the annual flow available for
storage.
MONTHLY AVAILABLE STORAGE REQUIRED. 95
75. Estimate of Monthly Available Storage Re-
quired. Computation of a supply, and the required
storage ; applied to one square mile of watershed as a unit
of area.
Assumed data: Population to be supplied. 6,500 per-
sons, consuming 7 cubic feet per capita daily,. each ;
Mean annual rainfall, 40 inches, and eight-tenths =
32 inches of rain, in the low-cycle years ;
Available flow of stream, fifty per cent. . of eight-tenths
of rain = 16 inches ;
Compensation each month, .168 of one-twelfth the mean
annual depth of rain = .56 inches each month uniformly ;
Evaporation annually from the reservoir surface , only,
sixty per cent, of the depth of mean annual rain, or 24
inches ; and monthly, sixty per cent, of one-twelfth the
annual evaporation = 2 inches.
Area of storage reservoir, .04 square mile,* or 25.6 acres,
with equivalent available draught of ten feet for that sur-
face. The evaporation of two inches from four hundredths
of a square mile = .08 inch from one square mile.
Volume of percolation assumed to equal volume of
evaporation from the reservoir surface.
The monthly ratios will be multiplied into
P " = '<* - ^r the monthly flow.
40 in. mean rain
=- = 3.3333 in. for monthly compensation.
*
.04 x - - ' ' - = .08 in. for monthly evaporation from reservoir.
12 months
" = .08 in. for monthly percolation from reservoir.
6500 x 7 cu. ft. x 30.4369 days = 1,384,879 cu. ft. for monthly con-
sumption.
* A unit of reservoir area, for each square mile unit of watershed.
96
SUPPLYING CAPACITY OF WATERSHEDS.
TABLE No. 28.
MONTHLY SUPPLY TO, AND DRAFT FROM, A STORAGE RESERVOIR.
MONTH.
Jan. |
Feb. |
Mar. j
Apr. j
(*
May |
June -j
July |
Aug. ]
Sept. |
Oct. -j
Nov. |
Dec. |
MONTHLY
FLOW.
cubic feet.
MONTHLY
COMPEN-
SATION.
cubic feet.
MONTHLY
EVAPORA-
TION FROM
RESER-
VOIR.
cubic feet.
MONTHLY
PERCOLA-
TION FROM
RESER-
VOIR.
cubic Jeet.
MONTHLY
DOMESTIC
CONSUMP-
TION.
cubic feet.
SURPLUS.
cubic feet.
DEFICIENCY.
cubic feet.
Gain,
Ratio, 1.65
5,111,040
Ratio, 1.50
4,646,400
Ratio, 1.65
5,111,040
Ratio, 1.45
4490,746
Ratio, .85
2,632,186
Ratio, .75
2,323,200
Ratio, .35
1,084,934
Ratio, .25
773,626
Ratio, .30
929,280
Ratio, .45
1,393,920
Ratio, 1.20
3,717,120
Ratio, i. 60
4,955,386
Loss.
Ratio, .168
1,300,992
.168
1,300,992
.168
1,300,992
.168
1,300,992
.168
1,300,992
.168
1,300,992
.168
1,300,992
.168
1,300,992
.,68
I,3OO,992
.168
I,3OO,992
.168
I,3OO,992
.168
1,300,992
Loss.
Ratio, .30
55,757
35
65,050
5
92,928
.80
148,685
i-45
269,491
1.70
315,955
1.85
343,834
2.OO
371,712
L45
269,491
75
I39,39 2
So
92,928
35
65,050
Loss.
Ratio, .30.
55,757
35
65,050
So
92,928
.80
148,685
i.45
269,491
1.70
315,955
1.85
343,834
2.00
371,712
i-45
269,491
75
139,392
5
92,928
35
65,050
Used.
Ratio, 1.05
1,454,123
1. 10
1,523,367
.90
1,246,391
.85
1,177,147
.90
1,246,391
1.00
1,384,879
1.20
1,661,855
1.25
1,731,099
1.05
1,454,123
.90
1,246,391
85
1,177,147
95
1,315,635
2,311,507
1,691,941
2,447,497
1,715.237
454,119
994,581
2,565,581
3,037,889
2,364,817
1,432,247
1,053.125
2,208,659
Totals
37,272,270
T5,6lI,9O4
2,232,072
2,232,072
16,618,548
11,427,966
10,849,234
From certain localities no claim will arise for diversion
of the water, or the diversion may be compensated for by
the payment of a cash bonus, in which case the proportion
of rainfall applicable to domestic consumption will be a
little more than doubled, and approximately as follows,
neglecting percolation from the storage reservoir.
MONTHLY AVAILABLE STORAGE REQUIRED.
97
The monthly ratios will here be multiplied into,
40 in. x .8 x .^o p. c. /-
- = 1.3333 m - for tne monthly flow. /, /
12 months , ^ / /J
40 in. x .60 p. c.
.04 x - = .08 m. for monthly evaporation fronvfraservoir. .<!
12 months * y,, fy
13,500 persons x 7 cu. ft. x 30.4369 days = 2,876,467! cu. ft 6$, x <
monthly consumption. ftp J"
TABLE No. 29. <\V
MONTHLY SUPPLY TO, AND DRAFT FROM, A STORAGE RESERVOIR
(without compensation).
MONTH.
MONTHLY
FLOW.
cubic feet.
MONTHLY
EVAPORATION
FROM
RESERVOIR.
cubic feet.
MONTHLY
DOMESTIC
CONSUMPTION.
cubic feet.
SURPLUS.
cubic feet.
DEFICIENCY.
cubic feet.
Jan. |
Gain.
Ratio, 1.65
5, 180,736
Loss.
Ratio, .30
Used.
Ratio, 1.05.
i Q2O 2QO
2 IO2 889
Feb. |
Ratio, 1.50
4,646,400
35
1. 10
3,164 114
1,417,2^6
Mar. -j
Ratio, 1.65
5,180,736
50
Q2,Q28
.90
2,588,820
2,4Q8,o88
April -j
Ratio, 1.45
4,400,746
.80
148 68^
.85
2 4.4.4. QQ7
I 897 064
May |
Ratio, .85
2,632,186
1-45
260,401
.90
2 588 82O
226 125
June -j
Ratio, .75
2,323,200
1.70
I.OO
2,876,467
869 222
July |
Ratio, .35
1,084,934
1.85
343,834
i. 20
3,451,760
2 7IO 660
Aug. -j
Ratio, .25
737,626
2.00
371,712
3,22Q,67O
Sept. |
Ratio, .30
Q2Q 28O
1-45
260 401
1.05
7 O2O 2QO
2 360 5OI
Oct. |
Ratio, .45
l.^Q^,Q2O
75
iqn -JQ2
.90
2 588,820
Nov. -j
Ratio, 1.20
3717 1 2O
5
Q2 928
.85
2 AAA QQ7
I 179 195
Dec. |
Ratio, 1.60
4,955,386
35
65,050
95
2,732,644
2,157,692
Totals,
37,272,270
2,232,072
34,517,603
11,253,064
10,730,470
98 SUPPLYING CAPACITY OF WATERSHEDS.
76. Additional Storage Required. Forty inches
of rainfall on one square mile equals a volume of 92,928,000
cubic feet. The deficiency as above computed is nearly
twelve per cent, of this quantity, and calls for an available
volume of water in store early in May, or at the beginning
of a drought, equal to about one-eighth the mean annual
rainfall.
The calculations of supply and draught in the two
monthly tables given above refer to mean quantities of low-
cycle years, and not to extreme minimums. The seasons of
minimum flow, which are also, usually, the seasons of
maximum evaporation from the storage reservoirs and of
maximum domestic consumption, are in the calculations
supposed to be tided over by a surplus of storage provided
in addition to the mean storage required for the series of
low-cycle years. The storage should therefore be in excess
of the mean deficiency as above computed at least twenty-
five per cent., or should equal at least fifteen per cent, of the
mean annual rainfall.
If the storage is less than fifteen per cent., the safe
available supply is liable to be less than the calculations
given.
If the area of the storage reservoir is greater per square
mile of watershed than assumed above, the loss by evapo-
ration from the water surface will be proportionately in-
creased, and must be compensated for by increased storage.
77. Utilization of Flood Flows. The calculations
as above assume that fifty per cent, of the annual rainfall
is the available annual flow in the stream. The remaining
fifty per cent, is assumed to be lost through the various
processes of nature and by floods. If the storage is still
further increased, an additional portion of the flood flow
can be utilized, and sometimes fifty per cent, or even sixty
INFLUENCE OF STORAGE. 99
per cent, of the annual rainfall utilized for domestic con-
sumption, or made applicable at the outlet of the reservoir
for power. Hence, when it is desired to utilize the greatest
possible portion of the flow, the storage should equal twenty
or twenty-five per cent, of the mean annual rainfall.
78. Qualification of Deduced Ratios. The ratios
of flow, evaporation, and consumption, as above used in
the calculations, are not assumed to be universally appli-
cable, but are taken as safe general average ratios for the
Atlantic Coast and Middle States. The winter consump-
tion will be less in the lower Middle and Southern States,
and also in very efficiently managed works of Northern
States ; but the summer consumption tends to be greater in
the lower Middle and Southern States, where the evapora-
tion and rainfall are greater also.
The results upon the Pacific slope can scarcely be gen-
eralized to any profit, since within a few hundred miles it
presents extremes, from rainless desert to tha maximum
rainfall of the continent, and from vaporless atmosphere to
constant excessive humidity.
79. Influence of Storage upon a Continuous
Supply. A safe general estimate of the maximum contin-
uous supply of water to be obtained from forty inches of
annual rain upon one square mile of watershed, provided
the storage equals at least fifteen per cent, of the rainfall,
gives 7 cubic feet (= 52.36 gals.) per capita daily, to from
13000 to 15000 persons, dependent upon the amount of
available storage of winter and flood flows ; or say, three-
quarters of a million gallons of water daily.
The same area and rain, with but one month's deficiency
storage, can be safely counted upon to supply but about
3,000 persons with an equal daily consumption, or 157,000
gallons of water daily. From the same area and rain, with
100 SUPPLYING CAPACITY OF WATERSHEDS.
no storage, a flashy stream may fail to supply 1,000 persons
to the full average demand in seasons of severe drought.
Hence the importance of the storage factor in the calcu-
lation.
The above estimates are based upon mean rainfalls of
low-cycle ( 47) years ; therefore the results may be ex-
pected to be twenty per cent, greater in years of general
average rainfall.
80. Artificial Gathering Areas. When resort is
necessarily had to impervious artificial collecting areas for
a domestic water supply, as when dwellings are located
upon vegetable moulds or low marsh areas, bituminous
rock surfaces, limestone surfaces, or, as in Venice, where
the sheltering roofs are the gathering areas of the house-
holds, the proportion of the rainfall that may be run into
cisterns is very large. If such cisterns are of sufficient
capacity and their waters protected from evaporation, eighty
per cent, of the rainfall upon the gathering areas may thus
be made available., though special provisions for its clarifi-
cation will be indispensable.
In such case, a roof area equivalent to 25 feet by 100
feet might furnish from a forty-inch rainfall a continuous
supply of 3 cubic feet (=22.44 gallons) per day to six per-
sons, which would be abundant for the household uses for
that number of persons.
81. Recapitulation of Rainfall Ratios. Recapitu-
lating, in the form of general average annual ratios, relating
to the mean rainfall upon undulating crystalline or diluvial
surface strata, as unity, we have :
Ratio of mean annual rainfall '. i.oo
Ratio of mean rainfall of lowest three-year cycles 80
Ratio of minimum annual rainfall 7O
Ratio of mean annual flow in stream (of the given year's rain) 60
RAINFALL RATIOS.
101
Ratio of mean summer flow in stream (of the given year's rain) 25
Ratio of low summer flow in stream " 05
Ratio of annual available flow in stream 50
Ratio of storage necessary to make available 50 per cent, of annual rain. .15
Ratio of general evaporation from earths, and consumption by the pro-
cesses of vegetation 40
Ratio of percolation through the earth (included also in the flow of
streams) 25
Ratio of mean rainfall collectible upon impervious artificial or primary
rock surfaces 80
The monthly ratios of these annual ratios are to be taken
in ordinary calculations of water supplies, and each annual
ratio to be subjected to the proper modification adapting it
to a special local application.
T A BL E No- SO.
RATIOS OF MONTHLY RAIN, FLOW, EVAPORATION, AND CONSUMPTION.
JQ
u
g
|
*
J
a~'
>
g
%
<5
s
3
3
<J
$
I
Q
Ratios of average monthly rain
Ratios of av. monthly flow of streams.
Ratios of av. monthly evap. from water
Ratios of average monthly consump-
.:
.30
8 3
1.50
35
50
1. 10
3
1. 08
75
1.70
1.12
sits
1.20
25
2.00
I.OO
30
i-45
95
45
75
93
1.20
50
.84
i. 60
35
tion of water ....
I.ZO
qo
gc
.00
I.OO
i. 20
1.25
1.05
9
gr
95
OHAPTEE VII.
SPRINGS AND WELLS.
82. Subterranean Waters. A portion of the rain,
perhaps one-fourth part of the whole, distilled upon the
surface of the earth, penetrates its soils, the interstices of
the porous strata, the crevices of the rocks, and is gathered
in the hidden recesses. These subterranean reservoirs were
filled in the unexplored past, and their flow continues in
the present as they are replenished by new rainfalls.
83. Their Source the Atmosphere. We find no
reason to suppose that Nature duplicates her laboratory of
the atmosphere in the hidden recesses of the earth, from
whence to decant the sparkling springs that issue along the
valleys. On the other hand, we are often able to trace the
course of the waters from the storm-clouds, into and through
the earth until they issue again as plashing fountains and
flow down to the ocean.
The clouds are the immediate and only source of supply
to the subterranean watercourses, as they are to the sur-
face streams we have just passed in review.
The subterranean supplies are subject indirectly to at-
mospheric phenomena, temperatures of the seasons, surface
evaporations, varying rainfalls, physical features of the
surface, and porosity of the soils. Especially are the shal-
low wells and springs sensitively subject to these influences.
84. Porosity of Earths and Rocks. Respecting the
porosity and absorptive qualities of different earths, it may
be observed that clean silicious sand, when thrown loosely
together, has voids between its particles equal to nearly
FIG. 131.
INTERCEPTING WELL, PROSPECT PARK, BROOKLYN.
THEIR SOURCE THE ATMOSPHERE. 103
one-third its volume of cubical measure ; that is, if a tank
of one cubic yard capacity is filled with quartzoid sand,
then from thirty-to thirty -five per cent, of a cubic yard of
water can be poured into the tank with the sand without
overflowing.
Gravel, consisting of small water- worn stones or pebbles,
intermixed with grains of sand, has ordinarily twenty to
twenty-five per cent, of voids.
Marl, consisting of limestone grains, clays, and silicious
sands, has from ten to twenty per cent, of voids, according
to the proportions and thoroughness of admixture of its
constituents.
Pure clays have innumerable interstices, not easily
measured, but capable of absorbing, after thorough drying,
from eight to fifteen per cent, of an equal volume of water.
The water contained in clays is so fully subject to laws
of molecular attraction, owing to the minuteness of the
individual interstices, that great pressure is required to give
it appreciable flow.
Water flows with some degree of freedom through sand-
stones, limestones, and chalks, according to their textures,
and they are capable of absorbing from ten to twenty per
cent, of their equal volumes of water.
The primary and secondary formations, according to
geological classification, as for instance, granites, serpen-
tines,- trappeans, gneisses, mica-slates, and argillaceous
schists, are classed as impervious rocks, as are, usually,
the several strata of pure clays that have been subjected to
great superincumbent weight.
The crevices in the impervious rocks, resulting from
rupture, may, however, gather and lead away, as natural
drains, large volumes of the water of percolation.
The free flow of the percolating water toward wells or
104 SPRINGS AND WELLS.
spring, is limited and controlled, not only by the porosity
of the strata which it enters, but also by their inclination,
curvature, and continuous extent, and by the impervious-
ness of the underlying stratum, or plutonic rock.
85. Percolations in the Upper Strata. Shallow
well and spring supplies are, usually, yields of water from
the drift formation alone. Their temperatures may be va-
riable, rising and falling gradually with the mean tempera-
tures of the surface soils in the circuits of the seasons, and
they may not be wholly freed from the influence of the
decomposed organic surface soils. Their flow is abundant
when evaporation upon the surface is light, though slack-
ened when the surface is sealed by frost.
A variable spring, and it is the stream at its issue that
we term a spring, indicates, usually, a flow from a shallow,
porous surface stratum, say, not exceeding 50 feet in depth,
though occasionally its variableness is due to peculiar
causes, as the melting of glaciers in elevated regions, and
atmospheric pressure upon sources of intermittent springs.
Porous strata of one hundred feet in depth or more give
comparatively uniform flow and temperature to springs.
86. The Courses of Percolation. Gravitation tends
to draw the particles of water that enter the earth directly
toward the center of the earth, and they percolate in that
direction until they meet an impervious strata, as clay,
when they are forced to change their direction and follow
along the impervious surface toward an outlet in a valley,
and possibly to find an exit beneath a lake or the ocean.
When the underlying impervious strata has considerable
average depth, it may have been unevenly deposited in
consequence of eddies in the depositing stream, or crowded
into ridges by floating icebergs, or it may have been worn
into valleys by flowing water. Subsequent deposits of
SUBTERRANEAN RESERVOIRS. 105
sand and gravel would tend to fill up the concavities and
to even the new surface, hiding the irregularities of the
lower strata surface.
The irregularities of the impervious surface would not
be concealed from the percolating waters, and their flow
would obey the rigid laws of gravitation as unswervingly
as do the showers upon the surface, that gather in the chan-
nels of the rocky hills.
Springs will appear where such subterranean channels
intercept the surface valleys. The magnitude of a spring
will be a measure of the magnitude of its subterranean
gathering valley.
87. Deep Percolations. The deep flow supplies of
wells and springs are derived, usually, from the older
porous stratifications lying below the drift and recent clays.
The stratified rocks yielding such supplies have in most
instances been disturbed since their original depositions,
and they are found inclined, bent, or contorted, and some-
times rent asunder with many fissures, and often intercepted
by dykes.
88. Subterranean Reservoirs. Subterranean basins
store up the waters of the great rain percolations and
deliver them to the springs or wells in constant flow, as
surface lakes gather the floods and feed the streams with
even, continuous delivery. A concave dip of a porous
stratum lying between two impervious strata presents favor-
able conditions for an " artesian" well, especially if the
porous stratum reaches the surface in a broad, concentric
plane of great circumference, around the dip, forming an
extensive gathering area.
Waters are sometimes gathered through inclined strata
from very distant watersheds, and sometimes their course
106 SPRINGS AND WELLS.
leads under considerable hills of more recent deposit than
the stratum in which the water is flowing.
The chalks and limestones do not admit of free percola-
tion, and are unreliable as conveyers of water from distant
gathering surfaces, since their numerous fissures, through
which the water takes its course, are neither continuous nor
uniform in direction.
89. The Uncertainties of Subterranean Searches.
The conditions of the abundant saturation and scanty
saturation of the strata, and their abilities to supply water
continuously, are very varied, and may change from the
first to the second, and even alternate, with no surface indi-
cations of such result ; and the subterranean flow may, in
many localities, be in directions entirely at variance with
the surface slopes and flow.
Predictions of an ample supply of water from a given
subterranean source are always extremely hazardous, until
a thorough knowledge is obtained of the geological posi-
tions, thickness, porosity, dip, and soundness of the strata,
over all the extent that can have influence upon the flow at
the proposed shaft.
Experience demonstrates that water may be obtained in
liberal quantity at one point in a stratum, while a few rods
distant no water is obtainable in the same stratum, an
intervening " fault" or crevice having intercepted the flow
and led it in another direction. Sometimes, by the exten-
sion of a heading from a shaft in a water-bearing stratum,
to increase an existing supply, a fault is pierced and the
existing supply led off into a new channel.
90. Renowned Application of Geological Science.
Arago's prediction of a store of potable water in the deep-
dipping greensand stratum beneath the city of Paris, was
one of the most brilliant applications of geological science
INFLUENCE OF WELLS UPON EACH OTHER. 107
to useful purposes. He felt keenly that a multitude of his
fellow-citizens were suffering a general physical deteriora-
tion for want of wholesome water, for which the splendors
of the magnificent capital were no antidote. With a fore-
sight and energy, such as displays that kind of genius that
Cicero believed to be "in some degree inspired," he pre-
vailed upon the public Minister to inaugurate, in the year
1833, that notable deep subterranean exploration at Gre-
nelle. By his eloquent persuasions he maintained and
defended the enterprise, notwithstanding the eight years of
labor to successful issue were beset with discouragements,
and all manner of sarcasms were showered upon the pro-
moters. In February, 1841, the augur, cutting an eight-
inch bore, reached a depth of 1806 feet 9 inches, when it
suddenly fell eighteen inches, and a whizzing sound an-
nounced that a stream of water was rising, and the well
soon overflowed.
91. Conditions of Overflowing Wells. An over-
flow results only when the surface that supplies the water-
bearing stratum is at an elevation superior to the surface of
the ground where the well is located, and the water-bearing
stratum is confined between impervious strata. In such
case, the hydrostatic pressure from the higher source forces
the water up to the mouth of the bore.
92. Influence of Wells upon Each Other. The
success of wells, penetrating deep into large subterranean
basins, upon their first completion, has usually led to their
duplication at other points within the same basin, and the
flow of the first has often been materially checked upon the
commencement of flow in the second, and both again upon
the commencement of flow in a third, though neither was
within one mile of either of the others. The flow of the
famous well at Grenelle was seriously checked by the open-
108 SPRINGS AND WELLS.
ing of another well at more than 3000 yards, or nearly two
miles distant.
The successful sinking of deep wells in Europe began at
Artois, in France, in the year 1126. The name " Artesian,"
from the name of the province of Artois, has been familiarly
associated with such wells from that date, notwithstanding
similar works were executed among the older nations many
years earlier. Since the success at Artois, this method has
been adopted in many towns of France, England, and Ger-
many, where the geological structure admitted of success.
The French engineers have recently sunk nearly one hun-
dred successful wells in the great Desert of Sahara ; and
Algeria and Northern Africa are beginning to bloom in
waste places in consequence of being watered by the pre-
cious liquid sought in the depths of the earth.
93. American Artesian Wells. Not less than 21
-yielding wells have been sunk in Chicago varying in depth
from 1200 to 1640 feet, the most successful of which is five
and one half inches diameter at the bottom, yielding about
900,000 gallons of water per 24 hours. The usual depth of
the Chicago wells is reported to be from 1200 to 1300 feet,
and the average cost of a five-and-a-half-inch well $6000, and
for a four-and-a-half-inch well $5000, for depth of 1200 feet.
A well for the Insane Asylum at St. Louis has reached
a depth of 3850 feet, or 3000 feet below the level of the sea.
Along the line of the Union Pacific Railroad, water is
obtained at certain points by means of Artesian wells, for
supplying the necessities of the road.
A few Artesian wells have been sunk in Boston, but the
water obtained has rarely been of satisfactory quality for
domestic purposes.
94. Watersheds of Wells. The watershed of a deep
subterranean supply is not so readily distinguishable as is
WATERSHEDS OF WELLS.
that of a surface stream, that usually has its limit upon the
crown of the ridge sweeping around its upper area.
The subterranean watershed may possibly lie in part
beyond the crowning ridge, where its form is usually that
of a concentric belt, of varying width and of varying sur-
face inclination. A careful examination of the position,
nature, and dip of the strata only, can lead to an accurate
trace of its outlines.
The granular structure of the water-bearing stratum, as
a vehicle for the transmission of the percolating water, is to
be most carefully studied ; the existence of faults that may
divert the flow of percolation are to be diligently sought
for ; and the point of lowest dip in a concave subterranean
basin or the lowest channel line of a valley-like subterra-
nean formation, is to be determined with care.
A depressed subterranean water basin, when first dis-
covered, is invariably full to its lip or point of overflow.
Its extent may be comparatively large, and its watershed
comparatively small, yet it will be full, and many centuries
may have elapsed since it was moulded and first began to
store the precious showers of heaven. A few drops accu-
mulated from each of the thousand showers of each decade,
may have filled it to its brim many generations since ; yet
this is no evidence that it is inexhaustible. If the perennial
draught exceeds the amount the storms give to its replen-
ishment, it will surely cease, in time, to yield the surplus.
Coarse sands will, when fully exposed, absorb the
greater portion of the showers, but such sands are usually
covered with more or less vegetable soil, except in regions
where showers seldom fall.
Fissured limestones and chalks will also absorb a large
portion of the storms, if exposed, but they are rarely en-
tirely uncovered except upon steep cliff faces, where there
110 .SPRINGS AND WELLS.
is little opportunity for the storms that drive against them
to secure lodgement.
95. Evaporation from Soils. Vegetable and surface
soils that do not permit free percolation of their waters
downward to a depth of at least three feet, lose a part of
it by evaporation. On the other hand, evaporation opens
the surface pores of close soils, so that they receive a por-
tion of the rain freely.
96. Supplying Capacity of Wells and Springs.
Percolation in ordinary soils takes place in greatest part
in the early spring and late autumn months, and to a lim-
ited extent in the hot months. In cold climates it ceases
almost entirely when the earth is encased with frost.
Permanent subterranean well or spring supplies receive
rarely more than a very small share of their yearly replen-
ishment between each May and October, their continuous
flow being dependent upon adequate subterranean storage.
Such storage may be due to collections in broad basins,
to collections in numerous fissures in the rocks, or to very
gradual flow long distances through a porous stratum where
it is subject to all the limiting effects of retardation included
under the general term, friction.
In the latter case a great volume of earth is saturated,
and a great volume of water is in course of transmission,
and the flow continues but slightly diminished until after
a drought upon the surface is over and the parched surface
soils are again saturated and filling the interstices of perco-
lation anew.
For an approximate computation of the volume of per-
colation into one square mile of porous gathering area,
covered with the ordinary superficial layer of vegetable soil,
and under usual favorable conditions generally, let us
assume that the mean annual rainfall is 40 inches in depth,
SUPPLYING CAPACITY OF WELLS AND SPRINGS. Ill
and that in the seasons of droughts, or the so-called dry
years, 60 per cent, of the mean monthly percolation will
take place.
TABLE No. 31.
PERCOLATION OF RAIN INTO ONE SQUARE MILE OF POROUS SOIL.
Assumed Mean Annual Rain 40 Inches Depth.
d
H
> >
j
.796
2.653
.40
1.061
637
5
9*736
i
Q,
<1
1.462
4-873
.055
.268
,i6 7
I
CO
2,552
1
l-
.964
3.213
.02
.06 4
.038
1
8
581
j>,
"5
H- i
1.077
3-59
.01
.036
.022
O
5>
336
1
1.251
4.170
.005
.021
.013
199
! s
>
O
fe
o
Q
Ratios of T \ of mean
annual rain
Inches of rain each
737
2.457
SO
1.228
737
1
cT
t*.
11,264
1.070
3-567
45
1.605
963
1
t**
1
14,719
.814
2.713
15
.407
.244
3.729
1.015
3-383
.01
034
.020
305
x.076
3-587
.20
.717
430
6,572
937
3-123
50
1.561
937
%
f
14,321
.801
2.670
.70
1.869
1. 121
s
1
eT
I7,i33
Ratios of Percolation. . .
Mean inches of Rain
Percolating
Sixty per cent, of do. in
dry years
Volume of Percola-J ^
tion in dry years. 1 .
[*
No. of persons it would
supply at 5 cu. ft. each
daily
From springs, with the aid of capacious storage reser-
voirs, it might be possible to utilize fifty per cent, of the
above volume of percolation. From wells, it would rarely
be possible to utilize more than from ten to twenty per cent,
of the volume.
Fifty per cent, of the above total estimated volume of
percolation would be equivalent to a continuous supply of
5 cubic feet per day each, to 3391 persons, or 126,823 gal-
lons per diem ; and ten per cent, of the same volume would
be equivalent to a like supply (37.4 gals, daily) to 678
persons, or 25,357 gallons per diem.
Wells sunk in a great sandy plain bordering upon the
ocean, or bordered by a dyke of impervious material, would
give greater and more favorable results, for in such case the
conditions of subterranean storage would be most favorable,
but such are exceptional cases.
CHAPTEK VIII.
IMPURITIES OF WATER.
97. The Composition of Water. If a quantity of
pure water is separated, chemically, the constituent parts
will be two in number, one of which weighing pne^iinth as
much as the whole will be hydrogen, and the other part
oxygen ; or if the parts of the same quantity be designated
by volume, two parts will be hydrogen and one part oxygen.
These two gases, in just these proportions, had entered
simultaneously into a wondrous union, the mystery of
which the human mind has not yet fathomed. In fact,
many years of intense intellectual labor of such profound
investigators as Cavendish, Lemery, Lavoisier, V olta, Hum-
boldt, Gray Lussac, and Dumas were consumed before the
discovery of the proportions of the two gases that were
capable of entering into this mystic union.
98. Solutions in Water. If two volumes of oxygen
are presented to two volumes of hydrogen, one only of the
oxygen volumes will be capable of entering the union, and
the other can only be diffused through the compound, water.
When alcohol is poured into water it does not become
a part of the water, but is diffused through it.
This we are assured of, since by an ingenious operation
we are able to syphon the alcohol out of the water by a
method entirely mechanical. If we put some sugar, or
alum, or carbonate of soda into water, the water will cause
the crystals to separate and be diffused throughout the
liquid, but they will not be a part of the water. The water
PROPERTIES OF WATER. 113
might be evaporated away, when the sugar, or alum, or
soda would have returned to its crystalline state. In these
cases, the surplus hydrogen, the alcohol, and the constitu-
ents of the crystalline ingredient are diffused through the
water as impurities.
If in a running brook a lump of rock salt is placed, the
current will flow around it, and the water attack it, and will
dissolve some of its particles, and they will be diffused
through the whole stream below. A like effect results when
a streamlet flows across a vein of salt in the earth. In like
manner, if water meets in its passage over or through the
earth, magnesium, potassium, aluminium, iron, arsenic, or
other of the metallic elements, it dissolves a part of them,
and they are diffused through it as impurities. In like
manner, if water in its passage through the air, as in
showers, meets nitrogen, carbonic acid, or other gases,
they are absorbed and are diffused through it as impurities.
99. Properties of Water. Both oxygen gas and
hydrogen gas, when pure, are colorless, and have neither
taste nor smell. Water, a result of their combination, when
pure, is transparent, tasteless, inodorous, and colorless,
except when seen in considerable depth.
The solvent powers of water exceed those of any other
liquid known to chemists, and it has an extensive range of
affinities. This is why it is almost impossible to secure
water free from impurities, and why almost every substance
in nature enters into solution in water. There is a property
in water capable of overcoming the cohesive force of the
particles of matter in a great variety of solids and liquids,
and of overcoming the repulsive force in gases. The par-
ticles are then distributed by molecular activities, and the
result is termed solution.
Some substances resist this action of water with a large
114 IMPURITIES OF WATER.
degree of success, though not perfectly, as rock crystals,
various spars and gems, and vitrified mineral substances.
1OO. Physiological Effects of the Impurities of
Water. When we remember that seventy-five per cent, of
our whole body is constituted of the elements of water, that
not less than ninety-five per cent, of our healthy blood, and
not less than eighty per cent, of our food is also of water,
we readily acknowledge the important part it plays in our
very existence.
Water is directly and indirectly the agency that dissolves
our foods and separates them, and the vehicle by which the
appropriate parts are transmitted in the body, one part to
the skin, one to the finger-nail, one to the eye-lash, to the
bones phosphate of lime, to the flesh casein, to the blood
albumen, to the muscles fibrin, etc. When the stomach is
in healthy condition, nature calls for water in just the
required amount through the sensation, thirst. Good
water then regulates the digestive fluids, and repairs the
losses from the watery part of the blood by evaporation
and the actions of the secreting and exhaling organs.
Through the agency of perspiration it assists in the regula-
tion of heat in the body ; it cools a feverish blood ; and it
allays a parching thirst more effectually than can any fer-
mented liquor. Water is not less essential for the regula-
tion of all the organs of motion, of sight, of hearing, and
of reason, than is the invigorating atmosphere that ever sur-
rounds us, to the maintenance of the beating of the heart.
If from a simple plant that may be torn asunder and yet
revive, or a hydra that may be cut across the stomach or
turned wrong side out and still retain its animal functions,
the water is quite dried away; if but for an instant, man,
with his wonderful constructive ability, and reason almost
MINERAL IMPURITIES. 115
divine, cannot restore that water so as to return the activity
of life and the power of reproduction.
The human stomach and constitution become toughened
in time so as to resist obstinately the pernicious effects of
certain of the milder noxious impurities in water, but such
impurities have effect inevitably, though sometimes so grad-
ually that their real influence is not recognized until the
whole constitution has suffered, or perhaps until vigor is
almost destroyed.
Note the effect of a few catnip leaves thrown into drink-
ing water, which will act through the water upon the nerves ;
or an excess of magnesia in the water will neutralize the free
acids in the stomach, or lead in the water will act upon the
gums and certain joints in the limbs, or alcohol will act
upon the brain ; and so various vegetable and mineral solu-
tions act upon various parts of the body.
It would be fortunate if the pernicious impurities in
water affected only matured constitutions, but they act with
most deplorable effect in the helplessness of youth and even
before the youth has reached the light. These impurities
silently but steadily derange the digestive organs, destroy
the healthy tone of the system, and bring the living tissues
into a condition peculiarly predisposed to attack by malig-
nant disease.
* 1O1. Mineral Impurities. The purest natural waters
found upon the earth are usually those that have come
down in natural streams from granite hills ; but if a thou-
sand of such streams are carefully analyzed, not one of them
will be found to be wholly free from some admixture. This
indicates that in the economy of nature it has not been
ordained to be best for man to receive water in the state
chemically called pure. A United States gallon of water
weighs sixty thousand grains nearly. Such waters as phy-
116 IMPURITIES OF WATER.
sicians usually pronounce good potable waters have from
one to eight of these grains weight, in each gallon, of certain
impurities diffused through them. These impurities are
usually marshalled into two general classes, the one derived
more immediately from minerals, the other derived directly
' or indirectly from living organisms. The first are termed
mineral impurities, and the other organic impurities.
The mineral impurities may be resolved by the chemist
into their original elementary forms, and they are usually
found to be one or more of the most generally distributed
metallic elements, as calcium, magnesium, iron, sodium,
potassium, etc. If as extracted they are found united with
carbonic acid, they are in this condition termed carbonates ;
if with sulphuric acid, sulphates ; if with silicic acid, sili-
cates ; if with nitric acid, nitrates ; if with phosphoric acid,
phosphates, etc. ; if one of these elements is formed into a
compound with chlorine, it is termed a chloride; if with
bromine, it is termed a bromide, etc. A few metallic ele-
ments may thus be reported, in different analyses, under a
great variety of conditions.
1O2. Organic Impurities. There are a few elements
that united form organic matter, as carbon, oxygen, hydro-
gen, nitrogen, sulphur, phosphorus, potassium, calcium,
sodium, silicon, manganese, magnesium, chlorine, iron, and
fluorine. Certain of these enter into each organized body,
and their mode of union therein yet remains sealed in mys-
tery. In the results we recognize all animated creations,
'from the lowest order of plants to the most perfect quadru-
peds and the human species. All organic bodies may,
however, upon the extinction of their vitality, be decom-
posed by heat in the presence of oxygen, and by fermenta-
tion and putrefaction.
The metallic elements are, in the impurities of good
ANALYSES OF POTABLE WATERS.
117
potable waters, usually much, in excess of the organic ele-
ments, but the contained nitrogenized organic impurities
indicate contaminations likely to be much more harmful to
the constitution, and especially if they are products of ani-
mal decompositions.
1O3. Tables of Analyses of Potable Waters. We
will quote here several analyses of running and quiet waters
that have been used, or were proposed for public water
supplies, indicating such impurities as are most ordinarily
detected by chemists in water. For condensation and for
convenience of comparison they are arranged in tabular
form.
TABLE No. 32.
ANALYSIS OF VARIOUS LAKE, SPRING, AND WELL WATERS.
1 Jamaica Pond, near
Brooklyn, L. I.
Flax Pond, near
Lynn, Mass.
Sluice Pond, near
Lynn, Mass.
Breeds Pond, near
Lynn, Mass.
Reeds' Lake, near
Grand Rapids, Mich.
Lake Konomac, near
New London, Conn.
Loch Katrine, near
Glasgow, Scotland.
1
a
It
wU
Well at Highgate,
England.
Artesian Well, at
Hatton, ( England.
4
i";
Jig
<5J3
6
5.420
I.IOI
5.921
Carbonate of Lime
Magnesia .
" Soda
1.092
.408
.700
.692
.400
.320
.600
.612
4.65
1-13
.096
*.'ai6
12.583
11.658
1.768
734
12.677
Protocarbonate of Iron. .
'Chloride of Sodium
" Magnesia . . .
Calcium. ...
Potassium
244
328
1 20
.612
.408
54
....
2.18
trace
....
9-556
8.032
7-745
3-553
4-930
....
1.62
Sulphate of Lime
" Magnesia...
Potash
" Potassa. . .
Soda
I2O
288
.300
'.'064
.300
.070
.270
.050
....
1.29
:$
12.775
....
3-798
14.217
trace
2.160
4.811
trace
'.880
5 662
.080
.086
8.776
7-935
8.719
trace
Phosphate of Lime
trace
Nitrate of Lime
" Magnesia. .
33-457
Oxide of Iron
Ammonia
.044
.840
trace
.096
85
035
trace
14.231
559
"Silica
'Organic Matter
.008
2.652
.156
2.208
.144
i-344
.120
2.184
5-3I6
&
3S
.170
.900
2.244
.200
3-4*9
747
.042
Total Solids
Soluble Organic Matter.
Hardness, Degrees by
Clark's Scale
5-652
3.072
17.750
7-831
64.629
83-549
35-685
27-323
392
o 80
118
IMPURITIES OF WATER.
TABLE
ANALYSIS OF VARIOUS
The quantities are expressed in
grains per U. S. Gallon of 231 cubic
inches, or 58,372 j 1 ^ grains.
Hudson River, above
Albany, N. Y.
Hudson River, above
Poughkeepsie, N. Y.
Connecticut River,
above Holyoke, Mass.
Connecticut River,
above Springfield, Mass.
Schuylkill River, above
Philadelphia, Pa.
Croton River, above
Croton Dam, N. Y.
<a>
JS&
ii
feS
&M
*0
o>*
il
o^;
Saugus River, near
Lynn, Mass.
Carbonate of Lime
1.050
8*
.00
1.56
2 67
" Magnesia
rfi
60
84.
" Soda
2.126
361
108
676
'
.QQ
.juj
86
" Potassium
.070
83
" and Sodium
080
156
jcg
280
" Magnesia
" Potash
028
" Potassa
" Soda
2.785
.48
Silicate of Potassa
" Soda
Oxide of Iron
jr6
.168
trace
Iron Alumina and Phosphates
Ammonia . t ... ....
Silica
408
62
A.6
Organic Matter ....
,4<jo
6qo
.776
I 728
T 'So
67
2 880
Total Solids ...
2 68n
6 624
Soluble Organic Matter
Solid residue obtained on evaporation
Free Carbonic Acid . . ....
Hardness, Degree by Clarke's Scale. ..
3'35
43
5 1
* Notwithstanding the exceeding importance of an intelligent microscopi-
cal examination of each proposed domestic water supply, in addition to the
chemical analysis, no record of such examination is found accompanying the
reports upon the waters herein enumerated. Lenses of the highest microscop-
ical powers should be used for such purpose, and immersion lenses are required
in many instances.
To obtain specimens of sedimentary matters, the sample of water may first
ANALYSIS OF POTABLE WATERS.
No. 33.
RIVER AND BROOK WATERS.*
Chickopee River, near
Springfield, Mass.
Mill River, near
Springfield, Mass.
Grand River, above
Grand Rapids, Mich.
White River, in Filter
Wells on Bank, at
Indianapolis, Md.
Fallkill Greek, near
Poughkeepsie, N. Y.
g tf
en S 4
3
C M
fi
U5
Thames River, above
London, Eng.
Dee River, near
Aberdeen, Scotland.
I
rf
r
<u
Hampstead Water Co/s
Supply, England.
Cowley Brook, near
Preston, Eng.
Loud Scales, Preston',"^
England. x * <N v
Dutton Brook, near
Preston, Eng.
.65
..jo
7-8
10.02
51
6.221
334
I3.X3
.709
6.521
4.128
.575
218
6.131
066
i.343
.217
7
- *
.242
.152
.532
.865
....
4.70
1.20
trace
....
1.56
....
1.442
5.662
938
55
.970
T -38
559
260
.105
.394
026
i 167
287
.150
trace
.150
1.242
12.625
780
.171
.348
.058
trace
trace
i 66
8<u
.167
trace
trace
trace
trace
.12
1.104
trace
3-864
1.37
18.75
5
trace
15
05
trace
275
.417
.27
2.37
....
.417
2.327
.058
1-535
.425
334
.401
4.516
7-339
31.24
20.99
6.74
"459
1.727
20.19
16.496
29.678
3-317
1.167
1-774
1.168
3.912
.785
2"5. "527
30
9.8
1.25
12
I.5O
rest a day in a deep, narrow dish, and then have its clear upper water syphoned
off . The remainder of the water may then be poured into a conical glass, such
as, or similar to, the graduated glasses used by apothecaries, and then again
allowed to rest until the sediment is concentrated, when the greater part of the
clear water may be carefully syphoned off and the sediment gathered and
transferred to a slide, where it should be protected by a thin glass cover.
120
IMPURITIES OF WATER.
TABLE No. 34.
ANALYSIS OF STREAMS IN MASSACHUSETTS.*
(Quantities in Grains per U. S. Gallon.)
SOLID RESIDUE OF
FILTERED WATER.
FREE
AMMONIA.
ALBUMINOID
AMMONIA.
INORGANIC.
ORGANIC AND
VOLATILE.
>j
J
CHLORINE.
Merrimac River Mean of n ex-
aminations above Lowell
0.0027
.0026
.0018
.105
.024
.004
0035
.0030
.0026
.0047
.0027
.0027
.0064
0.0066
.0064
.0074
.015
.012
.008
.0096
.0107
.0115
.0158
.0097
.0158
.0175
1.38
1.41
i-54
1.98
2.62
1.66
2.26
1.63
2.22
1. 80
2.85
1.40
2.10
I .OI
.98
1.05
1.98
i-75
.21
.07
50
31
.42
59
.98
77
2-39
2.39
2-59
3-96
4-37
2.87
3-33
4-13
3-53
3.22
4.44
3.38
3-87
0.08
.12
.11
50
37
.21
23
23
.18
.20
.26
.29
30
Merrimac River Mean of 12 ex-
aminations above Lawrence
Merrimac River Mean of n ex-
aminations below Lawrence
Blackstone River, near Quinsig-
amund Iron \Vorks .
Blackstone River, just above Mill-
bury. . ..
Blackstone River, below Black-
Charles River at \Valtharn .
Sudbury River, above Ashland. . . .
Sudbury River ajt Concord
Concord River at Concord
Concord River at Lowell
Neponset River, at Readville .
Neponset River, below Hyde Park.
1O4. Ratios of Standard Gallons. A portion of
above analyses were found with their quantities of im-
purities expressed in grains per imperial gallon, a British
standard measure containing 70,000 grains, and some of
them expressed in parts per 100,000 parts. They have all
been, as have those following, reduced to grains in a U. S.
standard gallon, containing 58372.175 grains.
The degrees of hardness are expressed by Clark's scale,
which refers to the imperial gallon.
* Selected from the Fifth Annual Report of the Mass. State Board of
Health.
ANALYSES OF WELL WATERS.
121
The other quantities may be easily reduced to equiva-
lents for imperial gallons, by aid of logarithms of the quan-
tities or of the ratios :
Imperial gallon No. of grains 70000 Logarithm, 4.845098
U. S. gallon No. of grains 58372. 175 "
Ratio of imp. to U. S. gallon 1. 199201 "
" of U. S. to imperial gallon 833886
" of cubic foot to one imp. gallon. . . 6.23210
" " " " " " U. S. " . . 7-48052
" " one imp. gall, to one cu. ft 16046 "
" " " U.S. " " " " " 13368
The following analyses of various well waters are in a
more condensed form :
TABLE No. 33.
ANALYSES OF WATER SUPPLIES FROM DOMESTIC WELLS.
(Quantities in Grains per U. S. Gallons.)
4. 766206
0.078892
1.921108
0.794634
0.873932
1.205367
WELLS.
MINERAL
MATTERS.
ORGANIC
MATTERS.
j
<a
od
Hcfi
HARDNESS,
CLARK'S
SCALE.
65 20
Lydius Street
IQ 24
48.60
50.00
Tremont Street
26 60
56 80
average of three
44 46
Old Artesian
CA ae
I 8c
c e 20
Brookline Mass . .
Q 80
4 08
TT Q7
Brooklyn L I i . ..
AC AQ
" average of several
48.8^
Cliarlestown Mass
26 4O
TO.OI
2.41
12 42
D p troit Mich
116 46
Dayton Ohio .
e6 co
Dedham Mass Driven Pipe
512
I 12
6 24
" " Artesian ....
4 08
I II
C IQ
Fall River, Mass., average of seventeen..
25.16
7.00
32.16
IQ-33
12 17
8 30
No 2
^2. l6
1*2 A A
No. 3
37. 10
No 4. .
4^.6o
IO ^^
" " No. *..,
6q.oc
iq 22
122
IMPURITIES OF WATER.
ANALYSES OF WATER SUPPLIES FROM DOMESTIC WELLS (Continued).
WELLS.
MINERAL
MATTERS.
ORGANIC
MATTERS.
P
II
HARDNESS,
CLARK'S
SCALE.
60 oo
3.Q. 3.-3
{
71
London Eng Leadenhall Street
QO.38
9CQ
QO O7
" " St. Paul's Churchyard
62 ^4.
Lambeth "
8-3 OQ
o^oy
74. 08
Manhattan, N. Y
104 oo
" average of several
4Q .OO
New Haven Conn average of five .
2O 32
New York west of Central Park. . .
38 QC
4 ^Q
AO. C.A
average of several
58 oo
Newark, N. J., average of several
IQ.^6
Providence R. I., average of twenty-four.
" " purest of "
" foulest of
Portland Me average of four
24.05
7.76
56.99
I" 7 , 3^
8.82
3-35
24.12
5 IT
33.02
II. II
81.11
1 8 48
1C
?
22
87
70
26
Pawtucket R I .
2Q l6
3.o / 3,
^2 IQ
y* xw
25. 08
2.7-3
28 81
18 68
362
22 3O
Paris France Artesian
9 86
Rochester, N. Y., average of several
30 oo
Rye Beach, N. H
6.08
2.43
8.<u
Springfield Mass
7 82
2 O^
o 8^
8.81
2.OI
10 82
ii ^3
I.QI
13 44.
K
14 8l
3 08
17 QI
Schenectady N Y State Street ....
46 88
2. -3-3
4Q 21
Taunton Mass
2O 14,
2.Q8
23 12
20 86
4OQ
4."3. O 1 ^
Wallham
7 68
4 08
II 76
Pump
17. 7Q
7 4.6
2C 2Z
Winchester,
4..OO
2.40
6. 40
M
8 OO
2 j.o
10 40
10 80
2.O4.
13 2O
ci C2
4.6o
c6. 12
1O5. Atmospheric Impurities. The constant disin-
tegration of mineral matters and the constant dissolutions
of organic matters, and their disseminations in the at-
mosphere, offer to falling rains ever-present sources of ad-
mixture, finely comminuted till just on the verge of trans-
formation into their original elements. The force of the
winds, the movements of animals, the actions of machines,
SUB-SURFACE IMPURITIES.
are every moment producing friction and rubbing off minute
particles of rocks and woods and textile fabrics. Decaying
organisms, breaking into fibre, are caught "up and wafted
and distributed hither and thither.
The atmosphere is thus burdened with a mass of lifeless
particles pulverized to transparency.
A ray of strong light thrown through the atmosphere in
the night, or in a dark room, reveals by reflection this sea of
matter that vision passes through in the light of noon-day.
These matters the mists and the showers absorb, and dis-
solve in solution.
The respirations of all animate beings, the combustions
of all hearth-stones and furnaces, and the decaying dead
animals and vegetables, continually evolve acid and sul-
phurous gases into the atmosphere. Chief among the del-
eterious gases arising from decompositions are carbonic
acid, nitrous and nitric acids, chlorine, and ammonia.
These are all soluble in water, and the mists and showers
absorb them freely. Ehrenberg states that, exclusive of
inorganic substances, he has detected three hundred and
twenty species of organic forms in the dust of the winds.
Hence the so-called pure waters of heaven are fouled, before
they reach the earth, with the solids and gases of earth.
1O6. Sub-surface Impurities. The waters that flow
over or through the crevices of the granites, gneisses, ser-
pentines, trappeans, and mica slates, or the silicious sand-
stones, or over the earths resulting from their disintegrations,
are not usually impregnated with them to a harmful extent,
they being nearly insoluble in pure water.
The limestones and chalks often impart qualities objec-
tionable in potable waters, and troublesome in the house-
hold uses and in processes of art and manufacture.
The drift formation, wherever it extends, if unpolluted
124 IMPURITIES OF WATER.
by organic remains upon or in its surface soil, usually sup-
plies a wholesome water.
The presence of carbonic acid in water adds materially
to its solvent power upon many ingredients of the soil that
are often present in the drift, such as sulphate of lime,
chloride of sodium, and magnesian salts, and upon organic
matters of the surface.
Carbonic acid in rain-water that soaks through foul sur-
face soils, gives the water power to carry down to the wells
a superabundance of impurities.
The presence of ammonia is a quite sure indication of
recent contamination with decaying organic matter capable
of yielding ammonia, whether in spring, stream, or well.
This readily oxidizes, and is thus converted into nitrous
acid and by longer exposure into nitric acid.
These acids combine freely with a lime base, as nitrate
and nitrite of lime.
Analysts attach great importance to the nature of the
nitrates and nitrites present, as indications of the nature of
the contaminations of the water.
Some of the subterranean waters penetrate occasional
strata that wholly unfit them for domestic use. A portion
of the carboniferous rocks are composed so largely of min-
eral salts that their waters partake of the nature of brine, as
in parts of Ohio ; in the Kanawha Valley, West Virginia ;
and in parts of New York State ; for instance, at Syracuse,
where the manufacture of salt from sub-surface water has
assumed great commercial importance. In other sections,
the bituminous limestones are saturated with coal-oils, as in
the famous oil regions of Pennsylvania. The dark waters
from the sulphurous strata of the Niagara group of the
Ontario geological division are frequently impregnated with
sulphuretted hydrogen.
HARDENING IMPURITIES. 125
All along the western flank of the Appalachian chain,
from St. Albans and Saratoga on the north to the White
Sulphur Springs on the south, the frequent mineral springs
give evidence of the saline sub-structure of the lands, while
like evidences have recently become conspicuous in certain
portions of Kentucky, Arizona, New Mexico, Utah, Califor-
nia, and Oregon.
107. Deep-well Impurities. Deep well and spring
waters, except those from dipping sand or sandstone strata,
are especially liable to impregnations of mineral salts.
These impurities from deep and hidden sources, when
present in quantities that will be harmful to the animal
constitution, are almost invariably perceptible to the taste,
and are rejected instinctively.
108. Hardening Impurities. The solutions of salts
of lime and magnesia are among the chief causes of the
quality called hardness in water. Their carbonates are
broken up by boiling, for the heat dissipates the carbonic
acid, when the insoluble bases are deposited, and, with such
other insoluble matters as are present, form incrustations
such as are seen in tea-kettles and boilers where hard waters
have been heated. The carbonates, in moderate quantities,
are less troublesome to human constitutions than to steam
users. The effects of the carbonates are termed temporary
hardness. The sulphates, chlorides, and nitrates of lime
and magnesia are not dissipated by ordinary boiling.
Their effects are therefore termed permanent hardness.
An imperial gallon of pure water can take up but about
two grains of carbonate of lime, when it is said to have two
degrees of hardness ; but the presence of carbonic acid in
the water will enable the same 70,000 grains of water to dis-
solve twelve, sixteen, or even twenty grains of the carbonate,
when it will have twelve, sixteen, or twenty degrees of
126 IMPURITIES OF WATER.
hardness, according to the number of grains taken into
solution.
These salts of lime and magnesia, and of iron, in water,
have the property of decomposing an equivalent quantity
of soap, rendering it useless as a detergent; thus, one
degree or grain of the carbonate neutralizes ten grains of
soap ; two degrees, twenty grains of soap ; three degrees,
thirty grains, etc.
This source of waste from foul hard waters, which extends
to the destruction of many valuable food properties, as well
as to destroying soap, is not sufficiently appreciated by the
general public.
It may be safely asserted that a foul hard well water
will destroy from the family that uses it, more value each
year than would be the cost in money of an abundant
supply of water for domestic purposes, from an accessible
public water supply ; and this refers to purchased articles
merely, and not to destruction of human health and energy,
which are beyond price.
1O9. Temperatures of Deep Sub-surface Waters.
Yery deep well and spring waters have, upon their first
issue, too high a temperature for drinking purposes, as from
the artesian wells of the Paris basin, which rise at a tem-
perature of 82 Fah., and as from hot springs, among which,
for illustration, may be mentioned the Sulphur Springs,
Florida, of 70 Fah., the Lebanon Springs, K Y., of 73 F. ;
and, as extremes of high temperature, the famous geysers
of the Yellowstone Valley, at a boiling temperature, and
the large hot spring near the eastern base of the Sierra
Nevadas and Pyramid Lake, whose broad pool has a tem-
perature of 206, and central issue 212. The springs at
Chaudes Aigues, in France, have a temperature of 176,
and the renowned geysers of Iceland, of 212.
DECOMPOSING ORGANIC IMPURITIES.
127
Artesian wells have temperatures for given depths ap-
proximately as follows :
TABLE No. 36.
ARTESIAN WELL TEMPERATURES.
Depth in Feet ....
TOO
500
IOOO
1500
2OOO
2^OO
^ooo
Temperature, deg. Fah
52
59
68
76
85
94
102
11O. Decomposing Organic Impurities. If we re-
solve, chemically, a piece of stone, ore, wood, fruit, a cup
of water, or an amputated animal limb, into their simple
elements within the limits of exact chemical investigation,
we shall find that their varied compositions and proper-
ties are results of combinations, substantially, of the same
few elements ; and that the organic substances that is, such
as are the result of growth under the influence of their own
vitality are composed chiefly of carbon, oxygen, hydrogen,
and nitrogen, with spare proportions of a few metalloids,
as above enumerated. The general order of predominance
of the gases and metalloids is not, however, quite the same
in mineral as in organic matters. But notwithstanding this
apparent similarity of chemical compositions, there is a
quality in organic substances accompanying the vital force,
that makes it as widely different in essential characteristics
from simple mineral compounds as life is from death.
The mysterious properties which accompany only the
vital force do not submit to analyses by human art. They
are known only by their results and their effects.
In the natural decomposition of animal matters, espe-
cially in their stage of putrefaction, their elements are often
in a condition of molecular activity that will not admit of
their being safely brought into contact with the human
123 IMPURITIES OF WATER.
circulation, where they will be liable to induce similar con-
ditions.
Witness the extreme danger to a surgeon who receives
a minute quantity of animal fluid into a sore upon his hand,
when dissecting a dead body, even though the life has been
extinct but one or two days.
The excreta of living animals also passes through a
decomposing transformation, in which stage they cannot
safely be brought into contact with the human circulation,
however finely they may be dissolved in water, when re-
ceived.
The process of decay in dead animal bodies, and of de-
composition of vegetable substances, is quite rapid when
moisture and an abundance of atmospheric air, or available
oxygen in any form, are present, and a warm temperature
promotes the activity of the elements ; hence the same mat-
ter does not long remain in its most objectionable state, but
from the multiplicity of bodies on every hand, a constant
source of pollution may be maintained.
Potable waters, when exposed to those organic matters
in process of rapid decay, meet perhaps their most fatal
sources of natural contamination, that are not readily de-
tected ~by tlie eye and tongue.
111. Vegetable Organic Impurities. Nature around
us swarms with an abundance of both vegetable and ani-
mal Me, in air, in earth, in stream and sea, and therefore
death is constantly on every hand, and its dissolutions
meet the waters wherever they fall or flow. There are
numerous plants, trees, insects, and animals that we recog-
nize day by day, but there are undoubtedly species and
classes more innumerable above and below, that we can dis-
cover only when our vision is aided by magnifying lenses.
Upon the meadow pools and small ponds of the swamps,
VEGETAL ORGANISMS IN WATER-PIPES. 129
species of microscopic fungi, not unlike the mould upon
decaying fruit, though, less luxuriant, are found in abun-
dance by searchers who suspect their presence. To the
general observer they appear as dust upon the water or
give to it a slight appearance of opaqueness.
There are species of fresh-water algse that thrive in
abundance, peculiar to all seasons, and they are said to have
been found in the heated waters of boiling spring basins,
and also in healthy life within an icicle, and they are the last
of life high up on the mountain slopes, near the borders of
eternal snows. Ditches, pools, springs, rivers, lakes, and
dripping grottoes have each their native class. In stagnant
waters abound the oscillatorise of dull-greenish or dark-
purplish or bluish color, forming dense slimy strata, and
the brighter green zygenemas which float or lie entangled
among the water plants.
The desmids abound in the early spring of the year, and
various algse flourish in the autumn. A thrifty fungus of
the genus Noctos frequents the quiet waters of lower New
England and the Middle States.
These plants at their dissolution often impart an oily
appearance, a greenish or brownish color, and a somewhat
offensive smell to the water. The noctos, while in active
growth, forms part of the green scum often seen upon the
surface* of still water. The fishy smell and the color which
they impart to the water in decomposing seems to be largely
due to an essential oil which they give out when breaking up.
113. Vegetal Organisms in Water-Pipes. A
species of confervso has been found growing and multiply-
ing rapidly within water-pipes, having taken root in the
le organic sediment deposited from feeble currents of
i/ter in the dead ends or in the large mains. These micro-
;opic plants, after maturing in abundance, are detached
130 IMPURITIES OF WATER.
by the current, decompose, and impart an appreciable
amount of odor and taste to the water, reduce its transpar-
ency and give a slight tinge of color.
113. Animate Organic Impurities. The waters are
not less pregnant with animate than vegetal life. The mi-
croscope has here extended our knowledge of varieties and
numbers of species also, especially in waters infused with
organic substances.
The tiny infusoria were first discovered in strong vegeta-
ble infusions, hence the name given to them ; but with the
extension of microscopical science, the class has been ex-
tended to include a variety of animate existences, from the
quiet fresh water sponge to the most energetic little creatures
that battle ferociously in a drop of water.
Dr. Grace Calvert has shown* that when albumen from
a new laid egg is introduced in pure distilled water and
exposed to the atmosphere, minute globular bodies soon
appear having independent motion. These he denominated
monads.
Their appearance was earlier in lake water than in dis-
tilled water, and earliest and most abundant in solutions
of largest exposure to the atmosphere.
These monads have diameters of about y^Wo f an
inch ; in their next successive stage, of about 2Tfihnr f an
inch ; and then of about ^TRT f an inch. He denominates
them vibrios in the two last stages. Then they change into
cells, having power to pass over the field of the microscope
rapidly.
The albuminous products of decaying leaves and plants
in water also promote the generation of aquatic life, and
dead animal substances are almost immediately inhabited
by a myriad of creatures.
* Papers read before the Royal Society, London.
AQUATIC ORGANISMS. 131
The discussion upon the question of spontaneous gene-
ration in progress at the opening of our centennial year, is
adding many new and interesting experimental results to
the researches of Pasteur and Schroeder, relating to the
propagation of bacterial life from atmospheric mote germs,
and the agency of germs in the spread of epidemic cSntagia.
Prof. Tyndall and Dr. Bastian, the leading controversialists
in this discussion, are agreed that both vegetable and animal
infusions, if exposed to the summer atmosphere, will, ordi-
narily, abound in bacterial life in about three days.
There are also in the streams and lakes the larger
zoophytes, mollusca, articulata, and Crustacea, some of which
are familiar products of the waters, and also fish in great
variety.
But all of these do not pass through the objectionable
putrefactive stage described above. The weaker classes
are food for the stronger, and the smaller of some classes
food for the larger of the same class. Of the many that
come into being, comparatively few survive till a natural
death terminates their existence, but each devours others
for a substantial part of its own nourishment, and hides,
fights, or retreats to preserve its own existence.
114. Propagation of Aquatic Organisms. A warm
temperature of both air and water are requisite for the abun-
dant propagation of aquatic life. The presence of a consid-
erable amount of either vegetable or animal impurities in
the waters seems also a requisite for the lower grades of life.
How far certain electrical influences in the air and water
itrol the results are not yet determined. Certain it is,
lowever, that the microscopic creatures sometimes swarm
suddenly in abundance in quiet lakes and pools, in a seem-
ingly unaccountable manner, remain in abundance for a
few days, or possibly a few weeks in rare seasons, and then
132 IMPURITIES OF WATER.
as mysteriously disappear. There is a similar appearance
of microscopic plants, when all the natural conditions favor-
able thereto occur simultaneously, but their coming cannot
always be predicted, neither can the time of their disap-
pearance be foretold.
A vf ry brief existence is allotted to a large share of the
minute vegetal and animate aquatic beings we have had in
consideration. Perhaps the greater share of the animate,
count scarce a single circuit of the sun in their whole term ;
others soon pass to a higher stage in their existence, and
are thereafter terrestrial in their habits.
115. Purifying Office of Aquatic Life. One of the
chief offices of the inferior inhabitants of the waters is to
aid in their purification by devouring and assimilating the
dead and decaying organic matters.
The infusorial animalculse are undoubtedly encouraged
in their propagation by the presence of impurities so far as
to be an unmistakable indication of such impurities ; and
they, on the other hand, attack and destroy such impurities
for their own nourishment, when they are devoured, and
their devourers devoured by higher existences, till the last
become food for fish that constitutes a food for man.
This, and this only, is the proper channel through which
the decomposing organic impurities in water should reach
the human stomach, having by Nature's wonderful pro-
cesses of assimilation been first converted into superior
living tissues.
A great variety of fish are daily consumed for our food,
also of mollusca from salt water, as clams, oysters, and mus-
sels, also of Crustacea, as lobsters, crabs, shrimp, etc. ; hence
we infer that the higher orders of fresh water inhabitants are
not harmful while living therein, and are nourishing as food,
if consumed while the influence of their vital force remains.
ABRASION IMPURITIES. 133
The action of oxygen upon organic bodies tends always
powerfully to decomposition, but is counteracted by the
vital force. When the vital force ceases then decomposi-
tion soon begins, and then the body acted upon is unfitted
for the human digestive organs.
116. Intimate Relation between Grade of Organ-
isms and Quality of Water. The grade and character
of the growths in fresh water are almost invariably reliable
tests of the quality of the water, and if the plants be fine-
grained, firm, and delicate in outline, or the fish trim in
form, lithe in motion, and fine in flavor, the water is most
sure to be good.
117. Animate Organisms in Water-Pipes. Nearly
all of the animate aquatic existences must rise frequently
to the water surface to secure their necessary share of at-
mospheric oxygen. If any of them, not having tracheal
gills, or their equivalents, to enable them to breathe a long
time under water, are drawn into the pipes, and are thus
ut off from their supply of oxygen, they soon perish.
Then, if the water is not of low temperature, their decom-
position soon commences, and an offensive gas from their
bodies enters into solution with the water.
118. Abrasion Impurities in Water. The most
prominent sources of the frictional impurities are the banks
of clay and sand bordering upon the running streams, and
the plowed fields of the hillside farms. The movement
of these sedimentary matters in suspension is dependent
largely upon the force of storms and floods, and in the ma-
jority of streams their movement is rapid toward the sea,
where they are massed in foundations of lagoons and islands.
With them are swept away a great bulk of the matured
products of vegetation that annually ripen in the forest, the
field, and upon the banks of the streams.
134 IMPURITIES OF WATER.
119. Agricultural Impurities. It remains now to re-
view in outline the artificial impurities, which are always
to be shunned if known to be present, and are to be sus-
piciously watched for, as secret poisons lurking in the clear
and sparkling water.
These are, it is true, compounds of mineral and organic
matters, similar in many respects to those already con-
sidered.
Nature provides prompt acting remedies for such nox-
ious impurities as she presents to the waters, and the
seasons of most rapid fouling have the most abundant
purifying resources. But when great bulks of decompos-
ing organic matters are massed and are permitted to foul
the streams with a blackening flow of disease-inducing
dregs, such as are washed from fertile gardens, or pour
from manufactories and sewers, no adequate, prompt, na-
tural remedy is at hand.
One of the first results of the massing of people together
is an increase in degree of fertilization of the land of their
neighborhood, and thus the lands over and through which
their waters flow are mixed with concentrated decomposing
vegetable and animal products.
2O. Manufacturing Impurities. Manufactories,
especially such as deal with organic products, are prolific
sources of contamination. Among their operations and
refuse may be enumerated as prominent polluters, washings
of wool and vegetable dyes of woollen mills, washing of old
rags and foul linens of paper-mills, the hair, scrapings,
bark, and liquors of tanneries, the refuse and liquors of
glue factories, bone-boiling and soap-works, pork render-
ing and packing establishments, slaughter-houses and gas-
works.
121. Sewage Impurities. Most foul and fearful of all
IMPURE ICE IN DRINKING WATER. 135
the artificial pollutions which ignorant and careless human-
ity permits to reach the streams are the drainage of cesspools,
sewers, pig-styes, and stable-yards.
The man who permits his family to use waters impreg-
nated with fecal substances that the bodies of other persons
or animals have already excreted, and the authorities who
permit their citizens to use such waters, opens for them
freely the gates to aches and pains, weaknesses of body and
mind, injuries of tissues and blood, attacks of chronic dis-
eases and epidemics, and surely permits destruction of
their vigor, shortens their average life, and also degenerates
the entire existence of the generation they are rearing to
succeed them, whom it is their duty as well as pleasure to
cherish and protect.
There is no community, there are very few families, and
comparatively few animals without disease. In large com-
munities there is rarely a time when some virulent disease
does not exist.
The products of the humors and fevers of each individual
in large part escapes from the body in the feces and urine.
If drinking water is allowed to absorb these festering mat-
ters, either in the ground or in the stream, it transmits them
directly to the blood and tissues of other individuals, and a
hundred deaths may result from the evacuations of a single
diseased person.
122. Impure Ice in Drinking Water. Ice is now
so generally used in drinking-water in summer, to cool it
immediately before drinking, that the people should be
warned against such use of ice gathered from water that
would have been unfit for drinking before freezing. Chem-
istry has fully demonstrated that ice is not entirely purified
by the process of crystallization, as has been popularly
believed.
136
IMPURITIES OF WATER.
The impurities that are in that portion of water that
freezes, some of which have just been brought from the
bottom by the vertical circulation that occurs when water
is chilled at the surface, are caught among the crystals and
preserved there, as even fresh meats, and fruits might be
preserved. The process of purification of the water that
would have gone on by the oxidation of the impurities, is
checked when they are surrounded by the ice crystals, and
proceeds again when the ice melts.
An instance, of much notoriety, of the effects of impure
ice, was that of the sickness among the numerous guests,
during the season of 1875, at one of the Rye Beach hotels,
a popular resort on the New Hampshire coast.
The sickness here, confined to one hotel in the early part
of the season, was, after much search by an expert physi-
cian, traced unmistakably to the ice, which was gathered
from a small stagnant pond, and all the peculiar unplea-
sant symptoms ceased when the source was located and a
purer supply of ice obtained.
An analysis of the impure ice in question, by Professor
W. R. Mchols, gave the following result, by the side of
which is placed a like analysis of water from Cochituate
Lake, for the purpose of comparison :
ICE FROM STAGNANT
POND.
WATER FROM
COCHITUATE
LAKE.
GRAINS PER U. S. GAL.
GRAINS PER
U. S. GAL.
Ammonia
Unfiltered.
O.OI2I
0.0410
4-55
3-33
Filtered.
O.OI24
.0096
4.01
1.66
0.0020
0.0068
1.61
1.22
Total solid residue at 212 Fahrenheit. .
Chlorine
7.88
5-67
1.88
0-495
2.8 3
.18
Oxygen required to oxidize organic matter.
DEFINITION OF POLLUTED WATER. 137
123. A Scientific Definition of Polluted Water.
Subject, as the sensitive water is, to innumerable deteriora-
ting and purifying influences, in its transformations and
varied course from the atmosphere to the household foun-
tain, it becomes of the greatest sanitary importance to know
when the deteriorating influences still predominate, and when
further purification is essential for the well being of the
consumers.
Professor Frankland, an eminent English authority on
the quality of drinking water, has clearly defined a mini-
mum limit, when, in his opinion, water contains sufficient
mechanical or chemical impurities, in suspension or solu-
tion, to entitle it to be considered bad, or a polluted
liquid, viz. :
(a.) Every liquid which has not been submitted to pre-
cipitation produced by a perfect repose in reservoirs of suf-
ficient dimensions during a period of at least six hours ; or
which, having been submitted to precipitation, contains in
suspension more than one part by weight of dry organic
matter in 100,000 parts of liquid ; or which, not having been
submitted to precipitation, contains in suspension more
than 3 parts by weight of dry mineral matter, or 1 part by
weight of dry organic matter, in 100,000 parts of liquid.
(.) Every liquid containing in solution more than 2
parts by weight of organic carbon or 3 parts of organic
nitrogen in 100,000 parts of liquid.
(c.) Every liquid which, when placed in a white porce-
lain vessel to the depth of one inch, exhibits under daylight
a distinct color.
(d.) Every liquid which contains in solution, in every
100,000 parts by weight, more than 2> parts of any metal,
except calcium, magnesium, potassium, and sodium.
(e.) Every liquid which in every 100,000 parts by weight
138 IMPURITIES OF WATER.
4 contains in solution, suspension, chemical combination, or
otherwise, more than 0.5 of metallic arsenic.
(/.) Every liquid which, after the addition of sulphuric
acid, contains in every 100,000 parts by weight more than
1 part of free chlorine.
(g.) Every liquid which, in every 100,000 parts by
weight, contains more than 1 part of sulphur, in the state
of sulphuretted hydrogen or of a soluble sulphuret.
(k.) Every liquid having an acidity superior to that pro-
duced by adding 2 parts by weight of hydrochloric acid to
1,000 parts of distilled water.
(i.) Every liquid having an alkalinity greater than that
produced by adding 1 part by weight of caustic soda to
1,000 parts of distilled water.
(/.). Every liquid exhibiting on its surface a film of
petroleum or hydrocarbon, or containing in suspension in
100,000 parts, more than 0.5 of such oils.
PUMPING STATION, NEW BEDFORD.
CHAPTER IX.
WELL, SPRING, LAKE, AND RIVER SUPPLIES.
It remains now to add to these general theories respect-
ing the purity of water some special suggestions relating to
the selection of a potable water.
WELL WATER.
124. Location for Wells. We have seen that the
source of water supply to wells is, immediately, the rain,
and that in the vicinity of dense populations the rain reaches
the surface of the earth, already polluted by the impurities
of the town atmosphere.
In the open country, the water reaches the ground in a
tolerably pure condition, and by judicious selection of a
site for a well, its water may usually be procured of excel-
lent quality. Country wells must, however, be entirely
separated from the drainage of the stable yards, muck
heaps, and house sewerage, and from soakage through
highly fertilized gardens.
In towns, surface soils are continually recipients of
household refuse, manures, and sewer liquors, and of dead
and decaying animal matters.
These have, by abundant examples, been proved to be
the most dangerous of the ordinary contaminations of shal-
low wells.
The strictly mineral impurities, to which all wells are
to some extent subject, are not usually injurious to human
constitutions, though in districts where lime is present in
140 WELL, SPRING, LAKE, AND RIVER SUPPLIES.
the soil in considerable quantity, the resulting hardness is
inconvenient and indirectly expensive.
An intelligent examination of the positions, dip, and
porosity of the earth' s superstrata in the vicinity of a pro-
posed well will be a more infallible guide to its location
where it will yield an unfailing, abundant, and wholesome
supply, than will reliance upon "hazel forks" and " divin-
ing rods," in which the superstitious have evinced faith and
by which they have often been deceived.
125. Fouling of Old Wells. The table of analyses
of well-waters above presented (page 121, et seq.) indicates
that the old wells of towns are among the most impure
sources of domestic water supply.
The continued increase in the hardness of well-water as
the population about them becomes more dense, indicates
that this increase is due to the salts of the dissolved organic
refuse with which the ground in time becomes saturated.
Mr. F. Button, an English analyst, states, that "out of
four hundred and twenty-nine samples of water sent him
from wells in country towns, he was obliged to reject three
hundred and seven as unfit for drinking." Another Eng-
lish chemist states that " much of the well-water he is called
upon to examine proves to be more fit for fertilizing pur-
poses than for human consumption."
Prof. Chandler, President of the New York City Board
of Health, and Professor of Chemistry in the School of
Mines, Columbia College, remarked : "In many cases, from
the proximity of cesspools and privy vaults, the well-water
becomes contaminated with filtered sewage, matters which,
while they hardly affect the taste or smell of the water,
have nevertheless the power to create the niiost deadly dis-
turbances in the persons who use the waters."
Hall's "Journal of Health" remarked that, "in the
HARMLESS IMPREGNATIONS. 141
autumn many wells, which supply families with drinking
and cooking water, get very low and their bottoms are cov-
ered with a iine mud, largely the result of organic decom-
positions, also containing poisonous matters of a very con-
centrated character. The very emanations from this well
mud are capable of causing malignant fevers in a few hours ;
hence many families dependent on well-waters are made
sick during the fall of the year by drinking these impreg-
nated poisons, and introducing them directly into the circu-
lation. Many obscure ailments and 'dumb agues' are
caused in this way."
SPRING WATERS.
126. Harmless Impregnations* The impurities of
spring water are chiefly mineral in character, derived from
the constituents of the earths through which their waters
percolate. Among the most soluble of the earths are mag-
nesium, calcium, potassium, and sodium, and these appear
in spring waters as carbonates, bicarbonates, chlorides,
sulphates, silicates, phosphates, and nitrates, and are usu-
ally accompanied by an oxide of iron and a minute quan-
tity of silica.
The above earths are harmless, and are, in fact, consid-
ered beneficial in drinking waters, when present in moderate
quantities, or not exceeding eight or ten grains per gallon.
Most persons are familiar with the medicinal properties of
the carbonate of magnesia, a mild cathartic, and of its sul-
phate (Epsom salts), a mild purgative, and with the carbon-
ate and nitrate of potassa (pearlash and saltpetre) in the
arts, and with the medicinal properties of the bromide of
potassium, a mild diuretic.
Sodium is more familiarly known as common sea-salt,
and calcium as common lime, of which it is the base, and
142 WELL, SPRING, LAKE, AND RIVER SUPPLIES.
silica as the base of quartz or common sand. Spring waters
are, by their passage through the earth, thoroughly filtered
and relieved of suspended impurities, and therefore appear
as the most clear and sparkling of all natural waters.
In the selection of a spring water, it is to be specially
observed that it is free from impregnation by decaying
organic matters.
127. Mineral Springs. In illustration of the facts
that clearness to the eye is not evidence of purity, or min-
eral impregnation of the most usual character immediately
dangerous to the constitution, we append a few analyses of
well-known mineral spring waters, with quantities of ingre-
dients expressed in grains per U. S. gallon. (See page 143.)
This formidable array of chemical ingredients indi-
cates that the waters have taken into solution the familiar
minerals, magnesia, common salt, lime, iron, potash, sul-
phur, quartz, and clay, and the gases, oxygen, hydrogen,
nitrogen, and carbonic acid.
It is much to be regretted that supplies from good springs
are usually so limited in quantity.
The water supply of Dubuque, Iowa, is obtained from
an adit pierced into the bluff near the city. The operations
of miners working in the bluff were seriously impeded by
water, and they relieved themselves by tunneling in from
the face of the bluff, and thus underdraining the mine. In
so doing, they intercepted numerous percolating streams of
water. This water is now utilized for the supply of the
city.
LAKE WATERS.
128. Favorite Supplies. Fresh water lakes and deep
ponds, whose watersheds have extents equal to at least ten
times their water surfaces, are ordinarily, of all ample
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144 WELL, SPRING, LAKE, AND RIVER SUPPLIES.
sources, least liable to objectionable impregnation in harm-
ful quantity. When such waters have been imprisoned in
their flow, by the uplifting of the rock foundations of the
hills across some resulting valley, or by more recent crowd-
ing by ice-fields of masses of rock and earth debris into a
moraine dam, they are bright and lovely features in their
landscapes, and favorite sources of water-supplies.
The accomplishments of scientific attainments are not
requisite to enable the intelligent populations to discover
in these waters wholesomeness for human draughts and
adaptability to quench thirsts.
When such waters are deep, and have a broad expanse
and bold shores, nature is ever at work with rain and wind
and sunshine, maintaining their natural purity and sparkle.
129. Chief Requisites. The prime requisites in lakes,
when to be used for domestic supplies, are abundant in-
flow and outflow, that will induce a general circulation ;
abundant depth, that will maintain the water cool through
the heats of summer and hinder organic growth ; and a
broad surface, which the wind can press upon, and roll,
and thus stir the water to its greatest depths.
These are features opposed to quietude, shallowness,
and warmth, which we have seen ( 114) to be promoters of
excesses of vegetal and animal life, accompanied by a very
objectionable mass of vegetable decay and animal decom-
position. Fortunately, the shallow waters are offcenest at
the upper ends, opposite to the usual points of draught from
the lake, or in indented bays along the sides, from whence
their vegetal products are least liable to reach the outflow
conduit.
130. Impounding. When supplying lakes have mod-
erate drainage areas in proportion to the total volume of
water required from them, it is then necessary to place the
PLANT GROWTH. 145
draught conduit below their natural surface or to raise
their natural surface Iby a dam at their outlet, to avail of
their storage, thus in a degree changing their condition of
nature into the artificial condition of impounding reser-
voirs.
The theory of volume of supply from given drainage
areas ( 53), and the theory of making available a large
proportion of the rainfall by impounding ( 75), have
already been discussed in their appropriate sections.
Important results, affecting the purity of the water, may
follow from the disturbance of the long-maintained condi-
tions of the shores, analogous to those of the construction
of artificial impounding reservoirs in valleys, by embank-
ments across the outflow streams.
The waves, of natural broad lakes that have but little
rise and fall, have long since removed the soil from large
portions of their shores, leaving them paved with boulders
and pebbles, which the ice, if in northern latitudes, has
crowded into close rip-raps, and the removed soil has been
deposited in the quiet shallow bays.
Upon the paved shores the lack of vegetable mold and
the dash of the waters are obstacles to the growth of vege-
tation.
131. Plant Growth. If, under the new conditions, the
waters are drawn down in the summer, the wave power re-
duced, the shallow bottoms of the bays uncovered, and an
entire shore circuit of vegetable deposit exposed to the hot
sun, a mass of luxuriant vegetation at once springs into ex-
istence upon this uncovered bottom, and the greater its thrift
the more rapid its decay, and the more objectionable its
gaseous emanations that will enter into solution in the water.
Such growths and transformations may continue to re-
>eat themselves through several successive years, and to
146 WELL, SPRING, LAKE, AND RIVER SUPPLIES.
some extent continuously. Under the former conditions of
deeper water the plant life was of less abundance, of less
thrifty growth, and of less rapid decay, and the natural
processes of purification were adequate to maintain the
natural purity of the water.
Stimulated vegetable growths result in quick decay and
the production of vegetable muck, the foulest solid product
of vegetable decompositions in water. Slow decompositions
of vegetable matter in water rarely affect the water to a
noxious degree, and result in the production of a peat de-
posit almost entirely free from deleterious qualities in the
water.
The presence of the fishy or cucumber odor is evidence
that the water, or a considerable portion of it, has been too
warm for stored potable water ; and that there is too much
of shallow margin, or that the storage lake has received too
much of meadow drainage. It is not, as many have sup-
posed, an evidence of dead fish in the reservoir, but an effect
tending to drive the higher orders of the fish more closely
about the springs or inflowing streams.
132. Strata Conditions. The winds assist the ready
escape of the odorous gases when they have risen near to
the surface, and the stratum of water of greatest purity, in
summer, is usually a little below the surface, and would be
at the surface were it not for the microscopic organisms that
exist there, and the floating matters.
The change of density of water with change of tempera-
ture produces a remarkable effect in autumn. Water is at
its greatest density at the temperature just above freezing
(392 Fah.), and when the frosts of autumn chill the surfs
water it is then heavier than the water below, and sinks,
placing the bottom water ; and the vertical circulation, sti]
ring up the whole body, continues until the surface is seaJe<
-
PLANT AND INSECT AGENCIES. 147
by ice, when quiet again reigns at the bottom. This action
stirs up the bottom impurities, and often makes them par-
ticularly offensive in autumn, even more than in mid-
summer.
In the case of new flowage of artificial reservoirs over a
meadow bottom, the live vegetable growth has all to go
through a certain chemical transformation, the influence of
which upon the water is often detectable, for a time, by the
sense of smell. This action in the water may be consider-
ably reduced by first burning thoroughly the whole surface,
and destroying the organic life and properties, leaving only
the mineral ash.
The breaking up of the vegetable fibres, if undestroyed
by fire, and their deposition in the quiet, shallow bays,
encourages the growth of aquatic plants, and, indirectly,
animal life there.
The protection of the shores by high water in winter, and
their exposure by drawing down the water in summer, is
favorable to aquatic growths upon them, as in the above-
mentioned lake examples.
133. Plant and Insect Agencies. In cases of ex-
cessive growths of either or both vegetal and animal life,
their products are liable to be drawn into the outflow con-
duit and the distribution pipes, where their presence becomes
disagreeably evident by the gaseous " fishy" or " cucum-
ber" odors liberated when the water is drawn from
faucets.
When conditions are favorable for the production of
either vegetal or animal life alone, in excessive abundance,
disagreeable effects, especially if the excess be animal, are
almost certain to follow, since both are among the active
agents employed by nature in the purification of water, and
natural laws tend to preserve the due balance in their
148 WELL, SPRING, LAKE, AND RIVER SUPPLIES.
growth, the one being producers of oxygen and the other
of carbon.
Newly flowed collecting or storage reservoirs should be
promptly stocked with a fine grade of fish, that will feed
upon and prevent the overabundance of the Crustacea,
which in turn will consume the organic decompositions, and
prevent their diffusion through the waters.
134. Preservation of Purity. General observation
teaches that neither vegetation or any species of the infu-
soria flourish to an objectionable extent in fresh waters in
the temperate zone where the depth exceeds about ten feet,
though it is true that insects are liable to swarm upon the
surface of all waters that arrive at a high temperature.
Stored waters, for domestic purposes, ought to have in our
American climate, depths of not less than twelve feet.
To insure purity of water, so far as protection from its
own products is concerned, it is necessary that the shallow
waters be cut off by embankments, or that they be deep-
ened, or that their place be supplied by clean sand or
gravel filling, raised to a level above high water. It is fre-
quently advisable, also, that the shores of artificial impound-
ing reservoirs of moderate extent be provided with an
equivalent for the natural rip-rap provided by nature
around natural lakes.
Each of the above expedients has been successfully
adopted by the writer in his own practice.
Fig. 7 is an illustration of the revetment of stone sur-
rounding the reservoir of the Norwich, Conn., water-works.
The reservoir in this case is two and one-half miles out
from the city, and fills the office of both a gathering and
distributing reservoir, for a gravitation supply. Its circum-
ference is two and one-quarter miles, and this revetment
protects the shore of the entire circuit. Its height above
NATURAL CLARIFICATION.
149
FIG. 7.
high water, in the vicinity of the dam, is four feet, and in
the tipper part of the valley three feet.
If the supplying streams of a small lake bring with them
much vegetable matter in suspension, and the flow reaches
the conduit before complete clarification by natural pro-
cesses is effected, some method of artificial filtration of the
water will be necessary, the details of which will be dis-
cussed hereafter.
135. Natural Clarification. The various sources of
chemical impregnation to which waters reaching lakes, usu-
ally are subject, whether flowing over or through the earth,
have been already herein discussed ( 1O1, et seq.\ so that
persons of ordinary intelligence and information may detect
them, and form a tolerably accurate estimate of their harm-
fulness, and if they ought to be considered objectionable
when they are to be gathered in a lake and there subjected
to the processes in Nature's favorite laboratory of purifi-
cation.
Waters flowing in the brooks from the wooded hills and
ie swamps almost always come down to the lakes highly
charged with the coloring matter and substances of forest
leaves and grasses, and not unfrequently have a very per-
150 WELL, SPRING, LAKE AND RIVER SUPPLIES.
ceptible reddish or chocolate hue. The waters are soon
relieved of these vegetable impurities by natural processes
in the lake, and their natural transparency and sparkle is
restored to them. Sunlight has been credited with a strong
influence in the removal of color from water. The chemical
transformation already begun upon the hills is continued in
the lake, and the atmospheric oxygen aids in releasing the
gases of the minutely subdivided vegetable products pro-
ducing the color, when the mineral residues have sufficient
specific gravity to take them speedily to the bottom. The
w T inds are the good physicians that bring the restoring
remedies.
Ponds and lakes often receive a considerable part of
their supply from springs along their borders, whose waters
have received the most perfect natural clarification. Such
springs, from quartzose earths, yield waters of the most
i/ ^ ** * ' "^} \$ ^Lt
desirable qualities.
136. Great Lakes. When lakes, on a scale of great
inland seas, like those lining our northern boundary, upon
which great marts of trade are developing, are at hand,
many of the above supposed conditions belonging to
smaller lakes and ponds, are entirely modified.
In such cases the cities become themselves the worst
polluters of the pure waters lying at their borders, and
they are obliged to push their draught tunnels or pipes
beneath the waters far out under the lakes to where the
water is undefiled.
This system was inaugurated on a great scale by Mr.
E. S. Cheesboro, C.E., for Chicago, and followed by the
cities of Cleveland, Buffalo, and with submerged pipe by
Milwaukee.
137. Dead Lakes. The waters of the Sinks, or Dead
Lakes of the Utah, Nevada, and southern California, Great
METROPOLITAN SUPPLIES.
151
Desert, from which there are no visible outlets, are notable
exceptions to general conditions of lake waters. Here the
salts gathered by the inflowing waters, for centuries, which
evaporating vapors can not carry away, have been accu-
mulating, till the waters are nauseating and repugnant.
The skill of the well-borer must aid civilization when
these desert regions are to become generally inhabitable.
RIVER WATERS.
138. Metropolitan Supplies. Rivers are of necessity
the final resort of a majority of the principal cities of the
world for their public water supply. The volume of water
daily required in a great metropolis often exceeds the com-
bined capacity of all the springs, brooks, and ponds within
accessible limits, and supplies from wells become impos-
sible because of lack of capacity, excessive aggregate cost,
and the sickening character of their waters.
Since rivers occupy the lowest threads of the valleys in
which they flow, their surfaces are lower than the founda-
tions of the habitations and warehouses along their banks.
Their waters have therefore usually to be elevated by
power for delivery in the buildings, the expense of conduct-
ing their waters from their sufficiently elevated sources being
greater far than the capitalized cost of the artificial lift
nearer at hand.
The theories by which the minimum flow of the stream
( 53), and the maximum demand for supply ( 19), are
determined and compared have been already herein dis-
cussed ; so we now assume that the supplies have, after
proper investigation, been determined ample, and also that
the geological structure ( 1O6) of the drainage area is found
to present no impregnating strata precluding the use of its
152 WELL, SPRING, LAKE, AND EIVER SUPPLIES.
waters for domestic and commercial purposes, or in the
chemical arts.
139. Harmless and Beneficial Impregnations.
The natural organic impurities of rivers are seldom other
than dissolving vegetable fibres washed down from forests
and swamps, and these are rarely in objectionable amount ;
and the natural mineral impurities in solution are usually
magnesia, common salt, lime, and iron, and, in suspension,
sand and clay. The lime, sand, and clay are easily detect-
ible if in objectionable amount, and the remaining natural
mineral impregnation are quite likely to be beneficial
rather than otherwise, since they are required in drinking
water to a limited extent to render them palatable, and for
promotion of the healthy activity of the digestive organs,
and the building up of the bones and muscles of our bodies.
140. Pollutions. We reiterate that it is the artificial
impurities that are the bane of our river waters. Manufac-
tories, villages, towns, and cities spring up upon the river-
banks, and their refuse, dead animals, and sewage are
dumped into the running streams, making them foul potions
of putrefaction and destruction, when they should flow clear
and wholesome according to the natural laws of their crea-
tion and preservation.
141. Sanitary Discussions. The prolific discussion
upon the sanitary condition of the water of the river
Thames, England, since the report of the Royal Commis-
sion of 1850, has brought out a variety of conflicting opin-
ions in regard to the efficiency of natural causes to destroy
sewage impurities in water.
About one-half the population of London, or one-half
million persons, received their domestic water supply from
the Thames in 1875. The drainage area above the pump-
ing stations is about 3675 square miles, and the minimum
SANITARY DISCUSSIONS. 153
summer flow is estimated to be about 350,000,000 imperial
gallons daily, and of this flow about 15,000,000 gallons is
pumped daily by the water companies. Upon the Thames
watershed above the pumping stations there resides a popu-
lation of about 1,000,000 persons, including three cities of
over 25,000 persons each, three cities of from 7000 to 10,000
persons each, and many smaller towns and villages. The
whole of the river and its principal tributaries are under
the strictest sanitary regulation which the government is
able to enforce, notwithstanding which a great mass of
sewage is poured into the stream.
Yet it is claimed by eminent authority that the Thames
water a short distance above London is wholesome, pala-
table, and agreeable, and safe for domestic use.
A remark by Dr. H. Letheby, medical officer of health
for the city of London until his decease in the spring of
1876, gives a comprehensive summary of the argument in
favor of the Thames water, viz. : "I have arrivec^at a very
decided conclusion that sewage, when it is mixed with
twenty times its volume of running water and has flowed a
distance of ten or twelve miles, is absolutely destroyed :
the agents of destruction being infusorial animals, aquatic
plants and fish, and chemical oxydation."
Several eminent chemists testify that analyses detect no
trace of the sewage in the Thames near London. Sir Benja-
min Broodie, Professor of Chemistry in the University of
Oxford, remarked in his testimony upon the London water
supply: "I should rely upon the dilution quite as much,
and more, than upon the destruction of the injurious
matter.
Dr. C. F. Chandler, President of the New York Board
of Health, and Professor of Chemistry in the School of
[ines, Columbia College^ has in his own writings quoted
154 WELL, SPRING, LAKE, AND RIVER SUPPLIES.
many eminent authorities,* with apparent indorsement of
their conclusions, supporting the theory of the wholesome-
ness and safety of the Thames water as a domestic supply
for the city of London.
142. Inadmissible Polluting Liquids. The Par-
liamentary Rivers Pollution Committee, when investigating
the subject of the discharge of manufacturing refuse and
sewage into the English rivers, Mersey and Bibble, and the
possibility of the deodorization and cleansing of the refuse
by methods then available, suggested f that liquids con-
taining impurities equal to or in excess of the limiting quan-
tity defined by Prof. Frankland (vide 123, p. 137), be
deemed polluting and inadmissible into any stream.
143. Precautionary Views. On the other hand,
many physicians, chemists, and engineers, whose scientific
attainments give to their opinions great weight, emphatically
protest against the adoption or use of a source of domestic
water supply that is at all subject to contamination by
sewage or putrefying organic matters of any kind.
There are certain laws of nature that have for their
object the preservation of human life to its appointed ma-
turity, which we term instinct, as, for instance, involuntary
grasping at a support to save from a threatened fall ; invol-
untary raising the arm to protect the eye or head from a
blow ; involuntary sudden withdrawal of the body from
contact with a hot substance that would burn. There is also
an instinctive repugnance to receiving any excrementitious
or putrefying animal substance, or anything that the eye or
sense of smell decides to be noxious, upon the tongue or
into the system. It is not safe to overlook or subdue the
natural instincts created within us for our preservation.
* Public Health Papers of American Public Health Association, vol. i.
f First Report. R. P. C., 1868, vol. i, p. 130.
PRECAUTIONARY VIEWS. 155
Following are a few opinions supporting the cautionary
side of the question :
" Except* in rare cases, water which holds in solution a
perceptible proportion of organic matter becomes soon
putrid, and acquires qualities which are deleterious. It is
evident that diarrhoea, dysentery, and other acute or chronic
affections have been induced endemically by the continued
use of water holding organic matter in large proportions,
either in solution or in suspension. It is admitted, as the
result of universal observation, that the less the quantity of
organic matter held by the water we drink, the more whole-
some it is."
"Nof one has conclusively shown that it is safe to trust
to dilution, storage, agitation, filtration, or periods of time,
for the complete removal from water of disease-producing
elements, whatever these may be. Chemistry and micro-
scopy cannot and do not claim to prove the absence of these
elements in any specimen of drinking water."
"It:}: is a well- received fact, that decomposing animal
matter in drinking water is a fertile producer of intestinal
diseases."
Dr. Wolf (in Der Untergrund und das Frinkwasser der
Stadte, Erfurt, 1873) gives a large number of cases, which
prove conclusively that "bad water produces diarrhoea,
and can propagate dysentery, typhoid fever, and cholera,
and that such water is frequently clear, fresh, and very
agreeable to the taste."
Dr. Lyon Playfair, of London, remarks : "The effect of
* Boutron and Boudet. Annual of French Waters, 1851.
f Testimony of Dr. R. A. Smith before the Royal Commission of Water
ipply of London.
\ Report of Medical Commission on Additional Water Supply for Boston,
1874.
156 WELL, SPRING, LAKE, AND RIVER SUPPLIES.
organic matter in the water depends very much upon the
character of that organic matter. If it be a mere vegetable
matter, such as comes from a peaty district, even if the
water originally is of a pale sherry color, on being exposed
to the air in reservoirs, or in canals leading from one reser-
voir to another, the vegetable matter gets acted upon by the
air and becomes insoluble, and is chiefly deposited, and
what remains has no influence on health. But where the
organic matter comes from drainage, it is a most formid-
able ingredient in water, and is the one of all others that
ought to be looked upon with apprehension when it is from
the refuse of animal matter, the drainage of large towns,
the drainage of any animals, and especially of human
beings."
The Massachusetts State Board of Health, in their fifth
annual report, remarking upon the joint use of watercourses
for sewers and as sources of water supply for domestic use,
remarks: "We believe that all such joint use is to be
deprecated The importance of this matter is under-
rated for two reasons: first, because of the oft-repeated
assertion, made on the authority of Dr. Letheby, ' that if
sewage-matter be mixed with twenty times its bulk of ordi-
nary river water, and flow a dozen miles, there is not a
particle of that sewage to be discovered by chemical
means ;' secondly, because of the feeling that to be in any
way prejudicial to health, a water must contain enough
animal matter to be recognized readily by chemical tests
enough, in fact, to be expressed in figures." ,
144, Speculative Condition of the Pollution
Question. Sanitary writings have abounded with dis-
cussions of this subject during the last decade ; still, look-
ing broadly over the field of discussion, it is evident that
the leading medical and chemical authorities have not
SPONTANEOUS PURIFICATION. 157
agreed upon the limit for any case, or class of cases, when
water becomes noxious or harmful.
Some of the consumers of the waters of the Thames in
England and of the Mystic and Charles rivers in New Eng-
land, have evinced a remarkable faith in the toughness of
human constitutions.
The whole subject of water contamination remains as
yet rather physiologically speculative than chemically ex-
act. It is earnestly to be desired that the present experi-
mental practice upon human constitutions, so costly in
infantile life, may soon yield a sufficiency of conclusive
statistics, or that science shall soon unveil the subtle and
mysterious chemical properties of organic matters, at least
so far as they are now concealed behind recombinations,
reactions, and test solutions.
145. Spontaneous Purification. The river courses
are the natural drainage channels of the lands, and it can-
not but be expected that a considerable bulk of refuse, from
populous districts, will find its way to the sea by these
channels, however strict the sanitary regulations for the
preservation of the purity of the streams. Therefore it is a
matter of high scientific interest, and in most cases of great
hygienic and national importance, to determine what pro-
portion of the organic refuse is destroyed beyond the possi-
bility of harm to animals that drink the water, by spon-
taneous decomposition, and what proportion remains in
solution and suspension.
In ordinary culinary and chemical processes we find
that temperature has an important influence upon the dis-
solving property of water. Water of temperature below
60 Fah. dissolves meats, vegetables, herbs, sugar, or gum,
slowly, comparatively, and a cold atmosphere does not pro-
mote decomposition of organic matter. We therefore infer
158 WELL, SPRING, LAKE, AND RIVER SUPPLIES.
that a temperature of both atmosphere and water as high,
or nearly as high, as 60 Fah. are required to promote
rapid oxydation of the organic impurities in water. In
winter the process must proceed slowly, and if the stream
is covered by ice, be almost suspended. Agitation of the
water is absolutely essential to the long-maintained pro-
cess of oxydation, in order that the water may continue
charged with the necessary bulk of oxygen in solution ;
therefore weirs across the stream, roughness of the bed and
banks of the stream, and rapidity of flow are essential ele-
ments in rapid oxydation.
Dr. Sheridan Murpratt remarks,* in respect to this spon-
taneous purification of river waters containing organic mat-
ters : "As a general rule, the carbon unites with oxygen to
form carbonic acid ; and with hydrogen to form marsh gas
or carbide of hydrogen ; hydrogen and oxygen unite to
form water ; nitrogen and oxygen with hydrogen to form
ammonia ; sulphur with hydrogen to form sulphide of hy-
drogen ; phosphorus with hydrogen to form phosphide of
hydrogen.
"The latter two are exceedingly o'ffensive to the sense of
smell, and are, moreover, highly poisonous. Thus in the
spontaneous decomposition of the organic matter contained
in water, there are produced carbonic acid, carbide of hy-
drogen, ammonia, sulphide of hydrogen, and phosphide of
hydrogen. These are the recognized compounds ;- but when
it is borne in mind that the gaseous emanations of decom-
posing animal matters are infinitely more offensive to the
sense of smell and injurious to health than any of the gases
above mentioned, or of any combination of them, it can
only be concluded that the effluvia of decaying organic
* Chemistry, Theoretical, Practical, and Analytical : Glasgow.
A SUGAR TEST OF WATER.
159
matter contains other constituents, of which the true char-
tacter has not yet been determined." This chemical puri-
fication is assisted by vegetal absorption and animalculine
consumption.
146. Artificial Clarification. While water subjected
at all to organic, especially drainage or animal impurities,
should be avoided, if possible, for domestic consumption,
it should, on the .other hand, when necessarily submitted
to, be clarified before use, of its solids in suspension, by
precipitation, deposition in storage or settling basins, or by
one of the most thorough processes of filtration.
147. A Sugar Test of the Quality of Water. The
Pharmaceutical Journal quotes Heisch's simple sugar test
for water, as follows :
"Good water should be free from color, unpleasant
odor and taste, and should quickly afford a good lather
with a small proportion of soap.
" If half a pint of the water be placed in a clean; color-
less glass-stoppered bottle, a few grains of the best white
lump-sugar added, and the bottle freely exposed to the day-
light in the window of *a warm room, the liquid should not
become turbid, even after exposure for a week or ten days.
If the water becomes turbid, it is open to grave suspicion
of sewage contamination ; but if it remain clear, it is
almost certainly safe.
STAND-PIPE, BOSTON.
SECTION II.
FLOW OF WATER THROUGH SLUICES, PIPES AND CHANNELS,
CHAPTER X.
WEIGHT, PRESSURE, AND MOTION OF WATER.
148. Special Characteristics of Water. If we con-
sider those qualities of water that have reference to its
weight, its pressure, and its motion, we shall observe, espe-
cially : That the volume of the liquid is composed of an
immense number of minute particles ; that each particle
has weight individually ; that each particle can receive
and transmit the effect of weight, in the form of pressure,
in all directions ; and that the particles mow past and
upon each other with very slight resistance.
We are convinced by the sense of touch that the parti-
cles of a body of water are minute, and have very little
cohesion among themselves or friction upon each other,
when we put our hand into a clear pool and find that the
particles separate without appreciable resistance ; and also
by the sense of sight, when we see fishes and insects, and,
with the aid of the microscope, the tiny infusorise, moving
rapidly through the water, without apparent effort greater
than would be required to move in air.
11
162 WEIGHT, PRESSURE, AND MOTION OF WATER.
149. Atomic Theory. Ancient records of scientific
research inform us that the study of the divisibility and
nature of the particles of matter occupied, long ago, the
most vigorous minds. It is twenty-two centuries since
Democritus explained the atomic theory to his fellow-
citizens, and taught them that particles of matter are capa-
ble of subdivision again and again, many times beyond the
limit perceptible to human senses, but that finally the atom
will be reached, which is indivisible, the unit of matter.
Anaxagoras, the teacher of Socrates, maintained, on the
contrary, that matter is divisible to infinity, and that all
parts of an inorganic body, to infinite subdivision, are simi-
lar to the whole. This latter theory has not been generally
accepted. The whole subject of the nature of matter, in its
various conditions, forms, and stages of progress, has main-
tained its interest through the succeeding centuries, and is
to-day a favorite study of philosophers and theme of dis-
cussion in lecture halls.
150. Molecular Theory. Modern research has dem-
onstrated that the unit of water is composed of at least two
different substances, and therefore is not an atom. The
unit is termed a molecule, and, according to the received
doctrine, the foundation of each molecule of water is two
molecules of hydrogen and one molecule of oxygen. These
latter molecules may possibly be ultimate atoms.
The theory is advanced that each molecule of water is
surrounded by an elastic atmosphere, and by a few that it
is itself slightly elastic.
Sir William Thompson estimated that between five hun-
dred millions and five thousand millions of the molecules
of water may be placed side by side in the space of one
lineal inch. To enable us to detect the outline of one of
these molecules, our most powerful microscope must have
INFLUENCE OF CALORIC. 163
its magnifying power multiplied as many times again, or
squared.
A film of water flowing through an orifice one-hundredth
of an inch deep, or about the thickness of this leaf, would
be, according to the above estimate, from five to fifty mil-
lion molecule diameters in depth. It is impossible to com-
prehend so infinitesimal a magnitude as the diameter of one
of these molecules, so we shall be obliged to imagine them
so many times magnified as to resemble a mass of transpa-
rent balls, like billiard balls, for instance, or similar spheres,
and to consider them while so magnified.
151. Influence of Caloric. There is also a theory,
very generally accepted, that the molecules of water, more
especially their gaseous constituents, are constantly subject
to the influence of caloric, the cause of heat, and are in
consequence in incessant compound motion, both vibratory
and progressive, and that they are constantly moving past
each other, progressing with wavy motion, or are rebound-
ing against each other, and against their retaining vessel.
This motion may be partially illustrated by the motion
of a great number of smooth, transparent, elastic balls, in a
a vessel when the vessel is being shaken. It may be dem-
onstrated by placing a drop of any brilliant colored liquid,
for which water has an affinity, into a vessel of quiet water,
when the drop will be gradually diffused throughout the
whole mass, showing not only that among the molecules of
colored liquid there is activity, but that certain of the mole-
cules before in the vessel plunge into and through the drop
from all sides, dividing it into parts, and its parts again
into other parts, until the particles are distributed through-
out the mass.
While the molecules are arranged in crystalline form,
they require considerably more space than when in liquid
164
WEIGHT, PRESSURE, AND MOTION OF WATER.
form, and there are a less number of them in a cubic inch ;
therefore a cubic inch of ice weighs less than a cubic inch
of water.
152. Relative Densities and Volumes. The rela-
tive changes in weight and volume of water at different
temperatures are shown graphically in Fig. 8. When
FIG. 8.
weight is maintained constant and the temperature of the
water is increased or decreased, the volume will change as
indicated by the solid lines. When volume is maintained
constant and the temperature increased or decreased, the
weight will change as indicated by the dotted lines.
WEIGHT OF WATER.
153. Weight of Constituents of Water. Water is
substantially the result of the union ( 15O) of two volumes
of hydrogen, having a specific gravity equal to 0.0689, and
one volume of oxygen, having a specific gravity equal to
1.102 ; but various other gases that come in contact with
this combination are readily absorbed.
Bulk for bulk, the oxygen is sixteen times heavier than
the hydrogen. Water at its greatest density is about eight
hundred and fifteen times as heavy as atmospheric air.
The density of the vapor or gases enveloping the liquid
molecules is greatest at a temperature of about 39. 2 Fah.
At this temperature the greatest number of molecules is
FORMULA FOR VOLUMES. 165
contained in one cubic inch, and the greatest weight for a
given volume obtains.
As the temperature of water rises from 39. 2, its gaseous
elements expand and are supposed to increase their activity ;
and a less number of molecules can be contained in a cubic
inch, or other given volume ; therefore the weight of water de-
creases as the temperature rises from 39. 2 Fall, (vide Fig. 8.)
154. Crystalline Forms of Water. As the temper-
ature falls below 39.2 Fah., the molecules, under one at-
mosphere of pressure, incline to arrange themselves in
crystalline form, their action is supposed to be more vibra-
tory and less progressive, and they become ice at a temper-
ature of about 32 Fah.
The relative weights and volumes of distilled water at
different temperatures on the Fahrenheit scale are shown
numerically in the table on the following page.
Although there is a slight difference in the results of
experiments of the best investigators in their attempts to
obtain the temperature of water at its maximum density, it
is commonly taken at 39.2 Fah., and the weight of a cubic
foot of water at this temperature as 62.425 pounds, and the
weight of a United States gallon of water at the same tem-
perature as 8.379927 pounds.
155. Formula for Volumes at Different Temper-
atures. The tables of weights and volumes of water is
extended, with intervals of ten degrees, to the extreme limits
within which hydraulic engineers have usually to experi-
ment. The intermediate weights and volumes for inter-
mediate temperatures, may be readily interpolated, or
reference may be had to the following formulas taken from
Watt's "Dictionary of Chemistry," combining the law of
expansion as determined by experiments of Matthiessen,
Sorby, Kopp, and Rossetti.
166
WEIGHT, PRESSURE, AND MOTION OF WATER.
TABLE No. 38.
WEIGHT AND VOLUME OF DISTILLED WATER AT DIFFERENT
TEMPERATURES.
Temperature
Fah.
Weight of a cu.
ft. in pounds.
Difference.
Ratio of volume to
volume of equal wt.
at max. density of
temperature,
39.2 Fah.
Difference.
Ice.
57.200
.916300
32
62.417
5- 2I 7
.000129
.083829
39-2
62.425
.008
.OOOOOO
.000129
40
62.423
.002
.000004
.000004
50
62.409
.014
.000253
.000249
60
62.367
.042
.000929
.000676
70
62.302
.065
.001981
.001052
80
62.218
.084
.00332
.001339
90
62. 119
.099
.00492
.OOl6o
100
62.OOO
.119
.00686
.00194
110
61.867
i33
.00902
.00216
120
61.720
.147
.01143
.00241
130
61.556
.164
.01411
.OO268
o
I4O
61.388
.168
.01690
.00279
15
6 i . 204
.184
.01995
.00305
160
6 i .007
.197
.02324
.00329
170
60.801
.206
.02671
.00347
1 80
60.587
.214
.03033
00362
o
IQO
60.366
.221
,03411
.00378
o
200
60. 136
.230
.03807
.00396
210
59- 8 94
.242
.04226
.00419
212
59-707
.187
.04312
.00086
Let V= ratio of a given volume of distilled water, at the
temperature, T, on Fahrenheit's scale, to the volume of an
equal weight, at the temperature of maximum density.
W= weight of a cubic foot of distilled water, in pounds,
at any temperature, Fahrenheit.
For temperatures 32 to 70 Fah.
V= 1.00012 0.000033914 x (T 32) + 0.000023822 x
(T 32) 2 0.000000006403 (T 32) 3 .
COMPRESSIBILITY AND ELASTICITY OF WATER. 167
For temperatures above 70.
Y = 0.99781 + 0.00006117 x (T - 32) + 0.000001059 x
(T - 32) 2 .
w= 62,425
156. Weight of Pond Water. Fresh pond and
brook waters are slightly heavier than distilled water, and
when not loaded with sediment have, for a given volume,
an increased weight equal to from 0.00005 to 0.0001 of an
equal volume of distilled water.
157. Compressibility and Elasticity of Water.
The compression of rain-water, according to experimental
results of Canton, is 0.000046 and of sea-water 0.000040 of
its volume under the pressure of one atmosphere.
According to experiments of Regnault, water suffers a
diminution of volume amounting to 48 parts in one million,
when submitted to the pressure of one atmosphere, equal to
14.75 pounds per square inch, and to 96 parts when sub-
mitted to twice that pressure.
Grassi found the compressibility of water to be 50 parts
at 37 Fah., and 44 parts at 127 Fah. in each million
parts, with one atmosphere pressure.
A column of water 100 feet high would, according to
these estimates, be compressed nearly one-sixteenth of an
inch.
The degree of elasticity of fluids was discovered by Can-
ton in 1762. He proved that the volume of liquids dimin-
ished slightly in bulk under pressure and proportionally
to the pressure, and recovered their original volume when
the pressure ceased.
This has been confirmed by experiments of Sturm,
(Ersted, Eegnault, and others.
168 WEIGHT, PRESSURE, AND MOTION OF WATER.
PRESSURE OF WATER.
158. Weights of Individual Molecules. If again
we consider the molecules of water magnified, as before ex-
plained, we can conceive that each molecule has its indi-
vidual weight, and is subject, independently, to the force
of gravity. Consider again the film of water of one-hun-
dredth of an inch in depth, flowing through the orifice of
same depth, and imagine the orifice to be magnified also in
the same proportion as the molecules have been imagined
to be magnified, that is, to five million molecule diameters ;
then the immense leverage that gravity has, proportionally,
upon each molecule to set it in motion and to press it out
of the orifice can be conceived, and the reason why there is
apparently so little frictional resistance to the passage of
the molecules over each other will be apparent.
159. Individual Molecular Actions. The magnified
molecule can also be conceived to be acting independently
upon any side of its retaining vessel, or upon any other
molecule, with which it is in contact, with the combined
weight or pressure of all the molecules acting upon it.
In a volume of fluid, each molecule presses in any
direction from which a sufficient resistance is opposed,
with a pressure due to the combined natural pressures of
all molecules acting upon it in that direction, and also
with the pressure transmitted through them from any
exterior force.
In treatises on hydrostatics, propositions relating to
pressures of fluids are commonly stated in some form sim-
ilar to the following :* " When a fluid is pressed by its own
weight, or by any other force, at any point it presses
equally in all directions."
* Vide Button's Mathematics, Hydrostatics, 310.
INDIVIDUAL MOLECULAR REACTIONS.
169
16O. Pressure Proportional to Depth. The pres-
sure of a fluid at any point on an immersed surface, is in
proportion to the vertical depth of that point below the sur-
face of the fluid ; but not in proportion to variable breadths
of the fluid.
In vessels of shapes similar to Fig. 9 and Fig. 10, con-
taining equal vertical depths of water, the pressures on
equal areas of the horizontal bottoms are equal ; also the
pressures on equal and similar areas of their vertical sides,
having their centres of gravity at equal depths, are equal.
FIG. 9.
FIG. 10.
ej
a
CLJ
161. Individual Molecular Keactions. Any parti-
cle of fluid that receives a pressure reacts with a force equal
to tlie pressure, if its motion is resisted upon the opposite side.
Any point of a fixed surface pressed by a particle of
water reacts upon the particle with a force equal to the
pressure of the particle.
The large body of water in the section A of the tank,
Fig. 9, is perfectly counterbalanced by the slender body
in the section a". A pressure equal to that due to the
weight of all the particles above the horizontal bottom sur-
face, /, acts upon that surface, and the surface reacts with an
equal pressure and sustains all those particles. The effect
would be similar if the surface, or a portion of it, was in-
clined or curved ; therefore, only a pressure equal to the
170 WEIGHT, PRESSURE, AND MOTION OF WATER.
weight of those particles vertically over the opening in the
partition, /, acts upon the column below the partition /.
The right and left horizontal pressures of the individual
particles of A are transmitted to the particles on the right
and left, which, in turn, react with equal pressures, and sus-
tain them from motion sideways. The particles in contact
with the partitions a and 5 transmit their pressures horizon-
tally to the partition, which in turn react and sustain them,
and all the particles remain in equilibrium.
162. Equilibrium Destroyed by an Orifice. If an
orifice is made at the bottom of the side #, then the particles
at that point will be relieved of the reaction of the point, or
of its support, equilibrium will be destroyed, and motion
will ensue, and all the particles throughout A will begin to
move toward the orifice, though not with equal velocities.
163. Pressures from Vertical, Inclined and Bent
Columns of Water. In Fig 10 the particles in the body
of water, B, are pressed with a pressure due to the weight
of any one vertical column of particles or molecules in the
body of water above the opening in the partition #, conse-
quently the reaction horizontally from any point in the
partition c', or downward from any point in the covering
partition g, or upward from any point in the bottom d, is
equal to the weight of a column of molecules pressing upon
that point, of height equal to the depth of the given point
below the surface of the water a'U. The pressure due to
this vertical column of molecules would still remain the
same if the colnmn a'g was inclined or bent, so long as the
water surface remained in the level a' V, as is evident by
inspection of the column ~b."
Since the downward reaction from, any point in the sur-
face g is equal to the pressure of a column of molecules
equal in height to a' g, this reaction is added to the action
PRESSURE UPON A UNIT OF SURFACE. 171
of gravity on all the molecules beneath the given point in g,
therefore the pressure on any point in d, beneath the given
point in g, is equal to the pressure of a column of molecules
of height a' d.
164. Artificial Pressure. If in the vessel illustrated
by Fig. 10, we close the openings 5' and 5" at the level of
the water surface, and fit a piston carrying a weight into
the opening a', then we will increase the pressure at points
d, g, <?', 5', &", etc., respectively, an amount equal to the
pressure received by a point in contact with the piston at a'.
This artificial pressure is equal in effect to a column of fluid
placed upon a' of weight equal to the weight of the loaded
piston.
165. Pressure upon a Unit of Surface. Since one
cubic foot of water, measuring 144 square inches on its
base and 12 inches in height weighs 62.425 pounds, there
must be a pressure exerted by its full bottom area of 62.425
pounds, and by each square inch of its bottom area of
32 425 Ibs \ V
v^tt 0.433472 pounds for each foot of vertical
144 sq. in. / j^>
depth of the water.
In ordinary engineering calculations 62.5 pounds is
taken as the weight of one cubic foot of water, and 0.434
pounds as the resulting pressure per square inch for each
vertical foot of depth below the surface of the water. These
weights used in the computation of the following table, give
closely approximate results, slightly in excess of the true
weights.
In nice calculations, as for instance, relating to tests of
turbines to determine their useful effect, or of pumping
engines to determine their duty, the weights due to the
measured temperatures of the water are to be taken.
172
WEIGHT, PRESSURE, AND MOTION OF WATER.
TABLE No. 39.
PRESSURES OF WATER AT STATED VERTICAL DEPTHS BELOW THE
SURFACE OF THE WATER, AT TEMP. 39.2 FAH.
DEPTH.
PRESSURE PER
SQ. INCH.
PRESSURE PER
SQ. FOOT.
DEPTH.
'RESSURE PER
SQ. INCH.
PRESSURE PER
SQ. FOOT.
Feet.
Pounds.
Pounds.
Feet.
Pounds.
Pounds.
I
4335
62.425
36
15.60
2247.30
2
.8670
124.85
37
16.04
2309.72
3
1.300
187.27
38
16.47
2372.15
4
1-734
248.70
39
16.91
2434-57
5
2.167
312.12
40
17-34
2497.00
6
2.601
374-55
4^
17.77
255942
7
3-035
436.97
42
1 8.21
2621.85
8
3.468
499.40
43
18.64
2684.27
9
3.902
561.82
44
19.07
2746.70
10
4-335
624.25
45
I9-5 1
2809.12
ii
4.768
686.67
46
19.94
287L55
12
5.202
749.10
47
20.37
2933-97
13
5-636
811.52
48
20.81
2996.40
14
6.069
873-95
49
21.24
3058.82
15
6-503
936.37
5
21.67
3121.25
16
6.936
998.80
60
26.01
3745-5
i?
7-370
1061.23
70
30.35
437o
18
7.803
1123.65
80
34-68
4994
19
8.237
1186.07
90
39.01
5618
20
8.670
1248.50
IOO
43-35
6242.5
21
9.104
1310.92
no
47.68
6867
22
9-537
1373-35
120
52.02
7491
2 3
9.971
1435-77
130
56.36
8115
2 4
10.40
1498.20
I4O
60.69
8739
25
10.84
1560.62
!5
65-03
9364
26
11.27
1623.05
1 60
69.36
9988
27
11.70
1685.47
170
73-70
10612
28
12.14
1747.90
1 80
78.03
11237
29
I2 -57
1810.32
190
82.36
11861
30
13.00
1872.75
200
86.70
12485
3i
13-44
I935-I7
210
91.04
13109
3 2
13-87
1997.60
220
95-37
13733
33
I4-3 1
2060.02
230
99.71
14358
34
14.74
2122.45
240
104.04
14982
35
I5-I7
2184.87
2 5
108.37
15606
166. Equivalent Forces. In many computations in
elementary statics we are accustomed to consider the force
A LINE A MEASURE OF WEIGHT.
173
acting from a weight as equivalent to the force of a pressure
and to place weights to represent statical forces.
On one square foot of the bottom of a vessel containing
one foot depth of water, a pressure is exerted by the water
that would tend to prevent any other force from lifting up
that bottom. We might remove that water and substitute
the pressure of a quantity of oil, or of stone, or of iron, as
an equivalent for the pressure of the water, but to be an
exact equivalent its weight must be exactly the same as the
weight of the water. In this case we should take for the
62.5 pounds pressure in the water, 62.5 pounds weight of
oil, or of stone, or of iron.
167. Weight a Measure of Pressure. Weight is,
then, a standard whose unit is one pound, by which pres-
sures may be compared and measured.
168. A Line a Measure of Weight In graphical
statics we are also accustomed to represent weights by lines
which are drawn to some scale.
If two forces act upon the centre of gravity of a body,
Fig. 11, one of which, a, is equal to 30 pounds, and the
other 5, to 40 pounds, we can, after adopting some scale,
174 WEIGHT, PRESSURE, AND MOTION OF WATER.
say one inch, to equal one pound, represent the force a by
a line 30 inches long, drawn from some given point, g, in its
direction of action, ga\ and the force b by a line 40 inches
long, drawn from the same point, in its direction, gb'. N"ow,
if we draw lines from the end of each line thus produced
parallel to the other line to r, completing the parallelogram,
and then draw the diagonal, gr, then the resultant of the
two forces will pass through the line gr, and the length of
gr will represent the combined effect of the two forces in
this direction. Its length will be 50 inches = V(gfff + (b'r) 2 ,
and the combined effect of the two forces in this direction
will be 50 pounds.
169. A Line a Measure of Pressure upon a Sur-
face. Let the dimensions of the top surface of the body A,
be 10 feet long and 3 feet wide, and its area be 30 square
feet ; let the side dimensions, B, be 10 feet long and 4 feet
high, and its area be 40 square feet ; let the pressure upon
each surface be one pound per square foot, and the direc-
tion of the pressure be shown by the arrows a and 5. The
body being solid, the forces are to be considered as acting
through its centre of gravity. We can now plot the pres-
sure upon A of 30 pounds in its direction, and upon B of
40 pounds in its direction, and the diagonal of the parallel-
ogram gr will give the direction and ratio of the resultant,
as before. The forces being equal to those before considered
as acting upon a point, will again give a diagonal 50 inches
long and indicating an effect of 50 pounds.
It is plain, then, that we can take the line ga', or the
line &'r, which is equal to it, to represent the force or pres-
sure a acting upon the point g or upon the surface A ; and
we can take the line gb', or the line a'r, to represent the
force or pressure ~b acting upon the point g or the surface B,
and the line gr to represent the combined effect of the two
ANGULAR RESULTANT
/
IF
ts
/y
,
RCE
4
p WF g> FORcsfcy , jt> ^ "
;V ^ / ^>
it is cbn^BOTr.tp be4"ble
Xj^Vv **/
forces. In various calculations
to do this.
170. Diagonal Force of Combined !*resstn:es
Graphically Represented. Again, if we know the mag-
nitude of the force r acting through the centre of the body,
and we desire to know the magnitude of the effects upon
the sides A and B, in directions at right angles to them,
that produced the force r, we draw the line r to a scale in
the direction the force acts, and from both of its ends draw
lines to the same scale in directions at right angles to the
sides A and B, and proportional to their areas, as^a' and gb',
and complete the parallelogram ; then will ga' measured to
scale indicate the effect of the force a upon A, and gb'
measured to scale indicate the force b upon B. If gr
measures 50 pounds, then will ga' measure 30 pounds and
gb' measure 40 pounds.
171. Angular Resultant of a Force Graphically
Represented. If a force represented by the line ag,
Fig. 12, acts upon and at right
angles to an inclined surface fe
at g, then its horizontal resultant
will be represented by the line
bg, and the end b will be perpen-
dicularly beneath a. The ratios
of the lengths of the lines ag and
ab and bg are the ratios of the
effects of the force in their three
directions respectively.
If a perpendicular line be let fall from / upon the hori-
zontal line ed, intersecting it in d, then the ratio of fe tofd
will be equal to the ratio of ag to bg ; consequently, the
horizontal pressure or effect of the force ag upon fe would
be to its direct effect as/<$ is tofe. Therefore, the ratio of
FIG. 12.
176
WEIGHT, PRESSURE, AND MOTION OF WATER.
the line fd to fe equals the ratio of the horizontal effect of
the direct force upon/b.
The ratio of the vertical downward effect of the force a
upon fe is to its direct effect as the length ab to the length
ag, and also as the length ed to the length ef. Therefore,
the ratio of the line or surface ed to the line fe represents
the ratio of the vertical downward effect of the direct force
uponfe.
172. Angular Effects of a Force Represented by
the Sine and Cosine of the Angle. Also, ab is the
sine, and bg the cosine of the angle agn, and we have seen
that their ratios are to radius ag as ed and fd are to fe;
therefore the vertical and horizontal effects of the force a
upon the inclined surface/*? are to its direct force as the sine
and cosine of the angle efd is to radius/e.
173. Total Pressure. To find the total pressure of
quiet water on any given surface : Multiply togetlier, its
area, in square feet; the vertical depth of its centre of
gravity, below the water surface, in feet; and the weight
of one cubic foot of water
c in pounds (= 62.5 Ibs.).
In the tank, Fig. 13,
filled with water, let the
depth ab be 9 feet ; then
the centre of gravity of
the surface ab will be at
a depth from a equal to
one-half ab = 4 J feet. If
the length of the side ab
is 1 foot, then the total pressure on ab will equal
9 ft. x 1 ft. x 4J ft. x 62.5 Ibs. = 2531.25 Ibs.
174. Direction of Maximum Effect. The direction
of the maximum effect of a pressure on a plane surface is
FIG. 13.
CENTRES OF PRESSURE AND OF GRAVITY. 177
always at right angles to the surface. The maximum hori-
zontal effect of the pressure on the unit of length of ab
equals the product of ab, into the depth of its centre of
gravity, into the unit of pressure. The horizontal effect of
pressure on the unit of length of cd equals the product of
its vertical projection ce, into the depth of its centre of
gravity, into the unit of pressure ; and the vertical effect of
pressure on cd equals the product of its horizontal projec-
tion de, into the depth of its centre of gravity, into the unit
of pressure.
175. Horizontal and Vertical Effects. Assuming
the length of the side cd to be radius of the angle dee, then
the total pressure on cd is to its horizontal effect as radius
cd is to the cosine ce of the angle dee, or as the surface cd
is to its vertical projection ce; and the total pressure is to
its vertical effect as radius cd is to the sine de of the same
angle, or as cd to de.
The total pressure on dg is to its horizontal effect as dg
is to/*/, or to the cosine of the angle dgf; and to its vertical
effect as dg to df, or to the sine of the angle dgf.
176. Centers of Pressure and of Gravity. The
centre of hydrostatic pressure, which tends to overturn or
push horizontally the surface of equal width, ab, is not in
the center of gravity of that surface, but in a point at two-
thirds the depth from a at p = 6 feet.
The center of gravity of the surface cd is at one-half the
vertical depth ce, at h, or at one-half the length of the slope
cd, at h. The points h and h' are both in the same hori-
zontal plane. When the water surface is at ac, the center
of pressure of the surface cd is at two-thirds of the vertical
depth ce, at p', or at two-thirds the slope cd, at p. The
points p' and p are in the same horizontal plane. If ce
equals six feet, then the center of gravity of cd or ce will be
12
178
WEIGHT, PRESSURE, AND MOTION OF WATER.
at the vertical depth of three feet = ch', and the center of
pressure at the vertical depth of four feet = cp'.
The center of gravity of the surface dg is at a depth
from the water surface c, equal to the sum of one-half the
-, and the
vertical depth fg added to the depth ce = ce
center of pressure of dg is at a vertical depth equal to
= c <= 7.6 feet.
FIG. 14.
177. Pressure upon a Curved Surface and Effect
upon its Projected Plane. In a vessel, Fig. 14, filled
with water, one of whose ends, a5, is a segment of a cylin-
der, and opposite end in
part of the vertical plane
a"/b", and in part of a
hemisphere cd, the total
pressure on ab will he
as the total surface ab;
but its horizontal effect
will be as the area of its
vertical projection a'b'. The total pressure on the end a"b",
will be as the remaining surface of the vertical plane a"b"
increased by the concave surface of the hemisphere cM, but
its horizontal effect will be equal to its vertical projection
a"'V" or a'V. The vertical effect on
the plane a"b" is equal to zero, but
the vertical effect of the pressure in
the hemisphere is represented by
the plan of one -half a sphere of
diameter equal to cd.
In a hollow sphere, Fig. 15, filled
with water, the total pressure will
be as the total concave surface a'Tib'k", but the horizontal
FIG. 15.
FLOATING AND SUBMERGED BODIES. 179
effect will be as its vertical projection at), which represents
a circular vertical plane of diameter equal to ab, and the
vertical effect will be as its horizontal projection bb", which
represents a horizontal circular area of diameter equal
to bb".
In a pipe, or cylinder, represented also in section by
Fig. 15, the total pressure within is as the inner circumfer-
ential area a'hb'h", and when the cylinder lies horizontally
the horizontal and vertical effects of its pressure in a unit
of length will be represented by its vertical and horizontal
projections ab and bb".
If the cylinder is inclined, the pressure at any point
upon its circumference is as the depth of that point below
the surface of the water, and the total pressure in pounds
upon any section of the cylinder will be found by multi-
plying its area in square feet into the depth of its center of
gravity, in feet, below the surface of the water and their
product into the weight, in pounds (62.5 Ibs.), of a cubic
foot of water.
178. Center of Pressure upon a Circular Area.
The center of pressure of a vertical circular area, repre-
sented also by Fig. 15, when its top a is in the water surface,
is at a depth below a equal to five-fourths the radius of the
circle.
179. Combined Pressures. The sum of pressures in
pounds, upon a number of adjacent surfaces, may be found
by multiplying the sum of their surfaces in square feet into
the depth of their common center of gravity, in feet, below
the surface of the water, and this product into the weight of
one cubic foot of water, in pounds (62.5 Ibs.).
ISO. Sustaining Pressure upon Floating and
Submerged Bodies. The pressure tending to sustain a
cylinder floating vertically in water c (Fig. 16) is equal to
180 WEIGHT, PRESSURE, AND MOTION OF WATER.
FIG. 16. FIG. 17.
fL
the vertical effect of the pressure on its bottom area. The
sustaining pressure may "be computed, in pounds, by mul-
tiplying the bottom area of the cylinder, in square feet, into
its depth, in feet (which gives the cubical contents of the
immersed portion of the cylinder), and this product into
the weight of a cubic foot of water.
The weight of water displaced may be computed also by
multiplying the cubic contents of the immersed portion of
the cylinder, in cubic feet, into the weight of a cubic foot
of water. The two results will be equal to each other ;
therefore the vertical effect tending to sustain the cylinder
is equal to the weight of water displaced.
To compute the pressure tending to sustain the trun-
cated cone, or pyramid, d, multiply the vertical projection
of the inclined surfaces (= top area bottom area), in feet,
into the depth of their common center of gravity, in feet,
and to this product add the product of its bottom area, in
feet, into its depth, in feet, and then multiply the sum of
the products into the weight of a cubic foot of water, in
pounds.
This sustaining pressure will also equal the weight of
the water displaced.
To compute the pressure tending to sustain the im-
mersed cube , multiply, in terms as before, the bottom
UPWARD PRESSURE UPON A SUBMERGED LINTEL. 181
area into the depth, and into the weight of water, and from
the final product subtract the product of the top area into
its depth and into the weight of water. This sustaining
pressure also equals the weight of water displaced.
The downward pressure on the top of e tends to sink it,
and the upward pressure on its bottom to sustain it. The
difference of the two effects is the resultant. The resultant
will act vertically through the center of gravity of the body.
If e is of the same specific gravity as the water, then its
weight will just balance the resultant, and it will neither
rise or fall ; if of less specific gravity it will rise ; if of
greater, it will sink. The cylinder c is evidently of less
specific gravity than the water, and d of the same specific
gravity.
Let c be a hollow cylinder with a water-tight bottom,
then although it may be made of iron, and weights be
placed within it, it will still float if its total weight, includ-
ing its load, is less than the weight of the water it displaces.
On the same principle iron ships float and sustain heavy
cargoes.
181. Upward Pressure upon a Submerged Lin-
tel. If _, Fig. 17, be a horizontal lintel covering a sluice
between two reservoirs, the upward pressure of the water
upon ij, tending to lift it, will be equal to the product of
the rectangular area ij into its depth and into the weight
of a cubic foot of water ; that is, the upward pressure in
pounds will be equal to the weight in pounds of a prism
of water having the rectangular area ij for its base and the
depth of ij below the surface of the water for its height.
If the lintel is constructed of timber, at a considerable
depth, and is not equally as strong as the enclosing walls
of the reservoir at the same depth, it may be broken in or
thrust upward.
182
WEIGHT, PRESSURE, AND MOTION OF WATER.
FIG. 18.
182. Atmospheric Pressure. Upon the particles of
all bodies of water resting in open vessels or reservoirs,
there is a force constantly
acting, in addition to the
direct force of gravity, upon
the independent particles.
This force comes from the
effect of gravity upon the
atmosphere. The weight
of the atmosphere produces
a pressure upon the sur-
face of the water of about
14.75 pounds per square
inch, or about 2124 pounds per square foot. This is equiv-
alent to a column of water (0^0470 ff ) 34.028 feet high.
In the open vessel, Pig. 18, filled with water to the level
a, the effect of the pressure of the atmosphere is transmitted
through the particles, and acts on all the interior surface
below the water surface abb' a', with a force of 14.75 pounds
on every square inch, in addition to the pressure from the
weight of the water. There is also an equal atmospheric
pressure on the exterior of the vessel of 14.75 pounds per
square inch ; therefore the resultant is zero, and the weighl
of the atmosphere does not tend to move either side of the
vessel or to tear the vessel asunder.
183. Rise of Water into a Vacuum. -If the tube cd
be extended to a height of thirty -five or more feet above th(
surface of the water, and a piston, containing a proper valve,
be closely fitted in its upper end, then by means of the pistoi
the air may be pumped out of the tube, and the surface of
water in the tube relieved of atmospheric pressure. The
equilibrium of the particles within the tube will then be de-
TRANSMISSION OF PRESSURE TO A DISTANCE. 183
stroyed, and the pressure of the atmosphere acting through
the particles in the lower end of the tube will press the
water up the tube to a height, according to the perfection
of the vacuum, of 34.028 feet approximately. It is atmos-
pheric pressure that causes pump cylinders to fill when they
are above the free surface of the water.
If the bottom of the immersed tube, cd, be closed by a
valve, and the tube filled with water, and the top then
sealed at a height of thirty-five or more feet above the sur-
face of the water aa', the valve at d may afterwards be
opened, and the pressure of the atmosphere acting through
the particles in the lower end of the tube will sustain the
column to a height of 34.028 feet approximately.
184. Siphon. If the bent tube or siphon, efg, Fig. 18,
having its leg/*? longer, vertically, than its leg ef, be filled
with water and its end e inserted in the water A, then the
action of gravity upon the water in the leg fg, will be
greater than upon the water in the leg ef, and the equi-
librium in the particles at / will be destroyed. The pres-
sure of the atmosphere on the surface aa', will constantly
press the water A up the leg ef, tending to restore the equi-
librium, and gravity acting in the leg fg will as constantly
md to destroy the equilibrium, consequently there will be
constant flow of the water A out of the end g, until the
rater surface falls nearly to the level e, or until the air can
iter at e.
185. Transmission of Pressure to a Distance.
The effect of pressure on a fluid is transmitted through Us
trticles to any distance, Tiowever indefinitely great, to the
imit of its volume.
If water is poured into the open top 5", Fig. 10, the divi-
sion b'c", will fill as fast as the division W, and the water
ill flow over Vg, and will reach the level a', at approxi-
184 WEIGHT, PRESSURE, AND MOTION OF WATER.
mately the same time as it reaches b" ; so in any inverted
siphon, or in a system of water pipes of a town, water will
in consequence of transmitted pressure, flow from an ele-
vated source down through a valley and up on an opposite
hill to the level of the source. If the syphon, or pipe, has
an indefinite number of branches with open tops as high as
the source, then the surface of the water at the source and
in each of the branches will rest in the same relative eleva-
tion of the earth's curvature.
186. Inverted Siphon. By transmission of pressure
through the particles, water in a pool or lake near the sum-
mit of one hill or mountain is sometimes, when the rock
strata have been bent into a favoring shape, forced through
a natural subterranean inverted siphon, and caused to flow
out as a spring on an opposite hill or mountain summit.
187. Pressure Convertible Into Motion. Thus we
see that the force of gravity in the form of weight is con-
vertible into pressure, and pressure into motion ; and that
motion may be converted into pressure, and pressure be
equivalent to weight.
Motion we are accustomed to measure by its rate, which
we term its velocity ; that is, the number of units of space
passed over by the moving body in a unit of time, as, feet
per second.
MOTION OF WATER.
188. Flow of Water. All forces tending to destroy
equilibrium among the particles of a ~body of water tend
to produce motion in that body.
We have above referred to the accepted theory of motion
due to the influence of caloric ; there is a motion of water
due to the winds, a motion due to the attraction of the
heavenly bodies, and an artificial motion, as, for instance,
ACCELERATION OF MOTION. 185
that due to the pressure of a pump-piston. The motion
herein to be considered is that originated by the influence
of gravity and termed the flow of water.
189. Action of Gravity upon Individual Mole-
cules. All natural flow of water is due to the force of
gravity, acting upon and generating motion in its indi-
vidual molecules.
If in the side of a vessel filled with water there be made
an orifice ; if one end of a level pipe filled with water be
lowered ; or if a channel filled with water have its water
released at one end, then equilibrium among the particles
of the water will be destroyed, and motion of the water will
ensue. Gravity is the force producing motion in either case,
and it acts upon each individual molecule as it acts upon a
solid body, free to move, or devoid of friction.
190. Frictionless Movement of Molecules. The
molecules of water move over and past each other with such
remarkable ease that they have usually been considered as
devoid of friction.
The formulas in common use for computing the velocity
with which water flows from an orifice in the bottom or side
of a tank filled with water, assume that the individual
molecules, at the axis of the jet, will issue with a velocity
equal to that the same molecules would have acquired if
they had fallen freely, in vacuo, in obedience to gravity, from
a height above the orifice equal to the height of the surface
of the water.
191. Acceleration of Motion. The force of gravity
perpetually gives new impulse to a falling body and accel-
erates its motion, if unresisted, in regular mathematical
proportion.
Experiment has shown that a solid body falling freely
in vacuo, at the level of the sea, passes through a space or
186 WEIGHT, PRESSURE, AND MOTION OF WATER.
height of 16.1 feet nearly, during the first second of time ;
has a velocity at the end of the first second of 32.2 feet
nearly, and is accelerated in each succeeding second 32.2
feet nearly. The usual symbol of this rate of acceleration
is g, the initial of the word gravity r , and we shall have fre-
quent occasion for its use.
The latitude and altitude, or distance from the centre of
the earth, affects the rate of motion slightly, but does not
affect materially the results of ordinary hydrodynamic cal-
culations.
The resistance of the air affects slightly the motion of
dense bodies, and retards them more if they are just sepa-
rating, as water separates into spray.
192. Equations of Motion. The velocity, v 9 acquired
by a solid body at the end of any time, t, equals the prod-
uct of time into its acceleration by gravity, g, and is directly
proportional to the time :
v : g : : t : 1, or v = gt.
The height, 7i, through which the body falls in one
second of time equals ^7, and the heights in any given
times, t, are as the squares of those times :
Ji : \g :: t* : (I) 2 , or
and, by transposition, we have
g
This value of t in the equation of v gives
From these equations we deduce the following general
equations of time, t; height, h; velocity, v; and accelera-
tion, g :
PARABOLIC PATH OF THE JET.
t = *- = M = J = .031063*
g v V ff
k = ^ = ^ = ~ = .015536* 2
187
(1)
= = =32.1908
(3)
(4)
The fo'me, space, and velocity are at the ends of the first
ten seconds as follows :
Time (zO
Space (A)
16.1
2
64.4
3
144.0
257.6
5
6
788 o
8
9
10
Velocity (z>)
644
06 6
1288
2898
Acceleration^)
^2.2
72.2
02.2
02.2
72.2
193. Parabolic Path of the Jet. If we plot the
spaces of the column of
spaces or heights to a
scale on a vertical line,
beginning with zero at
the top, and then from
the space points plot
horizontally to scale the
velocities, as in Fig. 19,
and then from zero draw
a curved line <zc, cutting
the extremities of the
horizontal lines, the
curve ac will be a pa-
rabola, the vertical line
ab its abscissa, and the
horizontal lines its ordi-
nates.
;S*j FIG. 19.
33 .fl Velocity in feet per second.
188
WEIGHT, PRESSURE, AND MOTION OF WATER.
194. Velocity of Efflux Proportional to the Head.
If in the several sides of a reservoir A, Fig. 19 a, kept
filled with water, orifices with thin edges are made at
depths of 20 feet, 25 feet, 50 feet, 75 feet, and 100 feet from
the surface of the water, then water will issue from each
FIG. 190.
orifice in a direction perpendicular to the side, with a veloc-
ity proportional to the square root of the head of water
above the centre of gravity of the orifice, and equal approx-
imately to the velocity one of its particles would have
acquired if it had fallen freely from the height of the head.
195. Conversion of the Force of Gravity from
Pressure into Motion. The accumulated vertical force
of gravity due to the head or " charge" will act upon the
EQUAL PRESSURES GIVE EQUAL VELOCITIES. 189
particles as pressure before the orifice is opened, but in-
stantly upon an orifice being opened pressure will impel
the particles of water in the direction of the axis of the
orifice, and gravity will begin anew to act upon the parti-
cles in a vertical direction. If the axis of the orifice is not
vertical, gravity will deflect the particles through a curved
path.
196. Resultant Effects of Pressure and Gravity
upon the Motion of a Jet. If on a line at, drawn
through the center of an orifice, perpendicular to the plane
of the orifice, we plot to scale the products of any given
times into a given velocity, and from each of the points
thus indicated we plot vertically downward the distance, a
body will fall freely in those times, op, and then from the
orifice draw a line through the extremities of the vertical
lines, the curved line thus sketched will indicate the path
of the jet flowing from the orifice. The curved line is a
parabola, to which the axis of the orifice is tangent ; and
the distances ao upon the tangent are equal and parallel to
ordinates, and represent the force per unit of time given to
the particles of the jet by pressure, and the verticals from
the tangent are equal and parallel to abscisses, and repre-
sent by their increase the accelerating effect of gravity upon
the falling particles. The distances ao and op, ordinates op,
and abscisses aa', form a series of parallelograms, one angle
of which lies in the orifice and the opposite angles of which
lie in the curved path of the jet, and the diagonals of which
are equal to resultants of the effects of pressure and gravity.
197. Equal Pressures give Equal Velocities in all
Directions, The velocities of issues, downward from the
orifice d and upward from the orifice c, and horizontally
from the lower orifice b', will be equal, since they all are at
the same depth.
190
WEIGHT, PRESSURE, AND MOTION OF WATER.
198. Resistance of the Air. Since the velocity of
upward issue from c is due to the gravity force of the head
dc, acting as pressure, the jet should theoretically reach the
level of the water surface d. The spreading of the particles
and consequent enhanced resistance of the air prevents such
result, and the resistance increases as the ratio of area of
orifice to height of head decreases.
199. Theoretical Velocities. The foUowing table of
theoretical velocities and times due to given heights or heads
has been prepared to facilitate calculation :
TABLE No. 4O.
CORRESPONDENT HEIGHTS, VELOCITIES, AND TIMES OF FALLING
BODIES.
H = ^
2<r
v = Vzgn
t= ^?M
U=^
2g
= V^H.
,.5
s
Head in feet
Velocity in feet
per second.
Time
in seconds.
Head in feet.
Velocity in feel
per second.
Time
in seconds.
.010
.80
.0248
145
3.05
.0949
.015
.98
.0304
.150
3-n
.0964
.020
13
0350
155
3.16
.0980
.025
27
0394
.160
3-21
0995
.030
39
.0431
.165
3-26
.1011
035
50
.0465
.170
3-31
.1016
.040
.60
.0496
-175
3.36
.1042
045
.70
.0527
.180
3-40
.1054
.050
79
0555
.185
3-45
.1069
055
.88
0583
.190
3-50
.1085
.060
97
.0611
-195
3-55
.1100
.065
2.04
.0632
.20
3-59
.1113
.O7O
2.12
.0657
.21
3-68
.1141
.075
2.20
.0682
.22
3-76
.1166
.080
2.27
.0704
23
3-85
1193
.085
2-34
.0725
.24
3-93
.1221
.090
2.41
.0747
25
4.01
.1243
.095
2.47
.0766
.26
4-09
.1268
.100
2-54
.0787
.27
4.17
.1293
.105
2.60
.0806
.28
4-25
1317
.110
2.66
.0825
.29
4-32
1339
.115
2.72
.0843
30
4-39
.1361
.120
2.78
.0862
31
4-47
.1386
.125
2.84
.0880
32
4-54
.1407
.130
2.89
.0896
33
4.61
.1429
135
2-95
.0914
34
4.68
1451
.140
3.00
0930
35
4-75
.1472
.
THEORETICAL VELOCITIES.
191
CORRESPONDENT HEIGHTS, VELOCITIES, AND TIMES OF FALLING
BODIES ( Continued. )
-5
v = V 2 U
l= m
s
H=^
2
v = y 2 n
f = ym
g
Head in feet.
Velocity in feet
per second.
Time
in seconds.
Head in feet.
Velocity in feet
per second.
Time
in seconds.
.36
4 .8l
.1491
83
7-31
.2266
37
4.87
.1510
.84
7-35
.2278
.38
4.94
1531
85
7.40
.2294
39
5-oi
1553
.86
7-44
.2306
.40
5-07
1572
87
7.48
.2319
.41
5-14
1593
.88
7-53
2334
.42
5-20
.1612
.89
7-57
2347
43
5.26
.1634
.90
7.61
2359
44
5-32
.1649
.91
7-65
2377
45
5.38
.1668
.92
7.70
.2387
.46
5-44
.1686
93
7-74
2399
47
5-50
1705
94
7-78
.2412
.48
5.56
.1724
95
7.82
.2424
49
5.62
.1742
.96
7.86
2437
50
5.67
1758
97
7.90
2449
5i
5-73
1779
.98
7-94
.2461
52
5-79
1795
99
7.98
.2474
53
5-85
.1813
8.03
.2491
54
5-90
.1829
.02
8.10
.2518
55
5-95
.1844
.04
8.18
2543
56
6.00
.i860
.06
8.26
.2567
57
6.06
.1879
.08
8-34
.2589
58
6. ii
.1894
.10
8.41
.2616
59
6.17
1913
.12
8.49
.2638
.60
6.22
.1928
.14
8-57
.2660
.61
6.28
1947
.16
8.64
.2685
.62
6. 3 2
.1959
.18
8.72
.2706
.63
6-37
1975
.20
8.79
.2730
.64
6.42
.1990
.22
8.87
2751
.65
6.47
.1999
.24
8.94
.2774
.66
6.52
.2O2I
.26
9.01
.2797
.67
6-57
2037
.28
9.08
.2819
.68
6.61
.2049
30
9- J 5
.2842
.69
6.66
.2065
32
9.21
.2866
70
6.71
.2080
34
9.29
.2885
7i
6.76
.2096
.36
9-36
.2906
72
6.81
.2111
38
9-43
.2927
73
6.86
.2127
.40
9-49
.2950
74
6.91
.2142
.42
9-57
.2968
75
6-95
.2154
44
9-63
.2991
.76
6.99
.2167
.46
9.70
.3010
77
7.04
.2182
.48
9-77
.3030
78
7.09
.2198
50
9-83
3052
79
7-13
.22IO
55
9.98
.3106
.80
7.18
.2226
.60
10.2
3137
.81
7.22
.2238
65
10.3
.3204
.82
7.26
.2251
.70
10.5
3238
192 WEIGHT, PRESSURE, AND MOTION OF WATERS.
CORRESPONDENT HEIGHTS, VELOCITIES, AND TIMES OF FALLING
BODIES (Continued?)
H=^
*g
v = VzgH
t= i/
g
H=^
2<r
v = V 2ig H
I= VM
g
Head in feet.
Velocity in feet
per second.
Time
in seconds.
Head in feet.
Velocity in feel
per second.
Time
in seconds.
1-75
10.6
.3302
8.4
23.3
.7210
i. 80
10.8
3333
8.6
23-5
.7319
1.85'
10.9
3394
8.8
23.8
7395
1.90
n. i
.3423
9
24.1
.7469
i-95
II. 2
.3482
9.2
24-3
.7572
2.
II.4
.3509
9.4
24.6
.7642
2.1
II.7
3590
9.6
24.8
.7742
2.2
II. 9
.3697
9.8
25.1
.7809
2-3
12.2
3770
10.
25.4
.7866
2. 4
12-4
.3871
10.5
26.
.8077
2-5
12.6
.3968
II.
26.6
.8277
2.6
I2. 9
.4031
II-5
27.2
.8456
2.7
13.2
.4091
12.
27.8
.8633
2.8
13.4
.4179
12.5
28.4
.8803
2.9
13.7
.4234
13-
28.9
.8997
3-
13-9
.4317
13.5
29-5
9*53
3-i
I4.I
-4397
14.
30.
9333
3-2
14-3
.4476
14-5
30-5
.9508
3-3
14.5
4552
IS-
3LI
.9646
3-4
14.8
4595
15.5
31-6
.9810
3-5
IS-
.4667
16.
32.1
.9969
3-6
15.2
4737
16.5
32.6
.0123
3-7
15.4
.4805
17-
33-1
.0272
3.8
I 5 .6
.4872
17.5
33-6
.0417
3-9
15.8
4937
18.
34-
.0588
4.
16.
.5000
18.5
34-5
.0725
4.2
16.4
5122
19.
35-
.0857
4-4
16.8
5238
19.5
35-4
.1017
4.6
17.2
5343
20.
35-9
.1142
4.8
17-6.
5454
20.5
36.3
.1295
5-
17.9
.5587
21.
36.8
1413
5-2
18.3
.5683
21.5
37-2
1559
5-4
18.7
5775
22.
37.6
.1702
5-6
19.
* .5895
22.5
38.1
.1811
5-8
19.3
.6010
23.
38.5
.1948
6.
19.7
.6091
23.5
38.9
.2082
6.2
20.
.6200
24.
39-3
.2214
6.4
20.3
6305
24.5
39-7
2343
6.6
20.6
.6408
25
40.1
.2469
6.8
20-9
.6507
26
40.9
.2714
7-
21.2
.6604
27
41.7
.2950
7.2
21.5
.6698
28
42-5
.3176
7-4
21.8
.6789
2 9
43-2
.3426
7.6
22.1
.6878
30
43-9
.3667
7-8
22.4
.6964
31
44.7
.3870
8.
22.7
.7048
32
45-4
.4097
8.2
23-
.7130
33
46.1
.4317
THEORETICAL VELOCITIES.
193
CORRESPONDENT HEIGHTS, VELOCITIES, AND TIMES OF FALLING
BODIES ( Continued?)
H=^
2-
v = VzgH.
,= ^H
S
H=^!
2<r
v= VzgH
* m y*
s
Head in feet.
Velocity in feet
per second.
Time
in seconds.
Head in feet.
Velocity in feet
per second.
Time
in seconds.
34
46.7
.4561
77
70.4
2.1874
35
47-4
.4768
78
70.9
2.2003
36
48.1
.4968
79
71-3
2. 2160
37
48.8
.5164
80
71.8
2.2284
33
49-5
5354
81
72.2
2.2438
39
50.1
.5569
82
72.6
2.25 9
40
50-7
5779
83
73-1
2.2709
4i
51-3
.5984
84
73-5
2.285 7
42
52.
.6154
85
74-o
2.2973
43
52.6
6350
86
74-4
2.3II8
44
53-2
.6541
87
74-8
2 . 3262
45
53-8
.6729
88
75-3
2-3373
46
54-4
.6912
89
75-7
2.35H
47
55-
.7090
90
76.1
2.3653
48
55-6
.7266
9i
76.5
2.3791
49
56.2
.7438
92
76.9
2.3927
50
56.7
.7637
93
77-4
2.4031
51
57-3
.7801
94
77.8
2.4165
52
57-8
7993
95
78.2
2.4297
53
58.4
.8151
96
78.6
2.4427
54
59-
8305
97
79.0
2.4557
55
59-5
.8487
98
79-4
2.4685
56
60.
.8667
99
79-8
2.4812
57
60.6
.8812
100
80.3
2.4907
58
61.1
.8985
125
89.7
2.7871
59
61.6
.9156
150
98.3
3-0519
60
62.1
9324
175
106
3.3019
61
62.7
9458
200
114
3.5088
62
63.2
.9620
225
1 20
3.7500
63
63.7
.9780
250
126
3-9683
64
64.2
1.9938
275
133
4-1353
65
64.7
2.0093
300
139
4.3165
66
65.2
2.0245
350
150
4.6667
67
65.7
2.0396
400
160
5.0000
68
66.2
2.0544
450
170
5-2941
69
66.7
2.0690
500
179
5.5866
70
67.1
2.0864
550
188
5.85H
7i
67.6
2.1006
600
197
6.0914
72
68.1
2.1145
700
212
6.6038
73
68.5
2.1313
800
227
7.0485
74
69.
2.1449
9OO
241
7.4689
75
69.5
2.1583
1000
254
7.8740
76
69.9
2.1745
CHAPTEE XI.
FLOW OF WATER THROUGH ORIFICES.
200. Motion of the Individual Particles. If an
aperture is made in the bottom or side of a tank, filled with
water, the particles of water will move from all portions of
the body toward the opening, and each particle flowing out
will arrive at the aperture with a velocity, T 7 , dependent
upon the pressure or head of water upon it, and, as we shall
see hereafter, upon its initial position.
201. Theoretical Volume of Efflux. If we assume
the fluid veins to pass out through the orifice parallel with
each other, and with a velocity due to the head upon each,
and the section of the jet to be equal to the area, &, of the
orifice, then the theoretical volume, or quantity, $, of dis-
charge will equal 8 x V= SV%gH; H being the head upon
the centre of the orifice, and g the acceleration of gravity
per second = 32.2 feet. We have then for the theoretical
volume
Q = 8 V2gH.
V 2O2. Converging Path of Particles. The particles
are observed to approach the orifice, not in parallel veins,
but by curved converging paths, and if the partition is
"thin" the convergence is continued slightly beyond the
partition, a distance dependent upon the velocity of the
particles.
2O3. Classes of Orifices. If the top of the orifice is
beneath the surface of the water, the orifice is termed a sub-
merged orifice, and if the surface of the water is below the
RATIO OF MINIMUM SECTION OF JET.
195
top of the orifice, the notch is termed a "weir." We are
now to consider submerged orifices.
2O4. Form of Submerged Orifice-jet. In Fig. 20
is shown a submerged circular orifice in thin partition.
FIG. 21.
FIG. 20.
In Fig. 21 are delineated more clearly the proportions
of the issuing jet at the contracted vein, or vend conlractd,
as it was termed by Newton. The form of the contracted
vein has been the subject of numerous measurements, and
as the result of late experiments writers now usually assign
to the three dimensions FK^ fJc, and LI, the ratios 1.00,
0.7854, 0.498, as mean proportions of circular jets not ex-
ceeding one-half foot diameter.
2O5. Ratio of Minimum Section of Jet. The par-
ticles of the jet that arrive at the centre of the orifice have a
direction parallel with the axis of the orifice. The particles
that arrive near the perimeter have converging directions,
and since they have individually both weight and velocity,
they have also individual force or momentum in their direc-
tions. This force must be deflected into a new direction,
and as it can be most easily deflected through a curved
196 FLOW OF WATER THROUGH ORIFICES.
path, the curve is continued until the particles have paral-
lelism. The point where the direction of the particles is
parallel is at a distance from the inside of a small square-
edged orifice, equal to about one-half the diameter of the
orifice, and the diameter of the jet at that point is equal
to about 0.7854 of the diameter of the orifice. The cross-
section of a circular jet at the same point has therefore a
mean ratio to the area of the orifice as (0.7854) 2 to (l.OO) 2 ,
or as 0.617 to 1.00.
206. Volume of Efflux. If the velocity due to the
head upon the center of the orifice is the mean velocity of
all the particles of the jet, then we have for the volume of
discharge,
Q = 0.617# x V, or Q = 0.617 SVZgH. (2)
The real volume, Q, of the jet, and its ratios of velocity
and of contraction, have been the subjects of many obser-
vations, and have engaged the attention of the ablest ex-
perimentalists and hydraulicians, from time to time, during
many years.
207. Coefficient of Efflux. In every jet flowing
through a thin orifice there is a reduction of the diameter
of the jet immediately after it passes the orifice. Some
fractional value of the area S, or the velocity F, or the
the theoretical volume $, must therefore be taken that is,
they must be multiplied by some fraction coefficient to com-
pensate for the reduction of the theoretical volume of the
jet. This fractional coefficient is termed the coefficient of
discharge. Place the symbol c to represent this coefficient,
and the formula for volume of discharge becomes
Q = cSVZgH. (3)
2O8. Maximum Velocity of the Jet. The point
where the mean velocity of the particles is greatest is in the
PRACTICAL USE OF A COEFFICIENT. 197
least section of the jet, and here only can it approximate to
V%gH. The mean velocity will be less at the entrance to
the orifice, and also after passing the contraction, than in
the contraction. When speaking of the velocity of the par-
ticles or of the jet hereafter, in connection with orifices, the
maximum velocity that is, the velocity in the contraction
is referred to, unless otherwise specially stated.
2O9. Factors of the Coefficient of Efflux. If the
edges of the orifice are square, the circumferential particles
of the jet receive some reaction from them ; therefore only
the axial particles can have a velocity equal to V%gH, and
the mean velocity is a small fraction less.
In such case the general coefficient of discharge (c) will
be the product of two factors, one representing the reduc-
tion of velocity, and the other the reduction of the sectional
area of the jet.
We shall have occasion to investigate these factors after
we have determined the value of the general coefficient.
21O. Practical Use of a Coefficient. The usefulness
of a coefficient, when it is to be applied to new computa-
tions, depends upon its accord with practical results.
All new and successful hydraulic constructions of orig-
inal design must have their proportions based upon com-
putations previously made. Those computations must be
founded upon hydrodynamic formulae in which the co-
efficient performs a most important office. In fact the
skillful application of formulae to hydraulic designs de-
pends upon the skillful adaptation of the one or more co-
efficients therein.
The coefficient product adopted must harmonize with
jsults before obtained, practically or experimentally, and
ie parallelism of all the conditions of the old or experi-
lental structure and the new design .cannot be too closely
198
FLOW OF WATER THROUGH ORIFICES.
scrutinized when an experimental result is to control a new-
design for practical execution.
211. Experimental Coefficients. A few experimental
results are here submitted as worthy of careful study.
From Michelotti. The following table of experi-
ments with square and circular orifices, by Michelotti, we
find quoted by Neville.* They refer to a very carefully
made set of experiments, with an extensive apparatus
specially prepared, near Turin, where the apparatus was
supplied with the waters of the Doire by a canal.
The table is given by Neville in French measures, but
they are given here as we have reduced ' them to English
measures.
TABLE No. 41.
COEFFICIENTS FROM MICHELOTTI'S EXPERIMENTS.
DESCRIPTION, AND SIZE OF ORIFICE,
IN FEET.
Depth upon
the center of
the orifice
in feet.
Quantity
discharged in
cubic feet.
Time of
discharge in
seconds.
Resulting
coefficients
of discharge.
7.05
561.240
600
.619
7-30
685.762
720
.619
Square orifice, 3.197" x 3.197"
12.43
625.652
510
.610
= .071 square foot section. . ..
12.59
741-036
600
.611
23.13
502.931
300
.612
23.14
604.362
360
.613
Square orifice, 2. 13156" x 2.13156"
= .0315 square foot section . .
7.06
12.17
22.86
399-266
512.650
466. 500
900
900
600
.660
.645
.643
Sq. orifice, 1.06578" x 1.06578"
= .0079 square foot section. .
7.20
12.59
22.90
191.940
198.300
681.500
1800
1440
3600
.628
.612
.625
Circular orifice, 3.197" diameter
.05577 square foot section..
7.13
12.31
23.03
657.130
691.200
631.090
900
720
480
.611
.610
.612
Circular orifice, 2.13156" diam.
= 0.2477 square foot section..
7-23
11.71
23-44
591.610
713.700
696. 700
1800
1680
I2OO
.616
.605
.605
Circular orifice, 1.06578" diam.
= .0062 square foot section. . .
7-33
12.51
23-45
299.449
392.370
538.158
3600
3600
3600
.619
.620
.621
Circular orifice, 6.378" diameter.
6.92
12.01
::::
.619
.619
Hydraulic Tables, by John Neville, C. E. ; M.R.I.A., London, 1853.
EXPERIMENTAL COEFFICIENTS.
199
From Abbe Bossut. From experiments made by the
Abbe Bossut we have the following results, as reduced to
English measures :
T A BLE No. 42,
COEFFICIENTS FROM BOSSUT'S EXPERIMENTS.
DESCRIPTION, POSITION, AND SIZE OF ORIFICE,
Depth of the
centre of
Discharge,
in cubic
Resulting
IN INCHES.
the orifice,
feet per
coefficient.
in feet.
minute.
Lateral and circular, .53289" diameter
I 006
61
1.06578"
Q *\O
6l7
" .53289" "
4 273
72-1
616
1.06578" "
4 2T\
j 952
619
1.06578" "
Horizontal and circular, .53289" diameter.. .
12 54
*2C5
" 1.06578"
12.54
5.040
.617
" 2.13156"
12.54
20. 201
.618
Horizontal and square, 1.06578" x 1.06578". . .
12-54
6.417
.617
" " 2.13156" x 2. 13156".. .
12.54
25.717
.618
Horizontal and rectangular, 1.06578" x .26644"
12.54
1-593
.613
From Rennie. We have also, from experiments of
Kennie with circular and square orifices, under low heads,
the following :
T A BLE No. 43.
COEFFICIENTS FOR CIRCULAR ORIFICES.
Heads at the centre
of the orifice,
in feet.
Jinch
diameter.
4 inch
diameter.
Jinch
diameter.
i inch
diameter.
Mean Values.
I
2
3
4
.6 7 I
.653
.660
.662
.634
.621
.636
.626
.644
.652
.632
.614
-633
.619
.628
584
645
.636
.639
.621
Means .
66 1
fiie
f\lf\
f\ie.
35
.35
200
FLOW OF WATER THROUGH ORIFICES.
COEFFICIENTS FOR RECTANGULAR ORIFICES.
Heads at the
centre of gravity,
in feet.
i inch x i inch.
2 inches wide
inch high.
i inches wide
x | inch high.
Equilateral
triangle of
i square inch,
base down.
Same triangle,
with base up.
.617
.635
.606
593
.617
635
.606
593
.663
.668
.606
593
593
.596
577
572
593
Means,
.632
593
From Castel. In 1836, M. Castel, the accomplished
hydraulic engineer of the city of Toulouse, made with care
certain experiments by request of D' Aubuisson, to determine
the volume of water discharged through apertures in thin
partitions.
He placed a dam of thin copper plate in a sluice which
was 2.428 feet broad, and in the plate opened three rectan-
gular apertures, each 3.94 inches wide and 2.36 inches high.
The distance between the orifices was 3.15 inches. The
flow took place under constant heads of 4.213 inches above
the centres of gravity of the orifices, with contractions as
follows :
{Coefficient for the middle 6198
" right ... .6192
" left 6194
{Coefficient for the two outsides 6205
" " middle and right 6205
" left 6207
Three orifices open, coefficient for all 6230
Subsequently, he experimented with two orifices, 1.97
inches wide and 1.18 inches high, with results as follows :
Head. No. of orifices open. Coefficient
3-379 \l Hi
^3..... \l ?
EXPERIMENTAL COEFFICIENTS.
201
When more than one aperture was open in these exper-
iments of Castel, the volume of water discharged induced
considerable velocity in each of the supplying sluices.
This actually increased the effective head. Its effect is here
recorded in the coefficient instead of in the head, conse-
quently an increased coefficient is given.
In such cases the real head is the observed head in-
creased by the head due to the velocity of approach =
F 2
64T
From Lespinasse. From among experiments on a
larger scale, the following by Lespinasse, with a sluice of
the canal of Languedoc, are of interest :
TABLE No. 44.
COEFFICIENTS OBTAINED BY LESPINASSE.
OPENINGS.
HEAD ON THE
DISCHARGE m
COEFFICIENT.
Breadth.
Height.
Area.
Feet.
Feet.
Sq.feet.
Feet.
Cubic feet.
4.265
1.805
7-745
14-554
145.292
.613
(i
1.640
6.992
6.631
92.635
.641
1.640
6.992
6.247
88.221
.629
H
1.509
6.466
12.878
138.937
.641
it
1-575
6.723
13.586
128.764
.647
(I
1-575
6.723
6-394
83.948
.616
"
1-575
6.723
6.217
79-857
594
<i
1-575
6.717
6.480
85-219
.621
From Gen. Ellis. Gen. Theo. G. EUis has reported
in a paper* presented to the American Society of Civil
Engineers, the results of some experiments very carefully
conducted by him at the Holyoke testing flume in the sum-
mer of 1874.
* Hydraulic Experiments with Large Apertures. Jour. Am. Soc. Civ. Eng.,
1876, Vol. V, p. 19.
202 FLOW OF WATER THROUGH ORIFICES.
The coefficients for the minimum, mean, and maximum
velocities are given to indicate generally the range, and the
results obtained by Gen. Ellis.
The volume of water discharged was determined by
weir measurement, and computed by Mr. James B. Fran-
cis' formula.
The edges of the orifices were plated with iron about
one-half inch thick, jointed square.
VERTICAL APERTURE, 2 ft. x 2 ft.
Minimum head, 2.061 feet. Coefficient, .60871 ) Centre of aperture, 1.90 feet
Mean " 3.037 " " .59676 > above top of weir.
Maximum " 3.538 " " .60325 ) Temp, of water, 73 Fah.
VERTICAL APERTURE, 2 ft. horizontal x i ft. vertical.
Minimum head, 1.7962 feet. Coefficient, .59748 } Centre of aperture, 2.40 feet
Mean " 5.7000 " " .59672 > above top of weir.
Maximum " 11.3150 " " .60572 ) Temp, of water, 76 Fah.
VERTICAL APERTURE, 2 feet horizontal x .5 feet vertical.
Minimum head, 1.4220 feet. Coefficient, .61165 J Centre of aperture, 2.15 feet
Mean " 8.5395 " " .60686 V above top of weir.
Maximum " 16.9657 " .60003 ) Temp, of water, 76 Fah.
VERTICAL APERTURE, i ft. x i ft.
Minimum head, 1.4796 feet. Coefficient, .58230 J
Mean " 9.8038 " " .59612 V
Maximum " 17.5647 " " .59687 )
HORIZONTAL APERTURE, i ft. x i ft. AND SLIGHTLY SUBMERGED
ISSUE.
Minimum head, 2.3234 feet. Coefficient, .59871 )
f Top surface of orifice .441
Mean 8.0926 " .60601 V
., \ feet above crest of weir.
Maximum 18.4746 ' .60517 ;
HORIZONTAL APERTURE (IN PLANK) WITH CURVED ENTRANCE AND
SLIGHTLY SUBMERGED ISSUE.
Minimum head, 3.0416 feet. Coefficient, .95118 }
, f Issue about level with crest
Mean 10.5398 " .94246 >
r, r \ of weir.
Maximum ' 18.2180 ' -94364 ;
COEFFICIENTS DIAGRAMMED.
203
The range, and results generally, of Gen. Ellis' experi-
ments with circular vertical orifices, are indicated by the
following extracts from his extended tables :
TABLE No. 45.
COEFFICIENTS FOR CIRCULAR ORIFICES, OBTAINED BY GEN. ELLIS.
DIAMETERS.
HEAD.
COEFFICIENTS.
2 feet.
it 11
11
1.7677 feet.
5.8269 "
9.6381 "
.58829
.60915
61530
i foot.
u
1.1470 feet.
10.8819 "
17.7400 "
57373
59431
59994
.5 foot.
u
u
2.1516 feet.
9.0600 "
17.2650 "
.60025
.60191
.59626
212. Coefficients Diagrammed. The coefficients, as
developed by the several experimenters, seem at first glance
to be very fitful, and without doubt the apparatus used
varied in character as much as the results obtained
To arrange all the series of coefficients that appeared to
have been obtained by a reliable method, in a systematic
manner, we have plotted all to a scale, taking the heads
for abscisses and the coefficients for ordinates. The curves
LUS developed were brought into their proper relations,
side by side, or interlacing each other.
Then we were able to plot in the midst of those curves
ie general curves due to each class of orifice under the
iveral heads, and those apparently due to the law govern-
the flow of water through submerged orifices.
From these curves we have prepared tables of coefficients
for various rectangular orifices, with greatest dimension.
204 FLOW OF WATER THROUGH ORIFICES.
both horizontal and vertical, with ratios of sides varying
from 0.125 to 1, to 4 to 1, and for heads varying from
0.2 feet to 50 feet.
All of the curves increase from that for very low heads
rapidly as the head increases, until a maxima is reached,
and then to decrease gradually until a minima is reached,
and then again to increase very gradually, the head in-
creasing all the time. This increase, and decrease, and
increase again of the coefficients, arranges them, when thus
plotted, into two curves of opposite flexure, and with all
the curves tending to pass through one* intermediate point.
213. Effect of Varying the Head, or the Propor-
tions of the Orifice. The effect of increasing or decreas-
ing the head upon a given orifice is clearly shown by the
several columns of coefficients in Tables 46 and 47.
The effect of increasing or decreasing the ratio of the
base to the altitude of an orifice will be manifest by tracing
the lines of coefficients horizontally through the two tables,
for any given head.
These effects should be duly considered when a coef-
ficient is to be selected from the table for a special appli-
cation.
The coefficients apply strictly to orifices with sharp,
square edges, and with full contraction upon all sides. The
heads refer to the full head of the water surface, and not to
the depressed surface over or just in front of an orifice when
the head is small.
A very slight rounding of the edge would increase the
coefficient materially, as would the suppression of the con-
traction upon a portion of its border by interference with
the curve of approach of the particles.
COEFFICIENTS DIAGRAMMED.
205
TABLE No. 46.
COEFFICIENTS FOR RECTANGULAR ORIFICES.
In thin vertical partition, with greatest dimension vertical.
BREADTH AND HEIGHT OF ORIFICE.
Head upon
centre of orifice.
4 feet high,
i foot wide.
2 feet high,
i foot wide.
ij feet high,
i foot wide.
i foot high,
i foot wide.
Feet.
Coefficient.
Coefficient.
Coefficient.
Coefficient.
.6
....
....
.5984
7
....
....
...
5994
.8
....
....
.6130
.6000
9
....
....
.6134
.6006
i
. . .
....
.6135
.6010
1.25
....
.6l88
.6140
.6018
1.50
....
.6187
.6144
.6026
J -75
....
.6186
.6145
6033
2
....
6183
.6144
.6036
2.25
....
.6l8o
.6143
.6039
2-5
.6290
.6176
.6139
.6043
2 -75
.6280
.6173
.6136
.6046
3
.6273
.6170
.6132
.6048
3-5
.6250
.6l6o
.6123
.6050
4
.6245
.6150
.6lIO
.6047
4-5
.6226
.6138
,6lOO
.6044
5
.6208
.6124
.6088
.6038
6
.6158
.6094
.6063
.6020
7
.6124
.6064
.6038
.6011
8
.6090
.6036
.6022
.6010
9
.6060
.6O2O
.6014
.6010
10
6 35
.6015
.6OIO
.6010
15
.6040
.6oi8
.6OIO
.6011
20
.6045
.6024
.6OI2
.6012
25
.6048
.6028
.6014
.6012
3
.6054
.6034
.6017
.6013
35
.6060
.6039
.6021
.6014
40
.6066
.6045
.6025
.6015
45
.6054
.6052
.6029
.6016
5o
.6086
.6060
.6034
.6018
206
FLOW OF WATER THROUGH ORIFICES.
TABLE No. 47.
COEFFICIENTS FOR RECTANGULAR ORIFICES.
In thin vertical partition, with greatest dimension horizontal.
BREADTH AND HEIGHT OF ORIFICE.
Head upon
centre of orifice.
0.75 feet high,
i foot wide.
0.50 feet high,
i foot wide.
0.25 feet high,
i foot wide.
0.125 feet high,
i foot wide.
Feet,
Coefficient.
Coefficient.
Coefficient.
Coefficient.
0.2
....
....
....
6333
3
....
....
.6293
6 334
4
....
.6140
.6306
6334*
'5
.6050
.6150
6313
6 333
.6
.6063
.6156
63*7
6332
7
.6074
.6l62
.6319
.6328
.8
.6082
.6165
.6322
.6326
9
.6086
.6l68
.6323*
.6324
i
.6090
.6172
.6320
.6320
!-25
.6095
.6l 73 *
.6317
.6312
1.50
.6lOO
.6172
6 3*3
6303
J -75
.6103
.6l68
.6307
.6296
2
.6104*
.6166
.6302
.6291
2.25
.6103
.6163
.6293
.6286
2. 5
.6102
.6157
.6282
.6278
2 -75
.6lOl
6155
.6274
.6273
3
.6100
6153
.6267
.6267
3-50
.6094
.6146
.6254
.6254
4
.6085
.6136
.6236
.6236
4-50
.6074
.6125
.6222
.6222
5
.6063
.6114
.6202
.6202
6
.6044
.6087
.6154
.6154
7
.6032
.6058
.6110
.6114
8
.6O22
6033
.6073
.6087
9
.6015
.6020
.6045
.6070
io
.6oiO
.6010
.6030
.6060
J 5
.6012
.6013
6033
.6066
20
.6014
.6018
.6036
.6074
2 5
.6016
.6022
.6040
.6083
30
.6018
.6027
.6044
.6092
35
.6022 *
.6032
.6049
.6103
40
.6026
.6037
6055
.6114
45
.6030
.6043
.6062
.6125
5
6035
.6050
.6070
.6140
PECULIARITIES OF EFFLUX.
207
214. Peculiarities of Efflux from an Orifice.
In Fig. 22, containing a horizontal orifice, the horizontal
line cutting a has an altitude above the orifice equal to 3.5
diameters, and the horizontal line cutting e equal to 10
diameters of the orifice. As the altitude of the water sur-
FIG. 22.
<
a
K
i
*
V\" "
^V?J^X-.
;
"~
^Vx \\
\\
\ \
\ X \ \
\ \
\ \ \ \
\ \\ \
\ \\
1 \
x ' \
\ \
\ \
\ \
N >
k \ \
X
\ \ \
\ \ i
\ ^ \
\ \ \
CL /
\\ \
"""^^"p
\ \
// 'i^/fi<
\ \ '
I i / / S/ \
\\1
/ //// .^\
i',"// x
\\1
1 // /
/ / /
/
Ml
|VJ
I///
1
face above a square orifice increases from very low heads to
the level a, the particles continually find new advantage or
less hindrance in their tendency to flow out of the orifice,
possibly by decrease of the vortex effect accompanying
very low heads over orifices nearly square ; afterwards the
resistance increases up to the altitude e, possibly by more
effective reaction from the inner edges of the orifice, is,
until gravity is enabled to gather the jet well into a body
and establish firmly its path. For altitudes greater than
ten diameters the coefficients for square orifices remain
nearly constant.
208 FLOW OF WATER THROUGH ORIFICES.
Similar effects are observed when the orifices are rectan-
gles, other than squares, though their first change occurs at
different depths.
These phenomena are not fully accounted for by ex-
periment.
215. Mean Velocity of the Issuing Particles.
We have heretofore assumed in our theoretic equations,
that all the particles of water bcdefg, Fig. 22, will arrive
at the point of greatest contraction of the issuing jet, with a
velocity equal to that which a solid body would have ac-
quired by falling freely from e to o, which, according to the
the theorem of Toricelli, and its demonstrations frequently
repeated by other eminent philosophers, would be equal to
V%gIL If being equal to the height e o.
The experiments of Mariotte, Bossut, Michelotti, Ponce-
let, Pousseile, and others, covering a large range of areas of
orifice, and of head, show that this is very nearly correct ;
and the velocity of issue of the axial particles has in some
of the experiments appeared to slightly exceed the value of
V2gH. An average of experiments gives the mean velocity
of the particles as a whole through the minimum section as
.974 VZgH.
Their dynamic effect if applied to work should have
.974 VZgH instead of V%gH as the factor of velocity.
216. Coefficients of Velocity and Contraction.
We have then, .974 for mean coefficient of velocity, indi-
cating a loss of .026 per cent, of theoretic volume or dis-
charge by reduction of velocity ; .637 for mean coefficient
of contraction, indicating a loss of 36.3 per cent, of theoretic
volume by contraction ; and .62 nearly for mean coefficient of
discharge, including all losses, a total of about 38 per cent.
The coefficient of velocity we will designate by <?<,, and
the coefficient of contraction by c c .
VOLUME OF EFFLUX FROM A SUBMERGED ORIFICE. 209
Then c x c c = c = coefficient of discharge or volume.
217. Velocity of Particles Dependent upon their
Angular Position. Bayer assumed the hypothesis that,
the velocities of the particles approaching the orifice from
all sides are inversely as the squares of their distances from
its centre, but this should undoubtedly be applied only to
particles in some given angular position.
Gravity will not act with equal force in the direction of
the orifice, upon each of the particles e,f, g, and ^, Fig. 22,
though they are all equally distant from o, but more nearly
in the ratios of the cosines of the angles eoe, eof, eog, etc.,
and it is not probable that the particle h will acquire a
velocity at its maximum through the contraction, quite
equal to that which e will acquire. If the velocity of e is
assumed equal to unity, and the mean velocity of all the
particles equal to .974, then, according to the hypothesis of
the angular distance, the mean velocity will be that due to-
particles having their cosines equal to .974, or an angular
distance of 13, as at b and/.
218. Equation of Volume of Efflux from a Sub-
merged Orifice. Neville suggests a formula* for the
discharge of water from rectangular orifices, more strictly
mathematical than the above simple formulas, as follows :
(4)
when D = volume of discharge,
A = area of orifice,
Ji = head upon the centre of the orifice,
d = depth of the orifice, or distance between its
bottom and top,
c = coefficient of discharge.
* Third Edition of Hydraulic Tables, page 48. London, 1875. Also vide
equation 3, page 283, ante.
210 FLOW OF WATER THROUGH ORIFICES.
This formula can be advantageously applied when the
orifice is large and but slightly submerged, as is frequently
the case with sluice gates controlling the flow of water from
storage reservoirs or canals into flumes leading to water-
wheels, or with head-gates of races or canals.
Good judgment must, however, be exercised in each case
in the selection of the coefficient of velocity (c v ) and the co-
efficient of contraction (<? c ), the factors of c, especially the
coefficient of contraction ( 216), which is usually much the
most influential of the two.
219. Effect of Outline of Symmetrical Orifices
upon Efflux. According to the various series of experi-
ments, the coefficient for a circular orifice under any given
head is substantially the same as for a square orifice under
the same head, and it is probable that the coefficients for
elliptical orifices is substantially the same as that for their
circumscribing rectangles.
220. Variable Value of Coefficients. The coeffi-
cients obtained by careful experiment and recorded above,
as also tables of coefficients, indicate unmistakably that the
value of c in the equation
is a variable quantity, and that a general mean coefficient
cannot be used universally when close approximate results
are desired, but that, for a particular case, reference shoiald
always be made to a coefficient obtained under conditions
similar to that of the case in question.
221. Assumed Mean Volume of Efflux. In ordi-
nary approximate calculations, and in general discussions
of formulas for square and circular orifices, whether the jet
issues horizontally or vertically, it is customary to assume
0.62 as the ratio of the actual to the theoretical volume of
CIRCULAR, AND OTHER FORMS OF JETS.
211
discharge. This makes the equation for ordinary calcu-
lations :
Q = 2SVZgH, or Q = .62SV. (5)
The expression for effect of acceleration of gravity
toeing a constant quantity, may be combined with the co-
efficient, when (.62 V2g = 4.9725) we have the equation
Q = 4.9725/S VTl, or approximately, Q = 5.
(6)
Q being the discharge in cubic feet in one second, it will be
multiplied by 60 to determine the discharge in one minute.
and by 3600 to determine the discharge in one hour.
222. Circular, and other Forms of Jets. A cir-
cular aperture, with full contraction, gives a jet always
circular in section, until it is broken up into globules by
the effects of the varying velocities of its molecules and the
resistance of the air. Through the vend conlractd its form
is that of a truncated conoid.
Polygonal and rectangular orifices give jets that continu-
ally change their sectional forms as they advance.
Fig. 22, from D'Aubuisson's Treatise on Hydraulics,
illustrates the transformations of
forms of a jet from a square orifice,
AC EG. The jet is square at the
itrance to the aperture, assumes
the form bcdefgha a short distance
front of it, and the form a'c'e'g' a
short distance further on, and con-
tinues to assume new forms until
its solidity is destroyed. Symmetrical orifices, without re-
entrant angles, give symmetrical jets that assume symmet-
rical, varying sections.
Star-shaped and irregular orifices, upon close observa-
212
FLOW OF WATER THROUGH ORIFICES.
tion, are found to give very complex forms of jets. Their
coefficients of efflux have not been fully developed by ex-
periment.
223. Cylindrical and Divergent Orifices. In Fig.
23 and Figi 24 showing cylindrical and divergent orifices,
if the diameters, is, of the orifices, are greater than the
FIG. 23.
FIG. 24.
FIG. 25.
FIG. 26.
thickness of the partitions, the coefficients of discharge will
remain the same as in thin plate. In such cases the jets
will pass through the orifices without touching them, ex-
cept at the edges, is. Such orifices are also termed thin.
224:. Converging Orifices. -In Fig. 25 and Fig. 26,
showing converging orifices in thin partitions, if the diam-
eters, is, are taken, the coefficients will be reduced to .58, or
a little less ; bat if the diameters, ot, are taken, the co-
efficients will be increased nearly to .90, and will be greater,
for any given velocity, in proportion as the forms of the
orifices approach to the form of the perfect wnd contractd,
for that velocity.
When the converging sides of the orifice in Fig. 25, pro-
longed, include an angle of 16, the coefficient should be
about .93, and when in Fig. 26 the sides of the orifice are in
the form of the vend contractd, the coefficient should be
about .95..
V
CHAPTEE XII.
FLOW OF WATER THROUGH SHORT TUBES.
225. An Ajutage. If a cylindrical orifice is in a parti-
tion whose thickness is equal to two-and-one-half or three
times the diameter of the orifice ; or if the orifice is a tube
of length equal to from two and one-half to three interior
diameters, then the orifice is termed a short tube, or ajutage.
The sides of short tubes may be parallel, divergent, or con-
vergent.
226. Increase of Coefficient. There is an influence
affecting the flow of water through short cylindrical tubes,
Fig. 28, sufficient to increase the coefficient materially, that
does not appear when the flow is through thin partition.
The contraction of the jet still occurs as in the flow through
thin partition, but after the direction of the particles has
become parallel in the vend contracta, a force acting from
the axis of the jet outward, together with the reaction from
the exterior air, begins to dilate the section of the jet and
to fill the tube again. The tube is in consequence again
filled at a distance, depending upon the ratio of the velocity
to the diameter, of about two and one-half diameters from
the inner edge of the orifice. The axial particles of the jet,
not receiving so great a proportion of the reaction from the
edges of the orifice as the exterior particles, obtain a greater
velocity. A portion of their force is transmitted to their
surrounding films through divergent lines, and the velocity
of the exterior particles within the tube is augmented, and
the section of the jet is also augmented, until its circumfer-
214 FLOW OF WATER THROUGH CHORT TUBES.
ence touches the tube. At the same time, the transmission
of force from the axis toward the circumference tends to
equalize the velocity of the particles throughout the section,
and to materially reduce their mean velocity, and conse-
quently the coefficient of velocity, c v .
227. Ajutage Vacuum and its Effect. Immedi-
ately upon the issue of the jet, beyond the contraction, the
velocity of the particles tends to impel forward the impris-
oned air, and as soon as the tube fills to cause a vacuum*
about the contraction. The full force of gravity is here act-
ing upon the jet in the form of velocity ; the jet is therefore
without pressure in a transverse direction.
As soon as the exterior of the jet is relieved from the
pressure of the atmosphere about the contraction, its par-
ticles are deflected to parallelism with less force and in a
shorter distance from the entrance to the aperture, and the
contraction is consequently lessened ; also the pressure of
the atmosphere upon the reservoir surface tends to augment
the velocity of entry of the particles into the aperture
toward the vacuum, and atmospheric pressure equally
resists the issue of the jet, the combined effect resulting in
the expansion of the jet.
22S. Increased Volume of Efflux. If the cylin-
drical tube terminates at the point where the moving par-
ticles reach the circumference and fill the tube, and
before the reaction from the roughness of the interior of
the tube has begun sensibly to counteract the accelerating
force of gravity, the capacity of discharge is then found to
be increased about twenty-five per cent., and the mean co-
efficient becomes .815 approximately, or if the tube projects
* If the inside of a smooth divergent tube is greased, so as to repel the par-
ticles of water and prevent contact, the vacuum cannot take place.
DIVERGENT TUBE.
215
into the reservoir, .72, instead of .62, as in the orifice in thin
plate. We have now for the volume of water discharged,
in cubic feet per second,
Q = .815 8 V2g&, orQ = .815 8 V, or Q = 6.54 8 VH. (1)
If the section of the tube is expressed in terms of the
diameter, in feet or fractional parts of feet, then since S =
.7854d 2 , the equation will become
Q = 6.54 (.
VH=
(2)
229. Imperfect Vacuum. If the tube is of less
length than above indicated, so that the vacuum is not
perfect, the conditions of flow and the coefficient will be
similar to that through thin plate ; and if the tube is length-
ened, the flow will be reduced by reaction from the interior
of the tube, in which case the tube will be termed a pipe.
FIG. 29.
FIG. 30.
23O. Divergent Tube. When a short divergent tube,
'ig. 29, is attached by its smaller base to the inside of a
plane partition, the phenomena of discharge will be similar
to that through an orifice in thin plate, unless a vacuum
shall be established about its contraction, as in the case of
216 FLOW OF WATER THROUGH SHORT TUBES.
short cylindrical tubes. This can only occur when the
divergence is slight, or the velocity great.
For ordinary cases, the mean coefficient of discharge
through square-edged divergent tubes may be taken as .62,
but it is subject to considerable variation in tubes of small
divergence, as the divergences, the ratio of length to diam-
eter, and the velocity of flow or head varies.
When a vacuum takes place in a divergent tube, the
discharge exceeds that from a cylindrical tube with diam-
eter equal to the smaller diameter of the divergent tube,
and the coefficient of volume may then even become greater
than unity.
231. Convergent Tube. When a short, convergent
tube. Fig. 30, is attached by its larger base to the inside of
a plane partition, and its coefficient of flow with a perfect
vacuum is determined for its diameter of entrance, as above
in the cases of thin plate, cylindrical and divergent tubes,
then the coefficient of volume will be found to decrease as
the angle of convergence increases.
Contraction will take place as in thin plate, until the
angle of convergence, that is, the included angle between
the sides produced, exceeds 13, and a vacuum will also be
produced ; but the exterior of the jet will reach the inner
circumference and fill the tube at a shorter distance from
the point of least contraction, as the angle increases, and
the augmenting effect of the vacuum will be reduced.
232. Additional Contraction. There is always an
additional contraction just after the exit of the jet from
convergent tubes.
The coefficient of discharge will remain in excess of the
coefficient for thin plate until the second contraction equals
that in thin plate, after which the coefficient will be less
than for thin plate.
COEFFICIENT OF SMALLER DIAMETER.
217
233. Coefficients of Convergent Tubes. In the
following table are given the coefficients of discharge for
the larger and the smaller diameters, also of the velocity,
for several angles of convergence. The table is based upon
careful experiments by Castel. The length of the tube was
2.6 diameters, and the smaller diameter and length of tube
remained constant.
TABLE No. 48.
CASTEL'S EXPERIMENTS WITH CONVERGENT TUBES.
Smallest diameter = .05085 feet.
Angle of convergence.
Larger diameter.
Smaller diameter.
Velocity.
Coefficient.
Coefficient.
Coefficient.
0'
0.829
0.829
0.830
1 36'
.809
.866
.866
3 TO'
.786
.895
.894
4 10'
.771
.912
.910
5 26'
747
.924
.920
7 5*
.691
.929
-931
8 58'
.671
934
.942
10 20'
.647
.938
95
12 4
.611
.942
955
13 24'
597
.946
.962
14 28'
577
.941
.966
16 36'
-545
.938
.971
19 28'
.501
.924
.970
21 0'
.480
.918
.971
23 o'
457
.913
974
2 9 5 8'
59
.896
975
40 20'
3i9
.869
.980
48 50'
.276
.847
.984
The coefficients for the larger diameter have been com-
puted from the remaining data of the table for insertion
here.
234. Increase and Decrease of Coefficient of
Smaller Diameter. When the coefficient of volume is
FIG. 31.
218 FLOW OF WATER THROUGH SHORT TUBES.
determined for the smaller diameter, or issue of a short,
convergent tube, the coefficient is found to increase from
that for cylindrical tubes at angle to an angle of about
13 30', when, under the conditions upon which Castel's
table was based, it has increased from .83 to .95. After-
wards, the coefficient gradually reduces, until at 180 it
becomes .62, as in thin plate.
235. Coefficient of Final Velocity The coefficient
of final velocity of issue gradually increases as the angle of
convergence increases, until it rises from .83* at angle to
nearly unity at angle 180 ; but that, for angles less than
13, is not the true coefficient of
velocity, since it refers to the ve-
locity of issue at the end of the
tube, instead of in the contrac-
tion.
236. Inward Projecting
Ajutage. When an orifice, or
the entrance of a short tube, is
projected into the interior of a
reservoir, as in Fig. 31, the angle
of approach of the particles be-
comes greater than when the orifice is in plane partition,
and the contraction becomes still more marked. Borda,
when experimenting with such a tube, in which the vacuum
was not perfected, found the coefficient to be .515. This
coefficient may be considered as an extreme minimum.
237. Compound Tube. When two or more of the
short tubes above described are joined together endwise
into one tube, as in Fig. 32, the new tube thus formed is
termed a compound tube.
* Its mean velocity, in a cylindrical tube, after the jet has expanded beyond
the contraction.
COEFFICIENTS OF COMPOUND TUBES.
FIG. 32.
219
Venturi experimented with various forms and propor-
tions of compound tubes, and observed remarkable results
produced by certain of them, which apparently augmented
the force of gravity.
With a tube similar to Fig. 32, but with less perfect
contraction, having the included angle of the divergent tube
equal to 5 6', the smallest diameter equal to 0.1109 feet,
and the length equal to nine diameters, the coefficient, com-
puted for the smallest diameter, when flowing under a con-
stant head of 2.89 feet, was 1.46, or about 2.4 times that of
an equal orifice in thin plate. *
238. Coefficients of Compound Tubes. Other forms
of compound tubes, with conical diverging ajutages of dif-
ferent lengths and angles, gave results as follows :
TABLE No. 49.
EXPERIMENTS WITH DIVERGENT AJUTAGES.
AJUTAGE.
COEFFICIENT.
AJUTAGE.
COEFFICIENT.
Angle.
Length.
Angle.
Length.
3 30'
4 38'
4 38'
4 38'
5 44'
Feet.
0.364
1.095
1.508
1.508
0-577
0-93
I.2I
1. 21
1-34
1.02
5 44'
10 16'
10 16'
14 14'
Feet.
193
.865
.147
.147
.82
.91
.91
.61
220
FLOW OF WATER THROUGH SHORT TUBES.
239. Experiments with Cylindrical and Coin-
pound Tubes. The following table gives interesting re-
sults of experiments by Eytelwein with both cylindrical
and compound tubes.
He first experimented with a series of cylindrical tubes
of different lengths, but of equal diameters ; he then placed
between the cylindrical tubes and the reservoir a conical
converging tube of the form of the verid contractd, and
repeated the experiments ; and afterwards added also to
the discharge end a conical diverging tube with 5 6' angle,
Fig. 33.
FIG. 33.
TAB LE No. 5O.
EXPERIMENTS WITH COMPOUND TUBES.
Length of tube P in
diameters.
Length of tube P
in feet.
Coefficient for
tube P.
Coefficient for
tube CP.
Coefficient for
tube CPD.
0.038
0.0033
O.62
I.OOO
0853
.62
.967
....
3.000
2559
.82
943
I.I07
12.077
1.0302
77
.870
.978
24.156
2.0605
73
.803
905
36.233
3.0907
.68
.741
.836
48.272
4.1176
63
.687
.762
60.116
5- T 479
.60
.648
.702
The diameter of the tube P was 0.0853 feet, and the flow
took place under a computed average head of 2.3642 feet.
The mean head was computed by the formula,
PERCUSSIVE FORCE OF PARTICLES.
(3)
in which ^T= maximum head, 7i = minimum head, H'
mean head.
24:0. Tendency to Vacuum. The effect of the per-
cussion of the axial particles, tending to produce a vacuum,
and of the enlargement of the circumference of the jet in Z>,
is apparent until the length reaches thirty-six diameters,
and is greatest at three diameters length, though still less
than with Fig. 28, because the surface of contact of the jet
against the tube is greater.
241. Percussive Force of Particles. The percus-
sive effect of particles of water in rapid motion is illustrated
by another experiment of Ventu-
ri's, with apparatus similar to
Fig. 34.
A is a high tank kept filled
with water, and C is a smaller
tank at its base, full of water at
the beginning of the experiment.
P is an open-topped pipe placed
in the small tank, and has holes
pierced around its base, so that
the water in C may enter it freely
and rise to the level c. From A a small tube, e, leads a jet
into P.
Upon the tube e being opened, the whole body of water
in P is set in motion and begins to flow over its top, and the
body of water in C is drawn into the pipe P through the
perforations, and the surface of C will be seen to fall grad-
ually from c to d, until air can enter through the perfora-
tions and destroy the partial vacuum in P.
222 FLOW OF WATER THROUGH SHORT TUBES.
For a clear conception of the effect of the particles of the
jet upon the particles in P, imagine all the particles and
the apparatus to be greatly magnified, so that there will
appear to be a jet, e, of balls, like billiard balls, for illus-
tration, through a mass, P, of similar balls.
242. Range of a Set of Eytelwein's Experiments.
In the last table (No. 50), there appears the mean coef-
ficients due to several distinct classes of apertures, viz. :
0.62 due to a tube orifice or orifice in thin plate, with length
equal to 0.038 diameters ; 0.82 due to a sJiort cylindrical
tube, with length equal to 3 diameters ; 0.943 due to lessened
contraction by the convergent entrance, with length equal
to 3 diameters ; and 1.107 (which in more perfect form of
compound tube we have found to be 1.46) due to convergent
entrance and divergent exit, with length equal 3 diameters.
There also appears the increase of coefficient from orifice
to short tube, and then the gradual reduction of all the
coefficients by increase of length of tube (into pipe) from 3
to 60 diameters long.
These phenomena cannot fail to be of interest to students
in that branch of natural philosophy which relates to hydro-
dynamics, and the practical hydraulician cannot afford to
overlook their effects.
243. Cylindrical Tubes to be Preferred. There is
rarely occasion for the practical and honest use of the
divergent tube, when its object cannot better be accom-
plished by a slightly increased diameter of cylindrical tube.
The capability of the divergent ajutage to increase the dis-
charge from a given diameter of orifice, was known to the
ancient philosophers, and to some of the Roman citizens who
had grants of water from the public conduits, andD'Au-
buisson states that a Roman law prohibited their use within
52 J feet of the entrance of the tube.
CHAPTER XIII.
FLOW OF WATER THROUGH PIPES, UNDER PRESSURE.
244. Pipe and Conduit. A cylindrical tube intended
to convey water under pressure is termed a pipe when its
length exceeds about three times its interior diameter ; or
immediately after its length has become sufficient for the
completion of the vacuum about the jet flowing into it.
A long pipe constructed of masonry is termed a conduit,
and when it is a continuous tube, or composed of sections
of tubes with their axes joined in one continuous line and
adapted to convey water under pressure, it is termed a main
pipe, sub-main, branch, waste, or service pipe, according
to its office.
245. Short Pipes give Greatest Discharge. The
greatest possible discharge through a cylindrical tube, due
to a given head, occurs when its length is just sufficient to
allow of the completion of the vacuum about the contrac-
tion of its jet at the influence, if its influent end is then
sufficiently submerged to maintain the pipe full at the
issue.
In the discussion of short tubes ( 228), we have seen
that their coefficient of discharge is increased from 0.62
(that for thin plate) to a mean of 0.815. There is still a loss
of eighteen per cent, of the theoretical volume, due chiefly
to the contraction of the vein at its entrance to the tube,
from which results a loss of velocity and a loss of energy as
the jet expands to fill the tube.
224 FLOW OF WATER THROUGH PIPES, UNDER PRESSURE.
LOSS OF FORCE, OR EQUIVALENT HEAD, AT
THE ENTRANCE TO A PIPE.
246. Theoretical Volume from Pipes. Let J., Fig.
35, be a reservoir containing water one hundred feet deep =:
H, to the level of its horizontal effluent pipe, P. Let the
pipe P be one foot in diameter = d.
Then the theoretical volume of discharge will equal
V%gH x .7854^ 2 = 63.028 cubic feet per second ; but when
the pipe is three diameters long (= 3 feet), the real discharge
according to experiment, will be
Q = .815 VtySx .7854^ a ,
(1)
= 51.40 cubic feet per second.
FIG. 35.
1000. feet*
Let V represent the theoretical velocity ; then will the
total head H = ^~ = 100 feet
<*9
Let v represent the measured velocity of discharge, and
h the head necessary to generate 0, then A =
MECHANICAL EFFECT OF THE
247. Mean Efflux from Pipes. The section of the jet,
having expanded beyond the contraction issues with a diain- r
eter equal to that of the tube, and the coefficient of velocity,
<?, is consequently equal to the coefficient of discharge, c,
which is, at a mean, .815 and the theoretical velocity V =
= 80.25 feet per second.
248. Subdivision of the Head. The total head ff y
acting upon a short cylindrical tube, consists of two por-
tions, one of which generates D = .815 V= 65.4 feet per
second. The other portion, capable of generating -r*
v 14.85 feet per second, acts in the form of pressure to
overcome the resistance of entry of the jet into the tube.
Let 7i' represent this force.
02
The head due to v is 7i = 5- , =66.5 feet in the above as-
sumed case.
The head due to - - ois *'=
(1 - l) | = 33.5 feet. ' . . .^
The ratio of h' to 7i is therefore ( t l) = .5055 for this
\c '
c v
case, and (7i + h') = (h + .5055 h) = H.
249. Mechanical Effect of the Efflux. Since the
dynamic force of the jet is as the effective head acting upon
it, the loss of .505 of Ti is a matter of importance, espe-
cially in cases of short pipes.
The theoretical velocity being = -^TK, the theoretical
energy of the jet, under the same assumed conditions, is -~-~- 3
2
x ^- x Q x w = 321250 foot pounds per second = 584.09
15
226 FLOW OF WATER THROUGH PIPES, UNDER PRESSURE.
H.P. ; w representing the weight in pounds (= 62.34) per
cubic foot of the water, and Q the volume or quantity of
water in cubic feet per second.
The energy E, due to v, is expressed by the equation,
= 213631.2 foot pounds per second = 388.42 H.P.
The loss of energy from the quantity of water Q during
the efflux in one second, being proportionate to the loss of
head, is,
' x |/) 4) X QW = (c* ~~ X )^ X W ' (3)
107618.75 foot pounds per second = 195.67 HP.
25O. Ratio of Resistance at Entrance to a Pipe.
The ratio, .505 of 7i' to h, is very nearly a mean for tubes
whose edges are square and flush in a plane partition. If
the entrance of the tube is well rounded in trumpet-mouth
form, corresponding to the form of the vend contractd, the
coefficient of velocity c v will be increased to about .98, and the
ratio of resistance will become f-^ l) = .0412, equal in
this case (Fig. 35) to about four feet head, and the head
that can be made available for work will equal ninety-six
feet.
The disadvantage of the square edges, as respects both
volume and dynamic force, is apparent. This resistance of
entry of the jet into a tube, whose ratio of head we have
determined, is force, or its equivalent head irrecoverably
lost. Its maximum for a given head occurs when the tube
is about three diameters long, the velocity being then at its
maximum, and thereafter its value is reduced as the pipe is
lengthened, and with the square of the velocity.
COEFFICIENTS OF EFFLUX FROM PIPES.
227
RESISTANCE TO FLOW WITHIN A PIPE.
251. Resistance of Pipe-wall. We have heretofore
considered the whole head H as applied to and entirely
utilized in overcoming the resistance of entry of the jet into
the pipe, and in generating the velocity among the particles
of the jet.
We will now consider the resistances within the pipe and
its appendages, and the portion of the velocity that must be
converted into pressure or dynamic force to overcome them.
252. Conversion of Velocity into Pressure. If
the pipe P, Fig. 35, of three diameters length, "be extended
as at P', a new resistance arising within the added length
acts upon the jet and again reduces the volume of flow. A
portion of the velocity of the jet is converted into pressure
or dynamic force, and is applied to overcome the resistances
presented within the pipe, and the proportion of the velocity
thus consumed is almost directly proportional to the length
added of the pipe, of the given diameter.
253. Coefficients of Efflux from Pipes. The effects
upon the volume of discharge through a given pipe conse-
quent upon varying its length will be apparent upon inspec-
tion of a table of coefficients of efflux, c, due to its several
lengths respectively.
We will assume the pipe to be one foot diameter, of
clean cast iron, when the coefficients determined experi-
mentally have mean values about as follows :
' TABLE No. 51.
COEFFICIENTS OF EFFLUX (c) FOR SHORT PIPES.
Lengths, in diameters . .
i
5
10
25
50
75
100 125
150
175
200
285
250
275
3 00
Coefficients (c)
.62
.792
.770
.714
.643
.588
.548 .5"
485
.462
.440
.420
405
.386
.378
228 FLOW OF WATER THROUGH PIPES.
Plotted as ordinates, beginning with the theoretical
coefficient, unity, they range themselves as in Fig. 36.
013.5 10 25 5O 75 100 425 50
254:. Reactions from the Pipe-wall. A fair sam-
ple of ordinary pipe casting, a cement-lined, lead, or glazed
earthenware pipe are each termed smooth pipes, but a good
magnifying lens reveals upon their surfaces innumerable
cavities and projections.
The molecules of water are so minute that many thou-
sands of them might be projected against and react from a
single one of those innumerable projections, even though it
was inappreciable to the touch, or invisible to the naked
eye.
A series of continual reactions and deflections, originated
by the roughness of the pipe, act upon the individual
molecules as they are impelled forward by gravity, and
materially retard * their flow.
In a given pipe, having a uniform character of surface,
the sum of the reactions, for a given velocity, is directly as
* The resistance was, by the earlier philosophers, attributed chiefly to the
adhesion of the fluid particles to the sides of the pipe, and to the cohesion
among the particles. Vide Downing, who accepts the views of Du Buat, D'Au-
buisson, and other eminent authorities. Practical Hydraulics, p. 200. Lon-
don, 1875.
FORMULA OF RESISTANCE TO FLOW. 229
its wall surface, or as the product of the inner circumfer-
ence into the length. Since in a pipe of uniform diameter
the circumference is constant, the sum of the reactions is
also directly as the length.
The impulse of the flowing particles, and therefore their
reactions and eddy influences, are theoretically proportional
to the head to which their velocity is due, which is propor-
tional to the square of the velocity, or, in general terms, the
effective reactions are proportional nearly to the square of
the velocity.
The resistances arising from the interior surface of the
pipe are, therefore, not only as the length, "but as the
square of the velocity, nearly.
The effect of the resistances is not equal upon all the
particles in a section of the column of water, but is greatest
at the exterior and least at the centre, or, in a given section,
approximately as its circumference divided ~by a function
of its area.*
255. Origin of Formulas of Flow. These simple
hypotheses constitute the foundation of all the expressions
of resistance to the flow of water in pipes, as they appear in
the varied, ingenious, and elegant formulas of those emi-
nent philosophers and hydraulicians who have investigated
the subject scientifically.
256. Formula of Resistance to Flow. Place R to
represent the sum of all the resistances arising from the
circumference of the pipe (excluding those due to the entry);
C for the contour or circumference of the pipe, in feet ; 8 for
the section of the interior of the pipe, in square feet ; I for
the length of the pipe, in feet ; and v for the mean velocity
* The law cf the effects of the resistances is believed to have been first for-
mulated in the simple algebraic expressions now in general use, by M. Chezy,
^about the year 1775.
230 FLOW OF WATER THROUGH PIPES.
of flow, in feet per second. Then the resistance to flow is
expressed by the equation
R = *JL x I x (m) &. (4)
257. Coefficient of Flow. In the equation a new
coefficient m appears, which also is to be determined by
experiment. It is not tb be confounded with the c hereto-
fore investigated, but will hereafter be investigated inde-
pendently.
258. Opposition of Gravity and Reaction. We
have seen that gravity ( 189) is the natural origin and the
accelerating force that produces motion of water in pipes.
Its effect, if no resistance was opposed, would be to con-
tinually accelerate the flow. On the other hand, if its effect
was removed, the resistances would bring the column to a
state of rest.
The two influences oppose each other continually, and
therefore tend to the production of a rate of motion in which
they balance eacji other.
259. Conversion of Pressure into Mechanical
Effect. When the motion has become sensibly constant,
a portion of the effect of gravity that appeared as velocity
in the cases of orifices and short tubes, or its equivalent in
the form of pressure or head, has been converted into
dynamic force and is acting to overcome the resistances,
and the remaining force due to gravity or head is producing
the velocity of flow then remaining.
260. Measure of Resistance to Flow. The effect
of the resistance along a main pipe, when discharging
water from a reservoir, as in Fig. 37, may be observed by
attaching a series of pressure gauges at intervals, or by at-
taching a series of open-topped pipes, as at p p l p^ etc.
RESISTANCE INVERSELY.
231
If the end/ of the pipe is closed, water will stand in all
the vertical pipes at the same level, oik, as in the reservoir.
If the diameter of the pipe is uniform throughout its
length, and the flow, the full capacity of the pipe, then
water will stand in the several vertical pipes up to the in-
clined line a'f; provided that the top of p 2 be closed so that
there may be a tendency to vacuum at n, and provided also
that n is not more than thirty feet, or the height to which
the pressure of the atmosphere can maintain the pipe full,
above the line a'f, at n'.
When / is an open end discharging into air, and the
vacuum at n is not maintained, a'n will be the total effec-
tive head, and the portion of the pipe nf will be only parti-
ally filled.
261. Resistance Inversely as the Square of the
Velocity. If the discharge of the pipe is throttled at /, by
a partial closing of a valve, by a contraction of the issue, or
by diversion of the stream into other pipes of less capacity,
and a portion of the velocity is in consequence converted
into pressure equivalent to the head//, then the resistance
will be lessened as the square of the velocity decreases, and
water will stand in the vertical pipes, or the gauges will in-
dicate the inclined line a"f. This is the usual condition of
mains in public water supplies.
232
FLOW OF WATER THROUGH PIPES.
262. Increase of Bursting Pressure. One effect of
throttling the discharge is seen to be an increase of bursting
pressure upon the pipes, which is greater when the exit is
entirely closed than when there is a constant flow, and which
decreases as the velocity increases, though a sudden clos-
ing of a valve against a rapid current will probably prove
disastrous to an ordinary pipe that is fully able to sustain
a legitimate pressure due to the head.
263. Acceleration and Resistance. Let db (Fig. 38)
be a vertical pipe discharging water from a reservoir A,
maintained always full. If, before the water entered the
FIG. 38.
pipe, a single particle had been dropped into its centre from
a, the velocity of movement of the particle would, in conse-
quence of the effect of gravity upon it, have been constantly
accelerated through its whole passage along the axis.
DESIGNATION OF h" AND I. 233
Its velocity, when it had reached 6, would have been
equal to V%gH, when H represents the vertical height ab
in feet.
The greater the height ab the greater the sum of the ac-
celerations by gravity, and also, if the pipe is flowing full,
the greater the length a'b the greater the sum of the resist-
ances acting upon the column of water to retard it.
264. Equation of Head Required to Overcome
the Resistance. Let v be the velocity of the jet issuing
from b, li the head due to #, and h" the head acting upon
the resistance, R.
Then the amount of the force of gravity, or equivalent
head, ^", converted into dynamic force in each second to
overcome the resistances within the length of pipe traversed
by the jet in one second = ~- x I x ~-, and we have the
equation,
,., mO 7 tf
A= ir xZx ^- < 5 >
representing the resistances overcome per second for the
given head and in the given length.
265. Designations of h" and I. In long pipes the
total head, H= h + h' + h".
The head, or charge of water h" acting upon the resist-
ances, is the vertical height of the surface of the reservoir,
less the height aa" = h (Fig. 38), necessary to generate the
velocity v, and also less the height a" a' = h' necessary to
overcome the resistance of entry, above the centre of the dis-
charging jet at the exit ; or if the discharge is into another
body of water, above the surface of the lower body.
The length I to be taken, is the actual length of the axis
of the pipe.
Then whatever the position or direction of the pipe a'b,
234 FLOW OF WATER THROUGH PIPES.
or a'f, or if, or onf (abstracting for the present any resist-
ance of curvature), we have for its dynamic equation of re-
sistance to the force of gravity,
Clm tf Clm .,
71 ~S~ x 2g = ~S~ x ^ ^ ^
unless, in the case of a pipe discharging near to its full capa-
city, an upward curve, n, shall rise more than thirty feet
above the line of hydraulic mean gradient a'f, when 7i" is
to be taken in two sections, first from a' to n vertically, and
second from n to f vertically reduced by the effect of the
vacuum, if any, or as a simple channel without pressure if
the length nf does not fill.
266. Variable Value of m. In the equation
,. Cl tf
we have the coefficient m, whose several values are to be
deduced from actual measurements of the flow of water
through pipes, and whose governing conditions are to be
closely observed and studied.
The physical conditions of various pipes are so different
that special coefficients are required for each class of con-
ditions.
A slight increase in the roughness of the interior surface
of the pipe, occasional sudden enlargements or contractions
of the diameter of the pipe, and sudden bends in the direc-
tion of the pipe, may be instanced as sufficient departures
from the conditions of straight pipes with uniform diameters
and surfaces to materially modify the value of its coefficient
of flow.
267. Investigation of Values of m. For the de-
termination of a series or table of coefficients, m, for full
DEFINITION OF SYMBOLS. 235
pipes, we will select data from published tables of* exper-
iments by Henry Darcy, made while he was director of the
public water service of the city of Paris ; fromf experiments
by Gfeo. S. Greene, made while chief engineer of the Croton
Aqueduct Department of New York city ; from experiments
by Geo. H. Bailey, Esq., made while chief engineer of the
Jersey City Water- works ; from some of the famous exper-
iments of Du Buat, Couplet, and Bossut, which furnished
the chief data for the elegant formulas of those eminent
philosophers, as well as those of PronyJ and Eytelwein,
and from several other sources.
68. Definition of Symbols. By transposition we
have
o $ h 1 /~\
m = g x C x T x If W
The member -=- is the ratio of the height which the par-
(/
tides fall through in the given length, equal = S__, or the
Jpngtn ^ ,
sine of the angle of inclination Tea 1 /, Fig. 38. The inclina-
tion a'fis termed the "slope," or the hydraulic mean gra-
dient, and is usually designated by the letter i. The point
a 1 is always beneath the surface of the water a depth aa'
necessary to generate the velocity v in the pipe, and to
overcome the resistance of entry, whether the pipe be in the
position a'f, if, or onf.
The depth aa' varies as the velocity varies, and the
"slope" i corresponds to an imaginary right line connect-
ing the points a 1 and/.
* Recherches experimentales relatives au movement de 1'eau dans le
tuyaux. Paris, 1857.
f Descriptive Memoir of the Brooklyn Water-works, by James P. Kirk-
wood. Van Nostrand, N. Y., 1867.
\ Vide Recherches Physico-Mathematiques sur la Theorie du Mouvement
des Eaux Courantes, 1804.
236 FLOW OF WATER THROUGH PIPES.
The member -^, as now inverted ( 256) refers to the
c
ratio of the section to the contour of the given pipe, or to the
sectional area T , . -, ,, ,.
- r It is termed the "mean radius*" or. in
wetted perimeter
the cases of pipes and channels partially filled, the hydrau-
lic mean depth, and is usually designated by the letter r.
The value of r for full pipes is always equal to one-fourth
of the diameter = , according to well-known properties of
the circle.
269. Experimental Values of the Coefficient of
Flow. We have then, as an equivalent for equation (7) :
(8)
EXPERIMENTAL COEFFICIENTS.
237
TABLE No. 32.
EXPERIMENTAL COEFFICIENTS (m) OF FLOW OF WATER IN Clean
PIPES, UNDER PRESSURE, m ?j = -~* -
ir
EXPERIMENTS BY H. DARCY (Cast-iron Pipes).
Diameter = </,
infect.
Head = h,
in feet.
Length = /,
in feet.
Velocity = v ,
in feet per sec.
Coefficient = m.
0.2687
O.O66
328.09
0.2885
.0104478
(t
1.742
tt
1.8399
.0067800
ct
3-347
(C
2.5946
.0065508
a
13.260
(t
5-i59
.0065850
u
39.299
tt
8.9242
.0065162
tt
56.011
tt
10.7115
.0064320
0.4501
0.079
328.09
0.4887
.0073054
a
.686
tt
i. 6021
.0059026
tt
1.558
tt
2.5021
.0054960
<(
54-975
tt
i5-39 2 9
.0051240
0.6151
0.089
328.09
0.6544
.0062884
u
1.207
tt
2.4991
.0058476
a
2.641
tt
3-7155
.0057898
a
4.369
tt
4.9045
.0055296
tt
12.500
tt
8.2564
.0055482
at
47.872
tt
16.2360
.0054948
0-975 1
0.092
328.09
0.7997
.0068802
tt
.883
tt
2.7134
.0057306
tt
1.762
tt
3-7863
.0058728
tt
3-625
tt
5.4039
.0059314
tt
7.562
tt
7.8330
.0058890
tt
13.473
tt
10-3575
.OO6OOIO
1.6427
0.148
328.09
1-3765
.0062950
tt
.148
tt
1.4685
0055310
tt
.197
tt
1-5549
.0065688
tt
394
tt
2-5954
.0047160
tt
.853
a
3.6637
.0051216
tt
.820
tt
3.6900
.0048536
238
FLOW OF WATER THROUGH PIPES.
TABLE No. 53.
EXPERIMENTAL COEFFICIENTS (m) OF FLOW OF WATER IN Clean
2ghS
Civ*
PIPES, UNDER PRESSURE, m
EXPERIMENTS BY THE WRITER (Wrought-iron Cement-lined
Pipe).
Diameter = </,
in feet.
Head = h,
in feet.
Length = /,
in feet.
Velocity = v.
in feet per sec.
Coefficient = m.
1.6667
1.86
8171.0
0.949
.006360
ft
3.60
tt
1.488
005335
((
5-93
ft
L9 2 5
.005251
8.48
((
2.329
.005347
{(
10.93
(e
2.598
005313
(6
12.91
((
2.867
005153
((
16.28
((
3.271
.004993
((
18.60
(C
3-439
.005160
((
22.22
tt
3-741
.005209
ft
24-54
(6
3.920
.005115
25.58
((
4.OO
.005110
(t
26.16
4.04
.005100
TABLE No. 84.
EXPERIMENTS BY DU BUAT (Tin Pipes).
0.0889
973
10.401
5- T 79
.004992
((
1.484
10.401
6-334
.005089
u
.0481
12.304
0.7717
.009393
((
375
12.304
2.606
.006424
tt
i. 220
12.304
5.220
.005207
t(
.013
65.457
0.1411
.014276
tt
1.022
tt
1-775
.007091
u
I -954 i
2.546
.006585
TABLE No. 5S.
EXPERIMENTS BY BOSSUT (Tin Pipes).
0.0889
o.33i
53-284
1.085
.001698
et
.976
86.094
1.979
.004142
.11841
.864
3L956
2-945
005943
it
2.066
191.840
1.679
.007282
tt
1.699
3L956
4.308
.005461
.178
.765
3I-956
3-581
.005363
tt
2.019
191.840
2.196
.006270
tt
1.892
95-95
2.250
.011190
tt
1.491
31.956
5-230
.004901
EXPERIMENTS COEFFICIENTS.
239
TABLE No. 56.
EXPERIMENTAL COEFFICIENTS (m) OF FLOW OF WATER IN Clean
2ghS
PIPES, UNDER PRESSURE, m =
Civ*
EXPERIMENTS BY COUPLET (Iron Pipes).
Diaameter = </,
in feet.
Head = k,
in feet.
Length = /,
in feet.
Velocity = ,
in feet per sec.
Coefficient = m.
0.4439
0.492
7481.88
0.1785
.001475
tt
1.005
7481.88
.2802
.012230
4374
1.484
7481.88
.3665
.010390
ft
1.670
ft
.4258
.008667
a
2.130
tt
.4640
.009309
ft
2.215
tt
.4728
.009323
1.5988
12.629
3836.66
3-4779
.007004
TABLE No. 57.
EXPERIMENTS BY W. A. PROVIS. (Lead Pipes.)
0.125
2.91666
20.00
6.1495;
.006465
ft
"
40.00
4.7588
.005398
"
((
60.00
3.9032
.005360
"
a
80.00 3-396I
.005287
(i
((
100.00
3.0897
.005122
TABLE No. 58.
EXPERIMENTS BY RENNIE.
With glass pipes slightly rounded at the ends.
0.0020833
I.O
I.O
7.1627
.000653
tt
2
tt
10.4196
.000408
ff
3
"
12.9409
.000601
tt
4
ft
14.6240
.000627
.0041666
I.O
I.O
5-6450
.001672
tt
2
tt
8.3676
.001916
"
3
"
10.0497
.001992
tt
4
"
11.6000
.001994
.00625
1.0
I.O
5-5487
.004162
ft
2
tt
8.1852
.004814
tt
3
ft
9-855 I
.003956
tt
4
ft
10.8320
.004378
.00833
I.O
I.O
6.1028
.004584
tt
2
ft
8.5386
.004684
3
ft
10.8003
.004392
tt
L
4
ft
13.0400
.004016
240
FLOW OF WATER THROUGH PIPES.
TABLE No. 59.
EXPERIMENTAL COEFFICIENTS (m) OF FLOW OF WATER IN Old
x i.r.no, UIN-U.EJK. JT KH/oa u K. n.. 7n ^,
EXPERIMENTS BY H. DARCY. (Foul Iron Pipes.)
Diameter = </,
in feet.
Head = h,
in feet.
Length = /,
in feet.
Velocity = ,
in feet per sec.
Coefficient = m.
0.1194
0.223
328.09
0.2669
.018342
tt
.600
tt
.4273
.OI92IO
et
2.198
"
.8291
018735
ft
5-03
ee
1.2494
.018784
((
10.630
ee
1.8079
.019055
te
13.632
ee
2.0772
.018511
0.2628
0.213
328.09
0.4040
.Ol68ll
"
.820
tt
.8242
.015551
"
2-379
ft
1.4645
.014288
((
5.282
66
2.2226
.013774
te
10.171
ee
3-05I7
.014082
ft
14.879
ee
3-7434
.013679
0.8028
0.308
328.09
i. 0080
.011934
tt
.663
ft
1.4824
.011878
a
i-SS 2
tt
2.3218
OII334
"
3-773
tt
3.6283
.011285
tt
7-5 J 3
tt
5.0727
.011494
tt
10.499
tt
6.0169
.011417
"
13.468
tt
6.8037
.011454
.6
45.870
tt
12.5779
.011415
TABLE No. 60.
EXPERIMENT BY GEN. GEO. S. GREENE, C. E.,
Upon a New York City cast-iron Main. (Tuberculated.)
3.0 | 20.215 | 11217.00 | 2.99967 .00966
1.6667
EXPERIMENT BY GEO. H. BAILEY, C. E.,
Upon a Jersey City cast-iron Main. (Tuberculated.)
I 28.1285 I 29715.00 I 1-43795 I .01228
EXPERIMENTAL COEFFICIENTS.
241
TABLE 6 O. (Continued.)
EXPERIMENTAL COEFFICIENTS (m) OF FLOW OF WATER IN Old
PIPES. UNDER PRESSURE, m
EXPERIMENT UPON THE COLINTON MAIN.*
Eight years in use.
Diameter = d,
in feet.
Head = h,
in feet.
Length = /,
in feet.
Velocity = z>,
in feet per sec.
Coefficient = m.
1-3334
tt
a
184
2 3
420
3815
25765
29580
14.500
5- 2 5 2
6.816
.004923
005556
.006559
LAMBETH WATER WORKS MAIN.
1.583
I
25
41
38
54120
2244O
52OO
1.772
2-734
4-353
.005918
.006229
.OO62O8
LIVERPOOL WATER WORKS MAIN.
I | 27 | 8140 | 2.644 | .007633
CARLISLE WATER WORKS MAIN.
I | 34.5 | 66OO | 3.568 .OO66lO
EXPERIMENTS BY THE WRITER.
With unlined wrought iron pipe (gas tubing), the jet entering through a stop-
cock and piston meter, with coefficient c = .58 when length = 0.25. The
pipe had been in use one week, but had rusted considerably.
0.08334
28.73
0.25
46.70
....
85.57
9
18.964
035467
98.34
735
4.850
.007636
96.38
1337
3.538
.007722
87.33
2040
2.722
.007746
* Vide Proceedings of Inst. Civ. Engineers, p. 4, Feb. 6th, 1855, London.
16
242
FLOW OF WATER THROUGH PIPES.
TABLE No. 6 1.
SERIES OF COEFFICIENTS OF FLOW (m) OF WATER IN CLEAN PIPES,
UNDER PRESSURE, AT DIFFERENT VELOCITIES, AND IN PIPES
OF DIFFERENT DIAMETERS, [m = -jrrr= -C-J.
\ Civ* v 2 I
VELOCITY.
DIAMETERS.
X inch.
.0417 /*.
K",
.0625'.
i"
.0834'-
i 1 //'
. 1250 .
*X"
.1458'.
2"
.1667'.
Feet per
Second.
Coefficient.
Coefficient.
Coefficient.
Coefficient.
Coefficient.
Coefficient.
.1
O.OI5O
O.OI3O
O.OII9
O.OIO7
O.0097O
0.00870
.2
.0143
.0126
.0116
.OIO5
.00952
.00860
3
.0137
.0123
.0113
.0103
.00937
.00850
4
OI 33
.0119
.0110
.OIOO
.00920
.00840
5
.0128
.OIl6
.0107
.00984
.00904
.00830
.6
.0124
.0113
.OIO4
.00960
.00890
.00822
7
.0120
.0111
.0102
.00940
.00873
.00813
.8
.0116
.OI08
.0100
.00922
.OO860
.00804
9
.0113
.OI05
.00972
.00910
.00850
.00798
1.0
.0110
.OIO2
.00950
.00893
.00840
.00790
i.i
.0107
.00995
.00933
.00880
.00826
.00783
1.2
.0104
.00973
.00913
.00867
.00817
.00776
*-3
.OIOJ
.00952 .00898
.00854
.00809
.O077O
1.4
.00992
.00930
.00882
.00843
.00800
.00763
'5
.00959
.00910
.00868
.00832
.00793 -00757
1.6
.00942
.00890
.00854
.00823
.00786
.00750
J -7
.00920
.00872
.00840
.00814
.00777
.00746
1.8
.00900
.00856
.00830
.00806
.00769
.00741
1.9
.00880
.00842
.O0820
.0080O
.00763
.00736
2.0
.00862
.00830
.Oo8lO
.00790
.00757
.00731
2.25
.00840
.00804
.00785
.00770
.00742
.OO72I
2-5
.00795
.00780
.00768
.00752
.00730
.OO7IO
2.75
.00775
.00761
.0075O
.00736
.00716
.O07OO
3-0
00753
.00745
.00734
.00722
.00707
.00692
3-5
.00732
.O0722
.OO7I2
.OO7O2
.00692
.OO680
4
.00722
.007IO
.OO7O2
.00692
.00682
.00671
5
.00704
.00693
.00684
.00675
.00664
.00654
6
.00689
.00678
.00670
.O066O
.00650
.00640
7
.00675
.00664
.00657
.00648
.00639
.00629
8
.00663
.00652
.00646
.00638
.00627
.00618
9
.00652
.00643
.00636
.00628
.00618
.00609
10
.00644
.00634
.00628
.OO620
.OO6IO
.OO6OI
12
.00630
.0062O
.00614
.00607
.00599
.00590
14
.00622
.00613
.OO6o6
.O0600
.00592
.00584
16
.00618
.00608
.0060O
00595
.00589
.00581
18
.00616
.00606
.00599
.00594
.00588
.00580
20
.00615
.00605
.00598
00593
.00587
.00579
COEFFICIENTS OF FLOW OF WATER.
243
TABLE No. 61 (Continued).
COEFFICIENTS OF FLOW (m) OF WATER IN CLEAN IRON PIPES
UNDER PRESSURE.
VELOCITY.
DIAMETERS.
3 inch
.250 feet.
4"
3333'-
6"
5'.
8"
.6667'.
10"
.8333'.
12"
!.</.
Feet per
Second.
Coefficient.
Coefficient.
Coefficient.
Coefficient.
Coefficient
Coefficient.
. I
O.OO80O
0.00763
0.00730
0.00704
0.00684
0.00669
.2
.00792
00755
.00724
.00698
.00678
.00662
3
.00784
.00750
.00720
.00693
.00673
.00657
4
.00780
.00742
.00713
.00688
.00668
.00652
5
.00774
.00737
.00708
.00682
.00663
.00648
.6
.00767
.00732
.00702
.00677
.00659
.00642
7
.00760
.00727
.00697
.00673
.00654
.00638
.8
.00754
.00722
.00693
.00668
.00651
00633
9
.00750
.00718
.00688
.00663
.00648
.00629
.0
.00743
.00712
.00684
.00659
.00643
.00624
. i
.00739
.00708
.00679
.00654
.00640
.0062O
.2
.00733
.00704
.00674
.00652
.00635
.00617
3
.00729
.00700
.00670
.00648
.00632
.00613
4
.00724
.00697
.00666
.00644
.00628
.Oo6lO
5
.00720
.00693
.00662
.00640
.00625
.00607
.6
.00716
.00690
.00658
.00637
.00622
.00603
7
.00712
.00687
.00655
.00633
.00618
.00601
.8
.00708
.00684
.00652
.00630
.00615
.00599
9
.00703
.00680
.00650
.00628
.00612
.00597*
2.
.00700
.00678
.00648
.00624
.00609
.00593 '
2.25
.00690
.00670
.00640
.00617
.00603
.00588
.2.50
.00683
.00662
.00634
.Oo6ll
.00596
.00581
2-75
.00675
.00655
.00629
.00605
.00590
00575
3-
.00670
.00650
.00623
.OO60O
.00584
00570
3-5
.00660
.00640
.00614
00593
00574
.00561
4-
.00651
.00631
.00607
.00586
.00568
00553
5-
.00636
.00618
.00594
00573
.00558
00543
6.
.00622
.00605
.00582
.00562
.00548
00534
7-
.00610
00595
.00572
.00552
.00540
.00527
8.
.00600
.00587
.00562
.00544
.00532
.00520
9-
593
.00578
00555
.00538
.00525
.00512
10.
.00585
.00572
.00549
.00530
.00520
.00508
12.
.00582
.00560
.00540
.00522
.OO5I2
.00500
'4-
00573
00554
00533
.00516
.00507
.00494
16.
.00570
.00552
.00530
.00513
.005O2
.00491
18.
.00576
.00550
.00528
.005IO
....
....
20.
.00566
.00549
244
FLOW OF WATER THROUGH PIPES.
TABLE No. 6 1 (Continued).
COEFFICIENTS OF FLOW (m) OF WATER IN CLEAN CAST-IRON
PIPES UNDER PRESSURE.
DIAMETERS.
VELOCITY.
14 inches
16"
18"
20"
24"
27"
1.1667 feet.
1-3333'-
i.5'.
1.6667'.
2.C/.
2.25'.
Feet per
Second.
Coefficient.
Coefficient.
Coefficient.
Coefficient.
Coefficient.
Coefficient.
. I
0.00650
0.00623
....
....
....
....
.2
.00644
.00619
O.OO6OO
0.00583
....
....
3
.00640
.00614
.00597
.00578 0.00548
0.00530
-4
.00634
.Oo6ll
.00592 | .00574 .00544
.00526
5
.00630
.00607
.00588 .00570 .00540
.00523
.6
.00625
.00603 .00584 .00567 .00537
.00520
7
.OO62I
.OO600 .00580 ! .00563
00533
.00517
.8
.00617
.00597 .00577
.00561
.00531
00513
9
.Oo6l2
00593 : .00573
.00558
.00528
.00511
.0
.00609
.00588 .00570
00555
.00525
.00508
. i
.00605
.00584
.00568
.00552
.00522
.00505
.2
.OO6OI
.00581
.00564
.00550
.00520
.00503
3
.00598
.00578
.00561
.00548
.00517
.00500
4.
00593
.00575
00559
.00545
.00514
.00498
5
.00590
.00572
00556
.00542
.00512
.00495
.6
.00587
.00569
00553
.00539
.00510
.00493
7
.00584
.00566
00551
.00536
.00508
.00491
.8
.00582
.00563
00549
"00534
.00506 .00489
-9
.00579
.00561
.00546
.00532
.00503
.00487
2.0
.00576
.00559
00543
.00529
.00501
.00485,
2.25
.00570
.00553
00538
.00524
.00497
.00480
2.50
.00564
.00548
00533
.00518
.00492
.00475
2-75
00559
.00543
.00528 i .00513
.00488
.00472
3-
00554
.00538
00523
.00509
.00483
.00468
3-5
00547
.00529
.00516
.00502
.00478
.00462
4-
.00540
.00524
.00511
.00498
.00473
.00458
5-
.00530
00515
.00501
.00490
.00466
.00451
6.
.00520
.00507
.00495
.00482
.00460
.00446'
7-
.00512
.00500
.00489
.00476
00453
.00440
8.
.00503
. 0049 1
.00483
.00470
.00450
.00435.
9-
.00498
.00489
.00478
.00466
.00445
.00431
10.
00493
.00483
.00473
.00462
.00443
.00429
12.
.00487
.00478
.00468
.00457
.00440
.00429
14.
.00482
.00473
.00463
.00452
.00434
.00422
16.
.00480
.00470 ! .00460
.00450
.00432
.00420
COEFFICIENTS OF FLOW OF WATER.
245
TABLE No. 61 (Continued).
COEFFICIENTS OF FLOW (m) OF WATER IN CLEAN CAST-IRON
PIPES, OR SMOOTH MASONRY, UNDER PRESSURE.
VELOCITY.
DIAMETERS.
30 inch
2.5' feet.
33"
2- 75'-
36''
3.<S.
40"
3-3333-
44"
3.6667'.
48"
4.0'.
Feet per
Second,
Coefficient.
Coefficient.
Coefficient.
Coefficient.
Coefficient.
Coefficient.
4
O.OO5JO
O.OO497
0.00476
....
....
...
5
.00507
.00492
.00473
0.00436
O.OO42O
O.OO4OO
.6
.00504
.00490
.00471
.00434
.00418
.00399
7
.O050I
.00488
.00469
.00432
.00416
.00398
.8
.00498
.00485
.00467
.00431
.00414
.00397
9
.00495
.00482
.00464
.00430
.00412
.00396
I.O
.00492
.00480
.00462
.00428
.OO4II
00395
i.i
.00490
.00478
.00459
.00426
.00410
.00394
1.2
.00488
.00475
.00457
.00424
.00409
.00393
i-3
.00486
.00472
00455
.00423
.00407
.00392
1.4
.00484
.00470
00453
.00422
.00406
.00391
i-5
.00482
.00468
.00451
.00421
.00404
.00390
1.6
.00480
.00466
.00450
.00400
.00403
.00388
i-7
.00477
.00464
.00448
.00419
.00402
.00387
1.8
.00475
.00462
.00446
.00418
.O04OI
.00386
1.9
.00473
.00460
.00444
.00417
.O04OO
.00385
2.
.00470
.00458
.00442
.00416
.00399
.00384
2.25
.00465
00453
.00437
.00413
.00397
.00382
2-5
.00460
.00449
.00432
.00410
.00394
.00380
2-75
.00456
.00444
.00428
.00408
.00391
.00378
3-
.00452
.00440
.00424
.00407
.00389
.00376
3 5
.00446
.00434
.00419
.00402
.00386
.00373
4
.00441
.00430
.00415
.00400
.00383
.00370
5-
.00436
.00423
.OO4IO
.00395
.00381
.00366
6.
.00430
.00418
.00405
.00391
.00377
.00363
7-
.00427
.00413
.OO4OI
.00388
.00373
.00361
8.
.00422
.00410
.00398
.00384
.00371
.00358
9-
.00418
.00407
00395
.00382
.00370
.00355
10.
.00415
.00404
.00392
.00380
.00367
-00353
12.
.00412
.00400
.00389
.00377
.00364
.00351
I 4 .
.00409
.00397
.00386
.00373
.00363
.00350
16.
.00406
00395
....
....
246
FLOW OF WATER THROUGH PIPES.
TABLE No. 61 (Continued).
COEFFICIENTS OF FLOW (m) OF WATER IN CLEAN CAST-IRON PIPES,
OR SMOOTH MASONRY, UNDER PRESSURE.
DIAMETERS.
VELOCITY.
54 inches.
60"
72"
84"
9 6"
4.5 feet.
5.</.
6.0'.
7.0'.
8.c/.
Feet per second
Coefficient.
Coefficient.
Coefficient.
Coefficient.
Coefficient.
.4-
T"
5
0.00378
0.00358
0.00339
0.00318
O.0029O
.6
.00377
.00357
.00338
.00317
.00289
7
.00376
.00356
.00337
.00317
.00288
.8
-375
.00355
.00336
.003 i 6
.00287
9
.00374
.00354
00335
00315
.00286
I.O
.00373
00353
00334
.00314
.OO286
.1
.00372
.00352
00333
.00313
.00285
.2
.00371
.00351
.00332
.00313
.00285
3
.00370
.00350
.00332
.00312
.00285
4
.00369
.00350
.00331
.00312
.00284
5
.00368
.00349
.00331
.00311
.00284
.6
.00368
.00348
.00330
.00311
.00284
7
.00367
.00347
.00329
.00310
.00283
1.8
.00366
00347
.00329
.00309
.00283
1.9
.00365
.00346
.00328
.00309
.00283
2
.00364
.00346
.00328
.00308
.O0282
2.25
.00362
.00344
.00327
.00307
.O0282
2 -5
.00360
.00342
00325
.00306
.00281
2 -75
.00358
.00341
.00323
.00305
.0028O
3
00357
00339
.00321
.00302
.00278
3-5
oo353
.00337
.00320
.00300
.00276
4
.00350
00333
.00318
.00298
.00274
5
00345
.00329
00313
.00294
.00272
6
.00340
.00324
.OO3IO
.00292
.O0268
7
.00338
.00322
.00308
.00289
.O0266
8
.00335
.0032O
.00304
.00286
.00264
9
.00332
.00318
.OO3O2
.00283
.O0262
10
.00331
.00316
.O03OO
.00282
.O026l
12
.00330
00313
.00299
.00280
.O026O
14
.00329
.O03I2
.00298
.00279
.00259
EFFECTS OF TUBERCLES. 247
270. Peculiarities of the Coefficient (HI) of Flow.
In the tables and diagram of coefficients (m) of flow in pipes,
as well as in those of coefficients of discharge (c) through
orifices, there is variation in value with each variation in
velocity of the jet. In the case of pipes, there is also a
variation with the variation of diameter of jet, that equally
demands attention.
It will be observed in the tables of experiment above
quoted that the coefficient decreases as the diameter or
hydraulic mean radius increases, and also that with a
given diameter the coefficient decreases as the velocity
increases; thus, with a given low velocity, we may trace
the decrease of the coefficient from 0.0128 for a half-inch
pipe to 0.0029 for a ninety-six inch pipe ; and with a given
diameter of one-half inch we may trace the decrease of the
coefficient from 0.0128 for .5 foot velocity per second to
0.00622 for 14 feet velocity per second, and with a given
diameter of 96 inches we may trace the decrease of the
coefficient from 0.0029 for a velocity of .5 foot per second to
0.00259 for a velocity of 14 feet per second.
We have then a large range of coefficients applicable to
clean, smooth, and straight bores. When the bores are of
coarse grain, or are slightly tuberculated, the range is still
greater, and the values of coefficients of the smaller diam-
eters quite sensibly affected ; and if the bores are very
mgh or tuberculated, the values of coefficient for small
Liameters and low velocities are very much augmented.
271. Effects of Tubercles. These effects, in tubercu-
ited pipes, as compared with clean pipes, are illustrated in
the following approximate table, which we have endeavored
adjust to a common velocity of three feet per second for
the diameters. The data for very foul pipes is however
scanty, though sufficient to show that the coefficients do in
248
FLOW OF WATER THROUGH PIPES.
extreme cases exceed the limits given for the small diam-
eters ; and that conditions from clean to foul may occur,
with the several diameters, that shall cover the entire range
from minimum to maximum coefficients, and calling for a
careful exercise of judgment founded upon experience.
TABLE No. 62.
COEFFICIENTS FOR CLEAN, SLIGHTLY TUBERCULATED, AND FOUL PIPES,
OF GIVEN DIAMETERS, AND WITH A COMMON VELOCITY OF 3 FEET
/ 2ghd * \2gri\*\
PER SECOND. \v = \ . 6 N 7 \ = 4 -
\ Urn) / I m /
Hydraulic
Mean Radius,
S d
C ~ 4
Diameter.
Clean.
Slightly
tuberculated.
Foul.
Feet.
Inches.
Coef., m.
Coef., tn.
Coef., m.
.0104
.0417
1
0.00753
.0156
.0625
i
.00745
,O2o8
o8^4
I
OO734.
0.00982
.0312
*-" J O'T
.1250
4
^r/O*r
.00722
.00940
.0364
.1458
i*
.00707
.00925
.0417
.1667
2
.00692
.OO9IO
O.OI4OO
.0625
.2500
3
.00670
.00862
.01300
.0833
3334
4
.00650
.00825
.OI20O
.1250
.5000
6
.00623
.00772
.OIIOO
.1667
.6667
8
.006OO
00733
.00922
.2083
.8334
10
.00584
.00706
.00868
.2500
.0000
12
.00510
.0068O
.00828
.2917
.1667
H
00554
.00657
.00792
3333
3333
16
.00538
.00636
.00760
375
.5000
18
.00523
.00616
.00733
.4167
.6667
20
.00509
.00598
.00710
.5000
2.0OOO
24
.00483
.00567
.00664
5 62 5
2.25OO
27
.00468
.00544
.00635
.6250
2.5OOO
30
.00452
.00525
.00604
.6875
2.7500
33
.00440
.00507
.00578
.7500
3.OOOO
36
.00424
.00490
.00554
.8333
3-3333
40
.00407
.00466
.00524
.9167
3.6667
44
.00389
.00443
.00500
I.OOOO
4.0000
48
.00376
.00422
.00477
EQUATION OF VELOCITY. 249
272. Classification of Pipes and their Mean Co-
efficients. In ordinary calculations, the mean coefficient
for medium diameters and velocities may be taken, for clean
pipes, as .00644 ; for rough or slightly tuberculated pipes,
as .0082 ; and for very rough or very foul pipes, as .012.
These coefficients apply approximately to pipes of about
five inches diameter, when the velocities are about three
feet per second, reference being made to the diameter of the
pipe itself when clean.
273. Equation of the Velocity Neutralized by Re-
sistance to Flow. Having now developed the several
values of m as applicable to the several conditions of pipes,
we will again transpose our equation and remove 0, the
member expressing velocity of flow, to one side by itself,
and we have the equation of velocity of flow :
or
( m
or = or =
or = (8)
In which h = thr li
I = the length of the pipe, in feet.
d = the internal diameter of the pipe, in feet.
C the contour of the unit of length of pipe, in feet.
8 = the sectional area of the pipe, in square feet.
i = the sine of inclination = -=-
L
r = the hydraulic mean radius = ^ = -j-
g = 32.2.
250
FLOW OF WATER THROUGH PIPES.
274. Equation of Resistance Head. By transposi-
tion again we have the equation for that portion, #', of the
total head ^included in the slope i :
Clmtf
or
or 7i" = m x
r 2
(9)
Let c r represent the ratio of 7i' to Ti, or coefficient of re-
sistance of entry of the jet = ( - 2 ij = (^ ~ l)*
. Equation of Total Head. Then
or*
and
ff =
g
(1
(10)
(11)
also, when c is the coefficient of discharge,
i
(12)
276. Equation of Volume. The velocity v having
been ascertained, we have, for volume of flow q per second,
and
* Compare Weisbach's Mechanics of Engineering, translated by E. B.
Coxe, A. M. N. T., 1870, p. 870.
SUBDIVISIONS OF TOTAL HEAD.
251
also, we have
_
.7854^
q ^=V2gNx
4)
or
or
Hd?
(1
(13 s )
. Equation of Diameter. By transposition again
for the value of d, we have
or
= .4788
c f ) d
JLZ
(14)
In this last equation of d, the assistance of the table of
velocities for given slopes and diameters (p. 259), and the
table of coefficients, m, for given velocities and diameters
( 269, p. 242), will be required, since the unknown quan-
tities d and m appear in the equation. The approximate
values of d and m for the given velocity can be taken from
the tables and inserted in the right-hand side of the equa-
tion, and a close value of d worked out for a first approxi-
mation, and then the operation repeated for a closer value
of d, if necessary.
278. Kelative Values of Subdivisions of Total
Head. Referring again to the extended pipe, P', Fig. 35,
assume it to be 1000 feet long, horizontal, 1 foot diameter,
and under a constant head of 100 feet ; then the velocity of
discharge, according to equation (11) will be
252 FLOW OF WATER THROUGH PIPES,
f 64.4 x 100
1+. 505 + . 00495 i feet per second;
[ = 17.;
and h = = 4.694 feet.
%9
= 2.370 "
h" = (. 00496^)^= 92.941
V .25/2^
and H=7i + ?i' + n" = 100.0 feet.
. Many Popular Formulas Incomplete. The
fact that the majority of popular formulas for flow of water
in pipes, as usually quoted in cyclopedias and text-books,
refer to 7i' + h", or in some cases to h" only, and not to If,
has led us to treat the subdivisions of If more minutely in
detail than would otherwise have been necessary.
Serious errors are liable to result from the application
of such hydrodynamic formulae by persons not familiar
with their origin, especially when the problem includes a
high head of water and short length of pipe.
We believe that the coefficient of flow, m, has not here-
tofore been as fully developed as its importance has
demanded.
28O. Formula of M. Chezy. The formula of
M. Chezy, proposed a century ago, and into which nearly
all expressions for the same object, since introduced, can be
resolved, refers to h" only, or h + ?i", and not to If. When
stated in the symbols herein used, it becomes
SUB-HEADS COMPARED.
253
As g is introduced in place of 2g in our equation, m' will
equal |-
281. Various Popular Formulas Compared. The
value of treating the question of flow of water in pipes in
detail may perhaps best be illustrated by computing the
velocity of flow from our pipe P , Fig. 35, as it is extended
to different lengths, from 5 feet to 10,000 feet, by a complete
formula, with m at its legitimate value, and then computing
the same by several prominent formulas, in the form in
which they are usually quoted. (See Table No. 63, p. 254.)
282. Sub-heads Compared. If we compute the total
head, to which the velocities, found by the first formula of
the table, are due, we shall have the sub-heads, as follows ;
when d = 1 foot.
LENGTHS IN FEET.
5-
5.
100.
1000.
10,000
VELOCITIES IN FT.
PER SECOND.
63.463-
51.111.
43i".
17-386.
5.392.
h
62.542
40.568
28.863
4.694
.451
h!
31-583
20.487
14-575
2.370
.228
h"
5.878
38.945
56.571
92.941
99-330
H
100. O
loo.o
IOO.O
IOO.O
IOO.O
It is here shown that the values of 7i and ~ti cannot be
neglected until the length of the pipe exceeds one thousand
diameters, under the ordinary conditions of public water
supplies.
In our first length of five feet, 7i is about ten and one-
half times 7i", and 7i' is about five and one-half times 7i".
254
FLOW OF WATER THROUGH PIPES.
T A BLE No. 63.
RESULTS GIVEN BY VARIOUS FORMULAS FOR FLOW OF WATER IN
SMOOTH PIPES, UNDER PRESSURE, COMPARED.
DATA. To find the velocity, given : Head, H = 100 feet ; Diameter, d = i foot ; and Lengths,
/, respectively as follows :
AUTHORITY.
EQUATIONS.
LENGTHS.
fe 5 et
<&
100
feet.
IOOO
feet.
10,000
feet.
Equation (n) . .
Chezy
\ ^ /i*
Veloc.
63.463
223.607
216.94
223.214
241.778
67.40
246.171
218.758
213.761
62.540
294.650
214.267
244.120
223.607
223.607
62.555
Veloc.
51.111
70.710
102.918
68.54
70.480
76.367
50.00
73-682
69.114
67.589
47.080
90.263
67-715
77.133
70.710
70.710
47.084
Veloc.
43.111
50.000
81.510
48.446
49.792
53-96o
40.82
51-247
48.845
47.804
38-75
63.070
47-9I3
54-640
50.000
50.000
38.724
Veloc.
17-386
15.810
13.662
15-258
15-641
16.975
15-427
15-232
15-384
15.114
14.780
18.917
15.140
17.279
15.810
15.810
14-797
Veloc.
5-392
5.000
3-9781
4.770
4.842
5.280
4-985
4-592
4.800
4.780
4.780
5-507
4.791
5-464
5.000
5.000
4.804
{ (i + <:,)*- J
v \** S \*
Du Buat
Prony (a)
" (6)
Eytelwein (a) . .
(*).-
Saint Vennant . .
D' Aubuisson (a)
* (*)
Neville (a)
" (*)
Blackwell
\lmlC\
88. 5 r -.03 ,i }
//\A // \i ^ 3)
(D^Ms* 1 *)
v (11703 95?"* + .01698) .1308.
( dk \\
50 i /+ 5 orf \
v 105.926 (rz)"
v 95.6 Vri
-- i Hr !*
( .0234r + .oooioSs/ J
v 140 (rz)* ii (rz') ?
( Arf) \
V '7 QI^ < t ....
-,7.913 | ^ f
j "' fc ) *
D' Arcy
Leslie
v = -\ .00000162 >
1 .00007726 + j
w = 100 ^ri
z/-5o<:(^/)5
Hawksley
. , j dk j i
P 48 - 45 i/ + 54^1
In which C - contour of pipe, in feet ; / = length of pipe, in feet.
c = unity for smooth pipes, and m = coefficient of flow.
is reduced for rough pipes. r = hyd. mean radius, in feet, =
d diam. of pipe, in feet. S = sectional area of pipe, in square feet.
H = entire head, in feet. / = sine of inclination, in feet, =
k = resistance head, in feet. v = velocity of flow, in feet per sec.
PEONY'S ANALYSIS. 255
In long pipes, sufficient velocity is converted into pres-
sure to reduce somewhat the contraction of the jet at its
entrance into the pipe. In very long pipes the effect of this
contraction becomes insignificant when compared with the
effect of reaction from the walls of the pipe.
283. Investigations by Du Buat, Coloumb, and
Prony. The investigations of Du Buat and Coloumb led
them to the conclusion that the velocity of the fluid occa-
sioned a resistance to flow, in addition to that arising from
the wet perimeter of a channel or pipe, which is propor-
tional to the simple velocity ; and afterwards Prony, coin-
ciding with this view, undertook the investigation of the two
coefficients thus introduced into the formula of resistance to
flow.
Since their new coefficient, 0, applied to the simple velo-
city and not to the square of the velocity, as does the co-
efficient m, their expression, in our symbols, became
- f g = (H- h) or K
284. Prony's Analysis. Prony analyzed the results
of fifty-one experiments to determine the values of m and 0,
including eighteen experiments by Du Buat with a tin
pipe of about one inch diameter and sixty -five feet long ;
twenty-six experiments by Bossut with pipes of about one,
one and one-quarter, and two-inch diameters, and varying
in length from thirty-two to one hundred and ninety -two
feet ; and seven experiments by Couplet. Six of these last
experiments were made with a five and one-quarter inch
pipe, under a head less than two and one-quarter feet, and
256 FLOW OF WATER THKOUGH PIPES.
one with, a nineteen-inch pipe with a head of about twelve
and one-half feet.
We have quoted above ( 269) eight of the experiments
by Du Buat, nine of those by Bossut, and the full seven
by Couplet, and in the two first included the extremes so
as to cover their entire range.
This was a limited foundation upon which to build a
theory of the flow of water in pipes, nevertheless the attain-
ments of this eminent investigator enabled him to deduce
from the limited data hypotheses which were valuable con-
tributions to hydrodynamic science.
From these experiments Prony deduced the values, as
reduced to English measures, m = .0001061473 ; and ft =
.16327.
285. Eytelwein's Equation of Resistance to Flow.
Eytelwein, investigating the question anew, and believing
the contraction of the vein at the entrance to the pipe should
not be overlooked, soon afterward modified the equation to
the form,
9 f}~l
H-, = .000085434 (v a + .2756 v\ (16)
in which d refers to the effect of the contraction.
286. D'Aubuisson's Equation of Resistance to
Flow. D' Aubuisson, more than a half-century later, hav-
ing regard more particularly to the experiments of Couplet,
gave to m and ft values as follows :
v* n
E-^ = .000104392 ^ (V + .180449 ). (17)
287. Weisbach's Equation of Resistance to Flow.
Weisbach, availing himself of eleven experiments of his
own with high velocities, and one by M. Gueymard, in ad-
UNINTELLIGENT USE OF PARTIAL FORMULAS. 257
dition to the fifty-one above referred to, proposed the fol-
lowing formula as coinciding better with the results of Ms
observations :
/ m
This coefficient (a + p), which replaces 4m in our sym-
\ i/fl/
bols, is founded upon the assumption that the resistance of
friction increases at the same time with the square and with
the square root of the cube of the velocity.
288. Transpositions of an Original Formula.
That Chezy's formula has been generally accepted as one
founded upon correct principles, we readily infer by its fre-
quent adoption, transposition and modification in the writ-
ings of many philosophers and hydraulicians. Note, for
instance, the second formulas (v) of Eytelwein and D'Au-
buisson in the above table (No. 63), and the formulas of
Beardmore, Blackwell, Downing, Hawksley, Jackson, Box,
Storrow, and others, which may be resolved into this orig-
inal form.
289. Unintelligent Use of Partial Formulas.
That serious errors may arise from an unintelligent and
improper use of these formulas is conspicuously apparent
in the above table of results, computed upon conditions in
the very midst of the range of conditions of ordinary muni-
cipal water supplies. A full knowledge of the origin of a
formula is essential for its safe practical application.
A solid body falling freely in a vacuum through a height
of 100 feet, acquires a rate of motion of only about 80.3 feet
per second, yet some of the formulas appear to indicate a
velocity of flow exceeding 200 feet per second, through five
feet of pipe, under 100 feet head pressure.
17
258 FLOW OF WATER THROUGH PIPES.
29O. A Formula of more General Application.
Weisbach has suggested a more comprehensive form of
expression which includes the head generating the velocity
of flow and the head equivalent to the dynamic force lost at
the entry of the jet into the pipe, as well as the head balanc-
ing the resistance to flow in the pipe, and therefore his
equation presents the equality between the total head H,
and the sum of the velocity and resistance heads equal
to Ti + Ti'+Ti".
Weisbach has also developed a portion of the values
of m.
291. Value of v for Given Slopes. We have here-
tofore insisted that m, as introduced into the equation, shall
approximate near to its legitimate value for the given condi-
tions. Its value for each given diameter, or hydraulic mean
radius, r, depends upon the velocity of flow, and therefore
upon the slope, s, generating the velocity.
To aid in the selection of m from the tables of m,
page 242, we have plotted the several velocities as ordinates
with given sines of slopes, *', as abscissas for such experi-
mental data as was obtainable, and have taken the interme-
diate approximate values of v from their parabolic curves
thus determined from the experimental data, and have
arranged the following table of v ; which of course refers to
the head 7i", balancing the resistance in the slope s.
VELOCITIES FOR GIVEN SLOPES ASD DIAMETERS.
TABLE No. 64.
VELOCITIES, v, FOR GIVEN SLOPES AND DIAMETERS.
FOR CLEAN IRON PIPES.
z; =
SLOPE.
in 250
" 200
" 167
" 143
; ' 125
1 in
" loo
" 83>3
" 62^5
" 55-6
" 50.0
" 33-3
25.0
" 20. o
" 16.6
" 14.3
" 12.5
" n. i
" 10.0
" 8.33
" 7-14
" 6.25
" 5.55
5.oo
" 4.00
" 3-33
" 2.50
" 2.00
1.66
1.43
1.25
i. ii
DlAMI
DTERS.
SINE OF
SLOPE.
X inch.
%"
j//
I#"
ifc"
2"
.0417 ft.
.0625'.
.0834'-
.1250'.
.1458'.
.1667'.
. k
Velocity.
Velocity.
Velocity.
Velocity.
Velocity.
Velocity.
~ T
Ft. per sec.
Ft. per sec.
Ft. per sec.
Ft. per sec.
Ft. per sec.
Ft. per sec.
OO4.
.184
.\J^JL^
.206
340
!oo6
.190
.360
.500
.007
.290
453
.600
.008
.0^8
.391
.580
.730
.009
\J^^>
.130
* JV
.480
.700
.870
.010
mo
.240
.600
.790
.980
.012
0.892
.140
.430
730
/ 7
953
2.219
.014
O.giO
.230
540
.860
2.130
2.360
.Ol6
0.990
.340
.640
2.010
2.220
2.500
.018
1.050
.450
. 7 60
2.100
2.350
2.630
.02
1. 100
.518
.813
2.276
2.530
2.800
.03
1.440
.920
2.280
2.810
3.100
3.390
.04
1.765
2.298
2.730
3.367
3.694
4.002
.05
2.O4O
2.600
i 3.050
3.730
4.280
5-020
.06
2.310
2.850
3-400
4.IIO
4-690
5.500
.07
2.490
3.100
3.640
4.420
5-020
5.900
.08
2.680
3.300
3.920
4.730
5.360
6.300
.09
2.850
3.540
4.180
5-045
5.630
6.610
.IO
3.040
3.730
4-437
5.480
6.009
6.979
.12
3.320
4.180
4.900
6.030
6.650
7.490
.14
3.460
4.500
5.290
6-535
7.190
8.010
.16
3.840
4-825
5.640
7.010
7.700
8.500
.18
4.090
5.108
5.998
7-500
8.221
8.960
.20
4.310
5.400
6.330
7.880
8.690
9.380
25
4.830
6.100
7.135
8.770
9.690
10.430
.30
.40
5-359
6.260
6.730
7.790
7.902
9.130
9.650
11.225
10.620
12.280
11.380
12.980
.50
7.070
8.818
10.339
12.600
.60
78OO
c\ *7r*/"\
OvAJ
9.790
11.5 y o
*7O
8.470
m^jf\r\
12 7IO
.80
9. 140
, ymj
1 1 7 2O
f\r\
9800
.yu
. OCMJ
IO. 3QO
I2.OOO
260
FLOW OF WATER THROUGH PIPES.
TABLE No. 64 (Continued).
VELOCITIES, v, FOR GIVEN SLOPES AND DIAMETERS.
FOR CLEAN IRON PIPES.
SLOPE.
SINE OF
SLOPE.
DIAMETERS.
3 inch.
.250 ft.
&.
6"
-5'.
8"
.6667'.
10"
.8333'-
12"
i.o'.
in mi
" 1000
" 909
" 833
" 769
" 714
" 667
" 625
" 588
" 556
" 526
" 5oo
" 455
" 417
" 385
' 357
44 333
" 286
" 250
" 200
" I6 7
* 143
" I2 5
" III
" 100
" 83.3
71.4
" 62.5
" 55.6
" 50.0
33-3
25.0
" 2O.O
16.6
' 14-3
1 12.5
1 1. 1
' IO.O
' 8.33
1 M4
6.25
5.55
5.00
* 4.00
3-33
h
' = 7'
.0009
.0010
.001 1
.0012
.0013
.0014
.OOI5
.OOl6
.OOI7
.0018
.OOlg
.0020
.0022
.OO24
.0026
.0028
.0030
0035
.004
.005
.006
.007
.008
.009
.010
.012
.014
.016
.018
.02
03
.04
05
.06
07
.08
.09
.10
.12
.14
.16
.18
.20
25
30
Velocity.
Ft. per sec.
Velocity.
Ft. per sec.
Velocity.
Ft. per sec.
Velocity.
Ft. per sec.
Volocity.
Ft. per sec.
Velocity.
Ft. per sec*
540
.610
.680
.785
.880
.940
2.OIO
2.080
2.148
2.200
2.27O
2.325
2.470
2.58o
2.695
2.810
2.925
3.140
3-390
3.845
4-215
4.585
4.910
5-185
5480
6.020
6.485
6.980
7-435
7.842
9.715
11.280
12.689
1.610
1.692
1.760
1.840
1.920
1.990
2.035
2.125
2.190
2.320
2.430
2.525
2.610
2.695
2.910
3-085
3-420
3.775
4.075
4.370
4.610
4.880
5-375
5.885
6.325
6.745
7.070
8.730
10.200
12.293
1.640
1.680
1.750
1.800
1.830
1.930
2.OI5
2. IIO
2.220
2.315
2.5IO
2.690
2-993
3-3I5
3.615
3.850
4.080
4.285
4.710
5-105
5-490
5.825
' 6.175
7.640
9-OIO
10.062
11.020
12.020
....
....
1.284
I.4IO
1.525
I.7IO
1.863
2.O2O
2.160
2.280
2.425
2.675
2.880
3.070
3.240
3-498
4.240
5.030
5.674
6.213
6.785
7.250
7-775
8.238
9.045
9-773
10455
11.075
11.883
13.289
I.4I5
1.480
1-530
1.680
1.790
2.030
2.2O4
2.460
2.670
2.820,
2.960
2.230
2.480
2.710
3-9 1
4-134
5.160
6.110
6.825
7-324
7.985
8.604
9- I2 5
9-703
10.625
11-531
12.383
515
.600
.680
.760
.830
.920
2.IOO
2.26O
2.525
2.790
3.000
3-215
3425
3.670
3-992
4-370
4.695
4-965
5.206
6.430
7.560
8-479
9.828
10.062
10.920
H.583
I2.2O9
VELOCITIES FOR GIVEN SLOPES AND DIAMETERS. 261
TABLE No. 64 (Continued).
VELOCITIES, v, FOR GIVEN SLOPES AND DIAMETERS.
FOR CLEAN IRON PIPES.
SINE OF
DlAM
ETERS.
SLOPE.
SLOPE.
14 inch
16"
18"
30"
24"
27 //
1.1667 ft-
I.3333'.
1.5'.
I.666/.
2.0'.
a.2 5 '.
,=*
Velocity.
Velocity.
Velocity.
Velocity.
Velocity.
Velocity.
/
Ft. per sec.
Ft. per sec.
Ft. per sec.
Ft. per sec.
Ft. per sec.
Ft. per. sec.
in 2500
.0004
2000
OOO5
2.O8O
1667
. \J\J*J$
. 0006
i .6;5
I . Q-1O
2. IO5
1428
.0007
....
1.610
1-755
* v 'DO
1.860
yt*'
2.115
2.285
1250
.0008
.610
1-738
1.850
1-995
2.265
2.385
mi
.0009
.710
1.855
1-975
2.145
2.405
2.580
1000
.0010
.800
1.950
2.070
2.255
2-530
2.700
909
.OOII
.895
2.065
2.195
2.360
2.655
2.880
833
.0012
975
2.I6O
2-295
2-475
2.785
3.000
769
.0013
2.040
2.275
2-395
2-575
2.910
3-155
714
.0014
2.130
2.350
2.400
2.675
3-015
3.260
667
.0015
2. 2OO
2.425
2.606
2-775
3.120
3-395
625
.0016
2.285
2.500
2.685
2.875
3-225
3.515
588
.0017
2-375
2.590
2-775
2.970
3.366
3.625
556
.0018
2.430
2.640
2.845
3-050
3-430
3-725
526
.0019
2.500
2.725
2.925
3.170
3-535
3.825
500
.0020
2-550
2.810
3.000
3-230
3.640
3-930
455
.0022
2.70O
2.950
3-187
3.400
3.835
4-135
417
.0024
2.825
3-095
3-320
3-570
4.015
4-335
385
.0026
2.950
3.230
3-495
3-730
4.210
4-530
357
.0028
3.080
3-355
3.610
3-885
4-388
4.715
333
.0030
3-200
3-490
3-755
4.020
4-535
4-905
286
0035
3-473
3.800
4.060
4-350
4-935
5.3I5
250
.OO4
3-735
4.060
4-330
4.655
5-290
5-690
200
.005
4.180
4-575
4.901
5.240
5-955
6-373
167
.006
4.602
5.025
5-400
5.770
6.502
6.975
143
.007
5-025
5.485
5-844
6.260
7.020
7.520
125
.008
5-400
5.845
6.275
6.718
7.515
8.045
in
.009
5-725
6.185
6.625
7.125
7.980
8-545
100
.OIO
6.030
6.515
7.000
7.550
8.410
9-025
83.3
.012
6-555
7.124
7.725
8.245
9.240
10.000
71.4
.014
7.120
7.785
8-345
8.935
10.025
10.870
62.5
.Ol6
7-655
8.330
8.965
9.640
10.790
11.715
55-6
.018
8.170
8.900
9-565
10.295
H.5I5
12.085
50
.02
8.667
9.409
10.104
10.801
12.238
....
" 333
03
10.691
11-583
12.369
13.229
....
I " 25
O4.
12.^8^
flAAC
g
ut+
j.^ j^fj
*O T"*TD
262
FLOW OF WATER THROUGH PIPES.
TABLE No. 64 (Continued.)
VELOCITIES, v, FOR GIVEN SLOPES AND DIAMETERS.
FOR CLEAN IRON PIPES.
SLOPE.
SINE OF
SLOPE.
DIAMETERS.
30 inch
2.5 feet.
33"
3-75'
3 6"
3-0 7
4 o"
3-3333'-
\
44" 48"
3.6667'. 4-c/.
. h
Velocity.
Velocity.
Velocity.
Velocity.
Velocity.
Velocity.
~ I
Ft. per sec
Ft. per sec.
Ft. per sec
Ft. per sec
Ft. per sec.
Ft. per sec.
in 5000
.OO02
....
....
1-457
1.590
1.719
1.829
" 3333
.0003
1.586
I.68I
1-797
1.948
2.104
2.220
" 2500
.0004
1.831
1.962
2.O6O
2.255
2.420
2.620
" 2000
.0005
2.085
2.175
2.313
2.530
2-735
2-945
" 1667
.0006
2.235
2.355
2.550
2.800
2.980
3.200
" 1428
.0007
2.425
2.550
2.796
3.010
3.265
3-475
" 1250
.0008
2.617
2-755
2.950
3-225
3-510
3.725
" IIII
.OOOg
2-745
2.960
3.155
3.4I5
3-695
3-904
" 1000
.0010
2.895
3.156
3.320
3.605
3-890
4.150
" 909
.OOII
3.065
3.290
3.525
3.810
4.080
4-375
" 833
.0012
3.220
3.415
3.695
3-975
4.260
4-565
" 769
.OOI3
3-355
3.585
3.848
4.150
4-430
4.780
" 714
.OOI4
3-500
3.703
3-995
4-305
4.625
4.936
" 667
.0015
3-655
3-875
4.130
4.490
4-795
5-130
" 625
.0016
3.785
4.000
4.285
4.645
4.970
5-295
" 558
.OOI7
3.9I5
4.120
4-445
4.800
5.H9
5-450
" 556
.0018
4.006
4.245
4-595
4-935
5-255
5.620
" 526
.0019
4.140
4.400
4.725
5-075
5-400
5.790
' 500
.0020
4-235
4-535
4.880
5.180
5.575
5-924
' 455
.0022
4-445
4.759
5-II5
5.515
5.845
6.230
i ' 417
.OO24
4-650
5-000
5.340
5.785
6.095
6.500
i ' 385
.0026
4-875
5.230
5-575
6.035
6.335
6.780
i ' 357
.0028
5.065
5-435
5-780
6.307
6.590
7.040
' 333
.0030
5.270
5.660
5.981
6-455
6.850
7.300
" 286
.0035
5-695
6.090
6.500
7.000
7.385
7.990
" 250
.OO4
6.080
6-493
6.907
7-495
7.920
8.425
" 200
005
6.835
7.260
7-765
8.375
8.845
9-497
" 167
.006
7-495
7.980
8.480
9-205
9.784
10.415
" 143
.007
8.080
8.645
9.220
9-935
10.585
11-307
" 125
.008
8.635
9-245
9.875
10.610
i i . 360
12.250
" in
.OOg
9.215
9.800
10.515
11.230
12.150
" 100
.OIO
9.720
10.375
II.IOO
11.919
....
....
" 8q ^
.OI2
10.780
1 1 4J.O
u . 720
u J'O
u 71-4
.014
n-745
** *t*ty
12.450
-
VALUES OF h AND h' FOR GIVEN VELOCITIES. 263
TABLE No. 64 (Continued).
VELOCITIES, v 9 FOR GIVEN SLOPES AND DIAMETERS.
FOR CLEAN IRON PIPES.
DIAMETERS.
SLOPE.
SINE OF
SLOPE.
54 inch
60"
72"
8 4 "
96"
4*5 feet.
5 .c/.
e.o'.
7 .</.
8.0'.
<=/
Velocity.
Ft. per sec.
Velocity.
Ft. per sec.
Velocity.
Ft. per sec.
Velocity.
Ft. per sec.
Velocity.
Ft. per sec.
in 10000
.0001
I.38I
I.5I6
I.66I
1.906
2.144
" 5000
.0002
1-993
1.945
2.039
2.719
3-033
" 3333
.0003
2.423
2.653
2.919
3-279
3-749
" 2500
.0004
2.837
3.007
3-395
3-779
4.352
" 2OOO
.0005
3.158
3-441
3.870
4.229
4.880
' 1667
.0006
3-49
3.785
4-300
4.600 *
5.320
' 1428
.0007
3.785
4-IOO
4.670
4.990
5.780
' I25O
.0008
4.000
4-395
4-950
5.400
6.185
' IIII
.0009
4-235
4.685
5.260
5.780
6.600
' 1000
.0010
4-550
4-939
5 580
6.110
6.972
909
.0011
4.760
5.215
5.870
6-583
7.285
" 833
.0012
4-975
5-465
6. 1 20
6.880
7.600
" 769
.0013
5.190
5.680
6.340
7-150
7.915
' 714
.0014
5-400
5-935
6.630
7-475
8.250
667
.0015
5-629
6.095
6.859
7.7oi
8.510
625
.0016
5.815
6.300
7.080
8.000
8.815
' 588
.0017
5-995
6.500
7.300
8.215
9.100
1 556
.0018
6.140
6.685
7.500
8.490
9.360
' 526
.0019
6.300
6.865
7.700
8.725
9.580
500
.0020
6.528
7.071
7-965
9.049
9.875
455
.0022
6.840
7-435
8.330
9.480
10.400
417
.0024
7-135
7.770
8.715
9.880
10.890
1 385
.0026
7-445
8.080
9.060
10.275
11.340
" 357
.0028
7-740
8.380
9-450
10.611
11.780
" 333
.0030
8.060
8.680
9.828
11.000
12.175
286
0035
8-735
9-370
10.615
12.550
" 250
.004
9.300
10.060
n-344
....
I " 200
005
10.425
11.304
12.680
....
I " 167
.006
11.470
12.440
I " 143
.007
12.450
....
292. Values of h and h' for Given Velocities.--
In Table 65 are given the values of Ji and 7i' for given
velocities, which are to be subtracted from H to ^compute
the height of the slope generating the velocity ?).
The velocity being known approximately, its correspond-
ing m for any given diameter may be taken from the table
of ra, page 242, and inserted in the formula :
(I + c r )+m -
1:
264
FLOW OF WATER THROUGH PIPES.
TABLE No. 65.
TABLES OF h AND k' DUE TO GIVEN VELOCITIES, h AND h' BEING
IN FEET AND V IN FEET PER SECOND.
Velocity
h
h'
h + k f
Velocity
h
h'
h + h'
.80
.010
.0050
.OI5O
4-47
31
1565
4665
.98
.015
.0075
.0225
4-54
32
.1616
.4816
I.X3
.020
.OIOI
.0301
4.61
33
.1666
.4966
1.27
.025
.0126
.0376
4.68
34
.1717
5117
1-39
.030
.0151
.0451
4-75
35
.1767
.5267
1.50
.035
.0177
.0527
4.81
36
.1818
.5418
1.60
.040
.0202
.O6O2
4.87
37
.1868
5568
1.70
045
.0227
.0677
4-94
.38
.1919
57^9
1.79
.050
.0252
.0752
5.01
39
.1969
5869
1.88
055
.0278
.0828
5-07
.40
.2020
.6060
1.97
.060
.0303
.0903
5-14
.41
.2O7O
.6170
2.04
.065
.0328
.0978
5.20
.42
.2121
.6321
2.12
.070
0353
1053
5-26
43
.2172
.6472
2.2O
075
0379
.II2g
5-32
44
.2222
.6622
2.27
.080
.0404
.1204
5.38
45
.2272
.6772
2.34
.085
.0429
.1279
5-44
.46
.2323
.6923
2.41
.090
0454
1354
5-50
47
2373
7073
2.47
095
.0480
.1430
5.56
.48
.2424
.7224
2-54
.100
.0505
.1505
5.62
49
.2474
7374
2.60
.105
.0530
.1580
5-67
50
.2525
7525
2.66
.110
0555
.1655
5-73
5i
2575
7675
2.72
.115
.0580
.1730
5-79
52
.2626
.7826
2.78
.120
.0606
.1806
5.85
53
.2676
.7976
2.84
.125
.0631
.l88l
5-90
54
.2727
.8127
2.89
.130
.0656
.1956
5-95
55
.2777
.8277
2-95
.135
.0672
.2022
6.00
56
.2828
.8428
3.00
.140
.0707
.2107
6.06
57
.2878
.8578
3-05
.145
.0732
.2182
6.ii
58
.2929
.8729
3.H
.150
0757
.2257
6.17
59
.2979
.8879
3-i6
.155
.0772
.2322
6.22
.60
.3030
.9030
3.21
.160
.0808
.2408
6.28
.61
.3080
.9180
3.26
.165
0833
.2483
6.32
.62
.3131
9331
3-31
.170
.0858
.2558
6.37
63
.3l8l
.9481
3.36
.175
.0883
.2633
6.42
.64
.3232
.9632
340
.180
.0909
.2709
6.47
65
.3282
.9782
345
.185
.0934
.2784
6.52
.66
3333
9933
3.50
.190
.0959
.2859
6-57
.67
.3383
1.0083
3-55
.195
.0984
2934
6.61
.68
3434
,0434
3-59
.200
.1010
.3010
6.66
.69
.3484
.0384
3.68
.21
.1060
.3160
6.71
70
3535
0535
3-76
.22
.1111
3311
6.76
.71
3585
.0685
3.85
23
.1161
.3461
6.81
.72
.3636
.0836
3-93
.24
.1212
.3612
6.86
73
.3686
.0986
4.01
25
.1262
.3762
6.91
74
.3737
II37
4.09
.26
.1313
39*3
6-95
75
.3787
.1287
4.17
.27
.1363
.4063
6-99
.76
.3838
.1438
4-25
.28
.1414
.4214
7.04
77
.3888
1.1588
4-32
29
.1464
.4364
7.09
.78
3939
i. 1739
4-39
30
.1515
.4515
TABLES OF h AND h'.
265
TABLE No. 65 (Continued).
TABLES OF h AND h' DUE TO GIVEN VELOCITIES, h AND h' BEING
IN FEET AND V IN FEET PER SECOND.
Velocity.
h
h'
k + h'
, Velocity.
h
h'
h + &'
7-13
79
.3989
.1889
22.34
7-75
3.914
11.664
7 .I8
.80
.4040
.2040
22.70
8
4.040
12.040
7.22
.81
.4090
.2190
23.05
8.25
4.166
12.666
7.26
.82
.4141
2341 '
23.40
8.50
4.292
12.792
7-31
.83
.4191
.2491
23-74
8.75
4.419
13-169
7-35
.84
.4242
.2642
24.07
9
4.545
13-545
7.40
.85
.4292
.2792
24.41
9-25
4.671
13.921
7.44
.86
4343
.2943
24-73
9-50
4-797
14.297
7.48
.87
4393
3093
25.06
9-75
4.924
14.674
7-53
.88
.4444
3244
25.38
10
5.050
15-050
7-57
.89
4494
3394
25.69
10.25
5.1/6
15-426
7.61
.90
4545
3545
26.00
10.50
5.302
15.802
7.65
.91
4595
.3695
26.32
10.75
5-492
16.242
7.70
.92
.4646
.3846
26.62
ii
5-555
16.555
7-74
93
.4696
.3996 ,
26.91
".25
5.681
16.931
7.78
.94
4747
.4147 !
27.21
11.50
5-807
17.307
7.82
95
4797
4297
27.51
11-75
5-934
17.684
7.86
.96
.4848
4448 !
2 7 .8
12
6.060
18.060
7.90
97
.4898
4598 1
28.4
12.5
6.186
18.686
7-94
.98
4949
.4749
28.9
13
6-565
19-565
7.98
99
4999
.4899
29.5
13.5
6.817
20.317
8.03
i
505
.505
30.0
14
7-070
21.070
8.97
1.25
.631
.881
30-5
14-5
7-322
21.822
9-83
1.50
757
2.257
3LI
15
7-575
22-575
10. 60
1-75
.884
2.634
31.6
15-5
7.827
23.327
zx .4
2
.010
3.010
32.1
16
8.080
24.080
11.35
2.25
.136
3.386
32.6
16.5
8-332
24.832
12.6
2.50
.362
3.862
33-1
17
8.585
25-585
13.30
2-75
389
4-139
33-6
17.5
8.837
26.337
13-9
3
SIS
4-515
34-0
18
9.000
27.090
14.47
3-25
.641
5.891
34.5
18.5
9-342
27.842
15-0
3-50
.767
5-267
35-0
19
9-595
28.595
15.54
3-75
1.894
5-644
35-4
19-5
9.847
29.347
16.05
4
2.020
6.020
35-9
20
10.100
30.100
16.54
4.25
2.146
6.396
36.8
21
10.352
3L352
I7.O2
4.50
2.272
6.772
37-6
22
II. IIO
33-110
17.49
4-75
2-399
7.149
38.5
23
11.615
34.615
17.94
5
2.525
7.525
39-3
24
I2.I2O
36.120
18.39
5.25
2.651
7.901
40.1
25
12.625
37 625
18.82
5-50
2.777
8.277
40.9
26
13.130
39.130
19.24
5-75
2.904
8.654
41.7
27
13.635
40-635
19.66
6
3-030
9.030
42.5
28
14.140
42.140
2O.O6
6.25
3-156
9.406
43-2
29
14.645
43.645
20.46
6.50
3.282
9.782
43-9
30
15.150
45.150
20.85
6.75
3-409
10.159
47-4
35
17.675
52.675
21.23
7
3-535
10.535
50.7
40
20.200
60.200
2I.6I
7-25
3.661
10.911
53.8
45
22.725
67.725
21.98
7-50
3.787
11.287
56.7
50
25.250
75-250
266 FLOW OF WATER THROUGH PIPES.
293. Classified Equations for Velocity, Head,
Volume, and Diameter. The coefficients of flow for the
given slopes and diameters being determined, they, with
the coefficients of resistance of entry for different forms of
entrance, may be introduced into the classified equations
for velocity, and their resolutions for head, volume, and
diameter ; when the equations will become,
H
^ ~ If I [ for pipes with well-rounded entrances. (n\
1.054471-
4 r\
_.j I } for pipes with square-edged flush entrances. (&} t (19^
1.505m-
A r\
2gN ] j
T^ J I for pipes with square-edged entrances pro- / \
l.OSw?^ I jecting into the reservoir.
* r
H= J
- (20)
77/7 s
6 - 303 ^.054^ ^^' - - W
? =^ 6 - 30 Ho05TO^P ' ' ' ^ (21 >
6 ' 803 |l956^ a 4mg[* . . .. (c)
.4788 -1 1.054^ + 4ml i* . . . (a)
.4788 1 1.505^ + 4mZ|i* . ... . (5) \- (22)
COEFFICIENTS FOR PIPES.
267
294. Coefficients of Entrance of Jet. Other values
of c r , for other conditions of pipe entrance, or other coef-
ficients of velocity c p , may be taken from, or interpolated
in the following table, computed from the formulas,
and
, - ( * y
* ~ \c, + i>
TABLE No. 66.
VALUES OF e. AND c FOR TUBES.
c v or c. .
.980
974
950
.925
.900
.875
.850
.825
.'Sis
.800
750
715
.700
c r
.041
054
.109
.169
235
.306
.383
.469
SOS
.563
.778
.956
1.041
I**,..
1.041
1.054
1.109
1.169
1.235
1.306
L383
1.469
1-505
1-563
1.778
1.956
2.041
295. Mean Coefficients for Smooth, Rough, and
Fonl Pipes. In ordinary approximate calculations for
long pipes, it is often convenient to select a mean coefficient
for medium diameters and velocities, and insert it in a fun-
damental formula as a constant. In such case we may
select, say, for clean and smooth iron pipes, .00644 ; for
rough or slightly tuberculated pipes, .0082 ; and for very
rough or very foul pipes, .012.
These coefficients are applicable more particularly (wit-
ness table No. 61) to pipes of about five inches diameter
with a velocity of flow of about three feet per second, and
to lengths exceeding one thousand diameters.
Since
1 h"
x -- x -7- x
m I
we have
268
FLOW OF WATER THROUGH PIPES.
We may now unite the constant 2g = 64.4 and our
assumed constant coefficients, and substitute their algebraic
equivalents in the equations :
- 1341 - 6666 -
The equations will in this case become :
j 2500 j y= 50 ! j- y for clean pipes. (a)
J 1 no At AC* "* d \ A ^ ( II d \ i for slightly tuber- /7A
j 1963.4146 -j- j- : = 44.31 j -y- j- culated pipes. (&)
1341.6666 -y- |- = 36.63 | -p i forvery foul pipes, (d)
296. Mean Equations for Smooth, Rough, and
Foul Pipes. From these expressions of velocity, in long,
full pipes, the equations for head, length, and diameter
may be deduced, thus :
v =
Kn
OU
h"= 4
( 7i' d I i / N
j j r for clean pipes . \O)
( f)"(J } x
44 3^ J J. 3 for slightly rough pipes. ()
( Z )
36.63 | -y- [ for very rough pipes . (c)
.0004 -g- . . ''; . (a)
.000508 ^ . ' - ( & )
.000745 ^ : . . * .- ( c )
(23)
" (24)
I =
2500
1963.4146
MEAN COEFFICIENTS.
dh"
V 2 ...
dh"
269
(b) j. (25)
1341.6666^
d= 4
,0004 ^77 .
7^2
.000508-^77 -
.000745 ^r,
. (a)
(26)
In which, = velocity of flow, in feet, per second ;
h" = head in slope, or mean gradient, in feet ;
I = length of pipe, in feet ;
d internal diameter of pipe, in feet.
It is sometimes convenient to express the volume of flow
per second in a term of quantity, g, rather than in a term of
velocity.
Since v= Jf> therefore,
y (h"d[i ,(h"d 5 n
q = Sv 50 S j -j- j- 39.27 j ^ [
The equations, in terms of quantity (q\ in cubic feet per
second, will then take the following forms :
q= .
39. 27 Yf't for clean pipes
34.80 j j- f for slightly rough pipes
28.77 j -y V for very rough pipes .
(27)
270
FLOW OF WATER THROUGH PIPES.
1 =
d =
,0006484 Jr
.0008257 |
,001208 ^
.00064845
.0008257
.001208
.23034 ]^r,
.24174 \ l f\
(28)
7i"d 5
q*
h"d 5
<f
. . (a)
(29)
. . (a)
.2609 i *,
, (30)
In which, g = volume of flow, in cubic feet per second ;
7i" head in slope, or mean gradient, in feet ;
I length of pipe, in feet ;
d = internal diameter of pipe, in feet.
297. Modification of a Fundamental Equation
of Velocity. The following expressions for velocity, con-
taining the assumed constant coefficient of flow .00644, are
equivalent to each other :
They are sometimes modified "by another coefficient,
thus :
(31)
VALUES OF c'.
271
to make them conform more nearly to experiment for cer-
tain classes of conditions.
This coefficient (c') equals unity (c' = 1) in cases when
.00644 is the proper coefficient of flow to embody in the
fundamental formula ; is greater than unity (c' > 1) when
the principal coefficient should be less than .00644, and
less than unity (c' < 1) when the principal coefficient should
exceed .00644. Generally, with medium velocities of say
two and one-half to three feet per second, this coefficient, c\
will exceed unity for long clean pipes exceeding five inches
diameter, and be less than unity for pipes of less than five
inches diameter.
298. Values of c'. When the legitimate coefficient, m,
is replaced by the assumed constant coefficient .00644, then
approximately,
j %g I* j 2H . . ., . .
1 .00644 ( ( m )
therefore,
C> '' \2g+ .00644) : tToOOOT/Tj
With a given velocity of flow of say three feet per second,
in pipes exceeding one thousand diameters in length, the
several values of c' for different diameters would be approx-
imately as follows :
TABLE No. 66a.
SUB-COEFFICIENTS OF FLOW (c') IN PIPES.
Diameter.
</.
Diameter.
c / .
Diameter.
c 1 .
^ inch.
.930
6 inches.
I.OI5
24 inches.
.150
J "
936
8 "
.031
27
.170
I "
.942
10 "
.050
30 "
.195
4 "
95
12 "
.060
33 "
.207
ij "
.960
14 "
.080
36 "
.225
2 "
.970
16
095
40 "
.245
3 "
.980
18 "
.110
44 "
.287
4 "
995
20 "
125
48
.308
272
FLOW OF WATER THROUGH PIPES.
These values of c' decrease as the velocity of flow de-
creases from three feet per second, and are approximately
correct for higher velocities up to ten feet per second.
BENDS AND BRANCHES
299. Bends. The experiments with "bends, angles, and
contractions in pipes, so far as recorded, have been with
very small pipes, and the deductions therefrom are of
uncertain value when applied to the ordinary mains and
distribution pipes of public water supplies.
Our pipes should be so proportioned that the velocity
of flow, at an extreme, need not exceed ten feet per second.
Our bends should have a radius^ at axis, equal at least to
four diameters.
Under such conditions, the loss of head at a single bend
will not exceed about one-tenth the height to which the
velocity is due (not including height balancing resistance
of pipe- wall).
In such case, we may for an approximation take,*
= /(l + Cf ) + 4m4\ (33)
(34)
According to this equation, if a pipe is 1 foot diameter,
1000 feet long, and flowing with free end under 100 feet
head, the loss at one 90 bend, whose axial radius of curva-
ture equals 4 diameters, will be .47 feet of head. If there
are two bends, the total head remaining constant, the loss
* The mean value of (1 + c r ) for short pipes is 1.505.
BENDS.
273
at both, will not be double this amount, for the velocity
through the first will be reduced by the resistance in the
second, and therefore the resistance in the first will be
reduced proportionally with the square of the reduction of
the velocity ; and a similar proportional reduction of resist-
ance will take place in the first and second bends when a
third is added.
Let v be the velocity due to the given head and length
of pipe without a bend, and Vi the velocity after the bend is
inserted, then the height of head lost, ^ 6 , in consequence of
the bend, is
and II 7i b is the effective remaining head.
After computing the new value of H beyond tne
bend, we may substitute that in the equationffiyimuf
ouMiyiaoi 1 .0^ and proceed to deduce the value of H beyond
the second bend, etc.
For larger pipes, or for larger radius of curvature, or
reduced velocity, the value of the subdivisor may ris3 to .94
or .96, or even near to w#or <M/l/K/wj^
When pipes exceed one thousand diameters in length,
the term (1 + c r ) may be neglected, and the equations
assume the more simple forms,
HfSS
<>
In which v = the rate of flow, in feet per second.
Ji = the head balancing frictional resistance of
pipe-wall, in feet.
i = the sine of inclination =
18
== '??-
length
i
274
FLOW OF WATER THROUGH PIPES.
r = the hydraulic mean radius = ^-i^.
contour
m = a coefficient (vide table of m, page 242).
%g = 64.4.
The experiments by Du Buat, Venturi, and other of the
early experimentalists, with pipes varying from one-half to
two inches diameter, and more recent experiments by Weis-
bach, have been fully and ably discussed by the latter, in
" Mechanics of Engineering" and elsewhere.
Weisbach's formula for additional height of head, Ji^
necessary to overcome the resistance of one bend, is
= z
180
(37)
in which z is a coefficient of resistance, the arc of the bend
in degrees, and h b the additional head required.
The value of z he deduces by an empirical formula :
z = .131 + 1.847 (j,
in which r is the radius or semi-diameter of the pipe, and R,
the axial radius of curvature of the bend.
For given ratios of r to R, z has the following values,
for pipes with circular cross- sections.
TABLE No. 67.
COEFFICIENTS OF RESISTANCE IN BENDS.
r
~R
z
.1
'5
.2
2 5
3
35
.178
4
45
5
55
131
133
.138
145
.158
.206
.244
.294
35
r
~R
z
.6
65
7
75
.8
85
9
95
i
.440
540
.661
.806
977
1.177
1.408
1.674
1.978
BRANCHES. 275
3OO. Branches. In branches, the sums of the resist-
ances due to the deflections of the moving particles, the
contractions of sections by centrifugal force, and the con-
tractions near square edges, if there are such, will for each
given velocity vary inversely as the diameters of the
branches.
Until reliable data for other than small pipe branches is
supplied, we may assume in approximate preliminary
estimates of head required, when the velocity of flow, under
pressure, is ten feet per second, a reduction of that portion
(tf\
= ) at a right-
angled branch, equal to about fifty per cent, in branches of
three to six inches diameter and thirty to forty per cent, in
larger branches.
The equations then take the following form :
a
.60
(1 + c r ) -
< *= _^/ x . (39 >
The value of the subdivisor will be changed according
to the special conditions of the given case, and the effects
of a series of branches will be similar to those above
^described for a series of bends, but enhanced in degree.
For long pipes, equivalent equations will be,
(40)
(41)
276 FLOW OF WATER THROUGH PIPES.
3O1. How to Economize Head. The losses of head
and of energy due to frictions of pipe- wall and to resistances
of angles, contractions, etc., increase with the square of the
velocity, and they occasionally consume so much of the
head that a very small fraction of the entire head only
remains to generate the final velocity of flow.
The losses, other than those due to the walls of the pipes,
originate chiefly about the square edges of the pipes,
orifices, and valves, where contractions and their resulting
eddies are produced, or are due to the centrifugal force of
the particles in angles and bends.
These losses about the edges may be modified materially,
even near to zero, by rounding all entrances to the form of
their vend contracta, and by joining all pipes of lesser
diameter to the greater by acutely converging or gently
curved reducers (Fig. 102), so that tJie solidity and sym-
metrical section of the column of water shall not be dis-
turbed, and so that all changes of velocity shall be gradual
and without agitation among the fluid particles.
It is of the utmost importance, when head and energy
are to be economized, that the general onward motion of
the particles of the jet be maintained, since wherever a
sudden contraction occurs an eddy is produced, and
wherever currents of different velocities and directions
intermingle an agitation results, both of which divert a
portion of the forward energy of the particles to the right
and left, and convert it into pressure against the walls of
the pipe, from whence so much reaction as is across the
pipe is void of useful effect, and the energy of the jet to a
like extent neutralized, and so much as is back into the
approaching column is a twofold consumption of dynamic
force.
CHAPTER XIV.
MEASURING WEIRS, AND WEIR GAUGING.
302. Gauged Volumes of Flow. A partially sub-
merged measuring orifice or notch in one of the upright
sides of a water tank, or a horizontal measuring crest with
vertical shoulders, in a barrier across a stream, equivalent
to a notch, is termed a weir.
Weirs, as well as submerged orifices ( 2O6) are used
for gauging the flow of water, and in their approved forms
give opportunity to apply the constant force and accelera-
tion of gravity, acting upon the water that falls over the
weir, to aid in determining the volume of its flow.
The volume of flow, Q, equals the product of the section
of the jet upon the weir, S, into its mean velocity, V.
Q = 8V. (1)
303. Form of Weir. For convenience in practical
construction and use, hydraulicians usually form their
measuring weirs with horizontal crests, (7Z>, and vertical
ends J.(7and BD^ Fig. 41.
FIG. 40. FIG. 41.
^ ~-
\
$
B
IB
rr- - '-ill
7'. ro^l
J
^
w///////.
^^^^^^^"^^^^^^w
'//''. .
278
MEASURING WEIRS, AND WEIR GAUGING.
FIG. 42.
The theory of flow over weirs of this description is more
accurately established by numerous experimental and posi-
tive measurements, than for any other form of notch.
The head of water upon rectangular weirs is measured
from the crest CD of the weir to the surface of still water, a
short distance above the weir, instead of from the centre of
pressure or centre of gravity ( 2O6) of the aperture, as in
the case of submerged orifices.
The weir is placed at right angles to the stream, with its
upstream face in a vertical plane.
The crest and vertical shoulders of the weir are cham-
fered so as to flare outward on the discharge side at an
angle not less than thirty degrees. The thin crest and
ends receiving the current must be truly horizontal and
vertical, and truly at right angles to the upper plane of the
weir, and sharp-edged, so
as to give a contracted jet
analogous to that flowing
through thin, square-edged
plate.
The edges are common-
ly formed of a jointed and
chamfered casting, or of a
jointed plate not exceeding
one-tenth inch thickness, as shown in Fig. 42.
3O4. Dimensions. The dimensions of the notch
should be ample to carry the entire stream, and yet not so
long that the depth of water upon a sharp crest shall be less
than five inches, and if contraction is obtained at the up-
right ends, the section of the jet in the notch should not
exceed one- fifth the section of the approaching stream, lest
the stream approach the weir with an acquired velocity that
will appreciate the natural volume of flow through the notch.
END CONTRACTIONS.
279
305. Stability. Care is to be taken to make the foun-
dation of the weir firm, the bracing substantial, and the
planking rigid, so there shall be no vibration of the frame-
work or crest, and its sheet piling is to go deep, and well
into the banks on each side, when set in a stream, so that
there shall be no escape of water under or around it, and a
firm apron is to be provided to receive the falling water and
to prevent undermining.
306. Varying Length. Upon mountain streams, it is
frequently necessary to provide for increasing or shortening
the length of the weir, so that due proportions of notch to
volume may be maintained. This may be accomplished by
the use of vertical stop-planks with flared edges, placed at
one or both ends of the weir, as at^, Fig. 41.
Sometimes it is necessary to make the notch of the entire
width of the stream, when there will be crest contraction
only, and no end contractions, in which case partitions E
(Fig. 44) should be placed against the upper side of the
FIG. 43. FIG. 44.
weir flush with its shoulders and at right angles to its
plane. On other occasions the weir may be so long as to
require intermediate posts, F (Fig. 44), in its frame- work,
when intermediate contractions, one to each side of a post,
will be obtained, in additions to the crest and end contrac-
280 MEASURING WEIRS, AND WEIR GAUGING.
tions ; each of which exerttan important diminishing influ-
ence upon the volume of flow.
307. End. Contractions. A short weir may be de-
fined, one which is appreciably affected by end contractions
throughout its entire length ; practically, when the length
of unbroken opening is less than about four times the
depth of water flowing over.
The end contractions affect a nearly constant length at
each end, for each given depth, on long weirs, and such
length increases with the depth of water upon the weir.
To obtain perfect end contractions, the distance from
the vertical shoulder to the side of the channel should
not be less than double the depth of the water upon the
weir.
If there is no end contraction, the volume for any given
depth is proportional to the entire length of the weir.
The flow, for a given length, on long weirs, or on weirs
without end contractions, is proportional to a power of the
depth on the weir.
308. Crest Contractions. To obtain perfect crest
contractions, the depth of water above the weir should not
be less than about double the depth upon the weir, especi-
ally when the depth flowing over is less than one foot j and
the clear fall below the crest to the surface of tail water
should be sufficient to maintain a perfect circulation of air
in the crest contraction, d (Fig. 42), under the jet, all along
the crest. Such supplies of air are to be provided for at
ends, and at central posts, F (Fig. 44), since a vacuum
under the jet would defeat the application of the ordinary
formula.
309. Theory of Flow over a Weir. To illustrate
the deduced theory of flow through rectangular notches, we
will first consider a case independent of contraction :
THEORY OF FLOW OVER A WEIR.
281
FIG. 45.
\
V
II^s:
\n
-x
Let #, 5, c, d, 6, /, etc. (Fig. 45), be orifices in the side
of a reservoir, at depths below the water surface, respec-
tively of 1, 2, 3, 4, 5, 6, etc., feet.
Then the velocity of issue of jet from each orifice will be
V= VfyH,
according to its depth, H, below the surface, viz. :
For orifice b, V = V2gi = 8.03 feet per second.
c, V=
d, V =
e,V =
/, T=
i, V=
*, V =
= 11.40 "
= 13.90 "
= 16.00 "
= 17.90 "
= 19.70 "
= 21.20 "
= 22.70 u
o,V=\ / 2g9 =24.10 "
p, V =
= 25.40
Plot each of these depth, a, >, c, etc., to scale upon the
same vertical line as abscisses and their corresponding
velocities of issue, W, cc\ dd\ etc., horizontally to the same
282 MEASURING WEIRS, AND WEIR GAUGING.
scale as ordinates ; then the extremities of the horizontal
lines will touch a parabolic line, a, &', d, p\ whose vertex
is at a, abscissa is ap, ordinates are bb', cc f , pp\ etc., and
whose parameter equals 2g.
Suppose now the lintels separating the orifices are in-
finitely thin, then the volume issuing per second from each
orifice will equal a prism, whose length and height equals
that of the orifice, and whose mean projection is equal to
its ordinate, bb', cc', dd, etc., or equals in feet, the feet per
second of velocity of issue from the orifice.
Again, suppose the partitions to be entirely removed
and the fluid veins to be infinitely thin and infinite in num-
ber as respects height, then the velocities of the veins plot-
ted to scale, will touch, as before, the parabolic line ab'd'p',
and the volume of issue per second will equal a prism whose
end area equals the notch ap, and whose area of projection
equals the area of the parabolic segment, app'd'a.
According to well known properties of the parabola, the
segment app'd'a is equal to two-thirds its circumscribing
parallelogram Aapp'.
Let I be the length of the notch, H the height = ap, and
VSglfihe length of the segment =pp ; then the area of the
circumscribing parallelogram equals II x V%gH and the
area of the segment equals H x f V2gH and the volume of
issue Q = I x H x f VfyH. (2)
Let V be the velocity of the film of mean velocity.
Since the volume of the segmental prism app'd'a equals
two thirds of the parallelepiped Ap of equal height, length,
and projection, it follows that the volume of the segment
equals the volume of a parallelepiped of equal height and
length and of f the projection = pp", and the mean velocity
of issue, V = pp" = I V2gff.
The volume Q = I x H x V= I x H x |
FLOW WITHOUT AND WITH CONTRACTIONS.
If the crest of the weir is raised to/, then let the height
of be ^, and the velocity of issue of the film at the crest f
will be ^2gkj and the volume of issue q from the notch of
will be, q = %l x h x Vk x V%g.
If the volume q of this segmental prism aff'b'a, be sub-
tracted from the volume Q of the segmental prism app'd'a,
the remainder will equal the volume of the prism fpp'f =
Q - q^(%lx H xVHx V2g) - (f I x h x Vh x V2g) =
(3)
31O. Formulas for Flow without and with Con-
tractions. The formula (2), Q = I x II x | Vty x t 7 ^
may take the form Q = VZg x I x \H*. (4)
Taking into consideration the complete contraction in a
rectangular weir, we observe first, that in addition to the
crest and end contractions, the surface of the stream, Fig. 42,
begins to lower at a short distance above the weir, and the
jet assumes a downward curve over the weir.
Experiments demonstrate that the measurements are
facilitated, both in accuracy of observations and in ease of
calculations, by taking the height of water upon the weir
to the true surface level a short distance above the weir,
instead of to the actual surface immediately over the crest.
In such case the top contraction has no separate coefficient
in the formula of volume.
Experiments demonstrate also, that a perfect end con-
traction, when depths upon the weir are between three and
twenty-four inches, and length not less than three times the
given depth, will reduce the effective length of the weir a
mean amount, approximately equal to one-tenth of the
depth from still water surface to crest.
If H is this depth from surface to crest, and I the full
length of the weir, and I the effective length of the weir,
then one end contraction makes l'= (I 0.1 H) ; and two
284 MEASURING WEIRS, AND WEIR GAUGING.
end contractions make l'= (I 0.2H) ; and any number,
n, of end contractions make l'= (I Q.lnH).
The reduction of volume by the crest contraction is com-
pensated for by a coefficient m introduced in the formula
for theoretical volume, as above deduced. This coefficient
(m) is to be determined for the several relative depths and
lengths by experiment.
If we insert the factors relating to end and crest contrac-
tions, the formula for volume becomes :
Q = lm x V2g x (I - O.lnlf)!?^ (5)
The factors f and V2g are constants, and for approximate
calculations within limits of 3 to 24 inches depths upon the
weir, m may be taken as constant.
Let O represent the product of these three factors, then
C=%m x Vfy.
The admirable experiments with weirs* upon a great
scale, which were conducted by James B. Francis, C. E.,
with the aid of the most perfect mechanical appliances, in a
most thorough and careful manner, give to C a mean value
of 3.33, and we have 3.33 = \m x Vty.
Transposing and assigning to V%g its numerical value,
we have,
O OO O OO
m = 2 "g7)25 ^35 = -622 as a mean coefficient.
The formula for volume of flow may take the following
forms :
Q=l VZg x m(l - Q.lnB)IT* = 5.35m(Z - 0.1nH)H^ (6)
or for approximate results,
Q = O(l 0.lnff)IT* = 3.33(Z - O.lnffjNl (7)
This last formula, suggested by Mr. Francis, assumes
* Lowell Hydraulic Experiments ; Van Nostrand, New York, 1868.
INCREASE OF VOLUME DUE TO INITIAL VELOCITY. 285
that the discharge is from a reservoir infinitely large, so that
the water approaching has received no initial velocity.
311. Increase of Volume due to Initial Velocity
of Water. When there is appreciable velocity of approach,
let $ be the section of stream in the channel of approach,
and Fthe mean velocity of flow in the section ', and h the
height to which the velocity V is due, and Q' the volume
enhanced by the initial velocity. Then
Q
SV= Q, and V= ^, and h = ^-.
If the mean velocity, F, is to be determined from the
surface motion of the water in the channel of approach, let
V be the surface motion ; then, as will be shown in the
consideration of flow of water in channels ( 332), the mean
velocity is, approximately, eight-tenths of the surface ve-
( 8 F'Y 8
locity, and V= .8V, and 7i = %
Referring again to a parabolic segment of length equal
to the unit of length of weir,
Fig. 46, and let If = ap, and FIG. 4r>.
Ji sa, and V%gH = pp and
Tfc) = pt.
The ordinate pp' of the seg-
ment app' is the projection of a
parabolic segment whose volume
equals the volume of flow when
the depth upon the weir equals
ap.
When the flow has no initial
velocity the ordinate at a = 0,
but when the flow has an initial velocity due to the height
sa = Ti, the ordinate at a equals V2gk = aa\ and the ordi-
nate at p = V%g(H + 7i) =pt, and any ordinate /, at a
286 - MEASURING WEIRS, AND WEIR GAUGING.
depth 7i' = sf, equals V2gh'=ff", therefore the increase
of volume of flow due to initial velocity is represented by
the volume aa'tp'f, and the whole volume of flow by the
volume apta'.
This last volume is the volume spt less the volume sad,
and equals, for unit of length,
.... (8)
Let Q' be the enhanced volume, and let H' be some
depth, yp, upon the weir, that substituted for H in the
ordinary formula for Q would give the value of Q'.
The formula then, if there are no end contractions, is
q = \ml^gH\ (9)
or, for approximate measures, including end contractions,
if any,
Q = 3.33 (I - O.lnlT) H\ (10)
To determine the value of H' from (H -f h\ substitute
the value of Q' in the equation (8) of volume for one unit of
length, and we have
and reducing, we have
If the volume of flow (Q = $ml V2g IT*) is known, and it
is desired to find the depth If upon a weir of given length,
then by transposition we have,
H= j ; (12)
\
*
lrnl
COEFFICIENTS FOR WEIR FORMULAS. 287
or, in case of initial velocity in the approaching water,
H = j 2 ^-J + *4 * - * ( 13 )
The first of these two values of H will give results suf-
ficiently near for all ordinary practice, if the initial velocity
does not exceed one-half foot per second.
In the above formulas of volume the symbols represent
values as follows :
Q = volume due to natural flow, in cubic feet per second.
I length of weir, in feet.
I = effective length of weir, in feet.
m = coefficient of crest contraction, determined by exper-
iment.
H= observed depth of water upon the weir, in feet.
S = section of channel leading to the weir, in square feet.
V = mean velocity of water approaching the weir, in feet
per second.
7i = head to which this velocity is due, in feet.
2# = 64.3896, or 64.4 for ordinary calculations.
H' = head upon the weir, when corrected to include effect
of initial velocity of approaching water.
Q' = volume of flow, including effect due to initial velocity
of approaching water.
312. Coefficients for Weir Formulas. The con-
trolling influence of the contractions entitle them to a
detailed study.
In Mr. Francis' formula for volume, quoted above, the
end contraction is assumed to be a function of the depth,
and the crest contraction to be compensated for by the
coefficient C, of which m is the variable factor dependent
upon the depth.
288
MEASURING WEIRS, AND WEIR GAUGING.
In the following table the quantities in columns A, B,
D, E, F have been selected from Mr. Francis' table, the
column C reduced from its corresponding column, and the
column G computed. Each of the columns are means of a
number of nearly parallel experiments, and they are here
arranged according to depth upon the weir.
TABLE No. 68.
EXPERIMENTAL WEIR COEFFICIENTS.
A.
B.
c.
D.
E.
F.
0.
II
&
i>.b.
if!
CL 5^ en
a T
w So
I Is
S V
s
||
g ^j
jte
H W S II
.b^ I <s
8 >, 3 s,
ni
1 7
o
0)
a
I"
g.jg
r; O.O N
5
^ l' s
s S a
a -
9-997
.62
16.2148
16.0382
16.0502
3.3275
.622
9-997
65
17.3401
17.1990
17.2187
3.3262
.622
9-995
.80
23-7905
23.8821
23.8156
3.3393
.624
9-997
.80
23.4304
23.4011
23.439!
3.3246
.621
9-997
83
25.0410
24.8313
24.7548
3.3403
.624
9-995
.98
32.5630
32.3956
32.2899
3-3409
.624
9-995
.00
33.4946
33.2534
33.2833
3.3270
.622
9-997
.00
32.5754
32.5486
32.6240
3-3223
.621
9-997
.06
36.0017
35.8026
35-5602
3-3527
.627
9-997
25
45-5654
45-4125
45.3608
3-3338
.623
9-997
-56
62.6019
62.6147
62.8392
3.3181
.620
7-997
.68
14.5478
14.4581
14.4247
3.3368
.624
7-997
i. 02
26.2756
26.2686
26.0333
3.3601
.628
1
Mean,
.623
Mr. Francis points out the necessity of caution in apply-
ing the above formula for Q' beyond the limit covered by
the experiments, but it occasionally becomes necessary to
use some formula for depths both less and greater than is
included in the above table.
After plotting with care the results obtained in various
DISCHARGES FOR GIVEN DEPTHS.
289
experiments by different experimentalists, we suggest the
following coefficients for the respective given depths, until a
series of equal range shall be established by experiments
with a standard weir gauge. At the same time, we advise
that weirs be so proportioned that the depths upon them
shall conform to the limits already covered by experiment,
or at least between 4 and 24 inches depths, and with length
equal to four times the depth.
TAB L E No. 69.
COEFFICIENTS FOR GIVEN DEPTHS UPON WEIRS (in thin vertical
plate).
Denths J
i in.
i* in.
2 in.
3 in.
4 in.
6 in.
Sin.
10 in.
.083 ft.
.124 ft.
.167 ft.
25ft.
333 ft-
.500 ft.
.667 ft.
.833 ft-
Value of nt ...
.6100
.6120
.6140
.6170
.6195
.6223
.6235
.6240
Value of C
3.285
o.oi4
3.329
3-336
3.338
Depths -j
12 in.
ift.
14 in.
1.167 ft*
i6iri.
1-333 ft-
i8in.
1.500 ft.
20 in.
1.667 ft
24 in.
2.oooft.
30 in.
2.500 ft.
40 in.
3-333 ft-
48 in.
4.000 ft.
Value of m...
.6241
.6242
.6243
.6242
.6241
.6240
.6232
.6226
.6200
Value of C
3-339
3-339
3-340
3-339
3-339
3.338
3-334
3-33i
3-317
313. Discharges for Given Depths. The following
table of approximate flow over each foot in length of a
sharp-crested rectangular weir has been prepared to aid in
adjusting the proportions of weirs for given streams. End
contractions are not here allowed for.* The coefficients C
(in CIH%) are taken from table above, and I equals unity.
The proportions of weir and its ratio to section of chan-
nel are here supposed to conform to the general suggestions
given above.
* To compensate for a single end contraction, on a weir of any length,
deductyOBe-tofitk the Tolmno duc-.to one foot length of th
290
MEASURING WEIRS, AND WEIR GAUGING.
TABLE No. 7O.
DISCHARGES, FOR GIVEN DEPTHS OVER EACH LINEAL FOOT OF WEIR.
Head from
still water
in ft,=H.
ff*.
11
31* "
1
*.
Cubic feet.
i
P5
**.
Cubic feet.
.04
.0080
.0261
.46
.3120
.0386
1.2
I.3I45
4.3904
05
.0112
.0365
.48
.3326
. 1072 i
i-3
1.4822
4.9506
.06
.0147
.0480
So
3536
.1771
1.4
1.6565
5-53H
.07
.0185
.0604
52
3750
.2483 i
i-5
1.8371
6.1341
.08
.0226
0737
54
.3968
.3209
1.6
2.0239
6-7558
.09
.0270
.0881
.56
.4191
3951
1-7
2.2165
7o987
.10
.0316
1035
.58
.4417
4724 i
1.8
2.4150
8.0516
.11
.0365
1195
.60
.4648
.5506 j
1.9
2 6190
8.7317
.12
.0416
.1369
.62
.4882
.6286
2.O
2.8284
9.4299
13
.0469
.1536
.64
.5120
.7080
2.1
3-0432
10.1460
.14
0524
.1718
.66
.5362
.7888
2.2
3.2631
10.8694
-15
.0581
.1906
.68
.5607
.8705
2-3
3.4881
11.6189
.16
.0640
.2102
.70
.5875
9599
2.4
3.7I8I
12.3850
17
.O7OI
.2303
.72
.6109
2.0380
2-5
3-9528
13.1668
.18
.0764
.2512
74
.6366
2.1237
2.6
4.1924
13.9649
.19
.0828
.2726
.76
.6626
2.2118
2-7
4.4366
14.7783
.20
.0894
.2951
.78
.6889
2.2996
2.8
4-6853
15.6067
.22
.1032
.3407
.80
.7155
2.3883
2.9
4.9385
16.4501
.24
.1176
.3882
.82
.7426
2.4788
3.0
5.I962
17.3086
.26
.1326
4377
.84
.7699
2.5699
3-i
5.4581
18.1809
.28
.1482
.4892
.86
7975
2 . 6620
3-2
5.7243
19.0676
-30
.1643
5445
.88
.8255
2-7557
3-3
-9948
19.9687
-32
.1790
5932
.90
-8538
2.8500
3-4
6.2693
20-7953
-34
.1983
.6572
.92
.8824
2.9463
3-5
6-5479
21.7194
.36
.2160
.7158
.94
.9114
3.0432
3-6
6.8305
22.6568
.38
.2342
.7761
.96
.9406
3.1407
3-7
7.II7I
23.6074
.40
.2530
.8384
.98
.9702
3-2395
3-8
7.4076
24.5710
.42
.2722
.9020
1. 00
I. 0000
3-339
3-9
7.7019
25.5472
44
.2919
.9717
i.i
1-1537
3.8522
4.0
8.0000
26.5360
The coefficients derived from the experiments of Castel
and D' Aubuisson, Du Buat, Poncelet and Lebros, Smeaton
and Brindley, and Simpson and Blackwell, have been
deduced by those eminent experimentalists to compensate
for all contractions. In such cases, the ratio of length of
weir to depth, especially where depth exceeds one-fourth
the length, and the ratio of length to breadth of channel by
which water approaches, exert controlling influences upon
the coefficient.
WEIR COEFFICIENTS.
291
The following table of coefficients, deduced "by Castel,
show the influence of depth and length.
In these experiments, Castel used for channel a wooden
trough 2 feet 5| inches wide, and the weir placed upon its
discharging end was in each case of thin copper plate.
TABLE No. 71.
WEIR COEFFICIENTS, BY CASTEL.
**
P.C
o| 8
CANAL, 2.427 feet wide. COEFFICIENTS, the lengths of the overfall being respectively
Ft.
2.42
Ft.
2.23
Ft.
1.96
Ft.
1.64
Ft.
1.31
Ft.
0.98
Ft.
0.65
Ft.
0.32
Ft.
0.16
Ft. \ Ft.
0.09 0.06
Ft.
0.03
Ft.
0.78
%
50
52
45
39
3
:S
13
.09
0.595
0.615
. '0.639
594
6x4
6?n
0.596
595
595
593
592
593
595
.604
.611
.619
.624
594
594
592
592
591
591
592
595
.618
.614
.6,3
.613
.612
.612
.612
.612
.612
.613
.614
0.629
.628
.628
.628
.628
.627
.627
.628
.629
A
.641
.642
.643
645
.648
.652
.658
66 3
.669
0.670
.672
.674
7i3
0.603
.604
.604
.606
.610
.616
.623
.631
0.621
.621
.620
.622
.626
.632
.636
0.662
.662
.662
.662
.663
-657
.656
.656
.656
656
.660
0.644
.644
.645
.644
.645
.651
0.631
.632
.632
633
.636
.642
If we plot certain series of experiments "by Smeaton and
Brindley, Poncelet and Lesbro, Du Buat, and Simpson and
Blackwell, and take the corresponding series of coefficients
from the resulting curves, we have the following results for
the given depths and lengths.
TABLE No. 72.
SERIES OF WEIR COEFFICIENTS.
EXPERIMENTERS.
!A&
fc
j-T
DEPTHS UPON WEIR, IN FEET.
Ft.
0.075
.682
.625
673
.740
.615
Ft.
O.I
.667
.618
.662
T 3 l
Ft.
015
.640
.608
6 45
Ft.
0.2
.623
.600
635
.678
.700
Ft.
0.25
613
597
.629
657
.718
Ft.
0-3
.605
.624
.638
735
Ft.
0.4
.596
'.608
754
Ft.
Ft.
0.6
'635
577
.780
Ft.
0.7
Ft.
0.8
.480
Ft.
0.9
478
Smeaton and Brindley
Poncelet and Lesbros
Du Buat
1-533
10.0
.482
.560
793
Simpson and Blackwell
292 MEASURING WEIRS, AND WEIR GAUGING.
Within the limits of depths covered by the above experi-
ments the coefficients all increase as the depths decrease,
except in the last series belonging to the 10 foot weir. The
curves in each instance begin to bend rapidly at depths of
about three-tenths feet. In the two last series above, the
convexities of the curves are opposed to each other, and the
curves cross at a depth of .275 feet.
314. Vacuum under the Crest. If the partitions E
(Fig. 44) are prolonged below the weir so as to close the
ends of the crest contraction, and the fall is slight to surface
of tail water, the moving current will withdraw sufficient
air from under the fall to produce a vacuum in the crest
contraction, from which will result an increased flow over
the weir. Such vacuum will take place if the surface of
the tail water rises to the level of the crest when there is
two and one-half or more inches depth flowing over the weir.
The tail water may rise near to the crest of the weir, if
no vacuum is produced, without materially affecting the
volume of flow.
315. Examples of Initial Velocity. Mr. Francis
found that with a half foot depth upon the weir, a half foot
per second initial velocity of approach increased the dis-
charge about one per cent., and with one foot upon the
weir, one foot per second initial velocity increased the dis-
charge about two per cent.
When initial velocity exists in the approaching water,
and the flow is irregular, with eddies, results of submerged
obstructions or irregular channel, the channel should be
corrected, and, if necessary, a grating placed in the stream
some distance above the weir, so that the water will ap-
proach with steady and even flow upon each side of the
channel's axis, so that correct measurements may be taken
of the height of the surface of the stream above the weir.
WIDE-CRESTED WEIRS. 293
316. Wide-Crested Weirs. If the crest of the weir is
thickened, as in the case of an unchamfered plank, the jet
tends to cross in contact with its full crest breadth, and the
contraction is distorted. This is especially the case when
the depth upon the weir is less than three inches.
If the edge receiving the current is not a perfect angle
not greater than a right-angle, that is, if it is worn or
rounded, the jet tends to follow the crest surface and dis*
tort the contraction.
In such cases the ordinary formula are not applicable,
'and the safest remedy is to correct the weir.
When the weir crest is about three feet wide, and level,
with a rising incline to its receiving edge, as in Fig. 47, Mr.
Francis suggests a formula for approximate measurements,
when end contractions are suppressed, for depths between
six and eighteen inches, as follows :
Q = 3.01208 IH* (12)
The coefficient m is here .563 approximately.
FIG. 47.
< 3-d'
In Mr. BlackwelTs experiments on weirs three feet wide,
both level and inclined downward from the receiving edge
to the discharge, coefficients m were obtained, as follows,
applicable to the formula
(13)
294
MEASURING WEIRS, AND WEIR GAUGING
TABLE No. 73.
COEFFICIENTS FOR WEIR CRESTS THREE FEET WIDE.
Depths from
still water
upon the
the weir.
3 feet long,
level.
3 feet long,
inclined,
i in 18.
3 feet long,
inclined,
i in 12.
6 feet long,
level.
10 feet long,
level.
10 feet long,
inclined,
i in 18.
Feet.
m.
m.
m.
m.
m.
in.
.083
452
545
.467
....
.381
.467
.167
.482
546
533
....
479
495
.250
.441
537
539
.492
....
....
333
.419
431
455
497
....
515
.417
479
.516
.518
.... s
.500
.501
....
531
507
513
543
.583
.488
.513
527
497
.667
.470
.491
....
....
'.468
507
750
.476
.492
.498
.480
.486
833
....
....
465
455
.917
....
....
....
.467
1. 000
....
....
....
....
. . .
....
317. Triangular Notches. Prof. James Thomson, of
the University of Glasgow, proposed, in a paper read before
the British Association at Leeds, in 1858, a triangular form
of measuring weir. In his experiments with such weir, the
depths of water varied from 2 to 4 inches, and the volumes
from .033 to .6 cubic feet per second. From his experi-
ments he derived the formula
Q = 0.317
(14)
The flow for all depths would be through similar tri-
angles, therefore an empirical formula applies with greater
reliability to varying depths.
Prof. Thomson claimed that "in the proposed system
the quantity flowing comes to be a function of only one
variable namely, the measured head of water while in
the rectangular notches it is a function of at least two vari-
ables, namely, the head of water, and the horizontal width
OBSTACLES TO ACCURATE MEASURES 295
of the notch ; and is commonly also a function of a third
variable, namely, the depth from the crest of the notch
down to the bottom of the channel of approach."
When the stream is of such magnitude as to require a
considerable number of triangular notches (say of 90
angles, or isosceles right-angled triangles) for a single gauge,
the greatest nicety will be required to place the inverted
apices all in the same exact level, so one measurement of
depth only may suffice for all the notches.
The angles of the notches in each weir must conform
exactly to the angles of the notch from which the empirical
formula, or series of coefficients for given depths, was de-
duced.
For large volumes of water, the great length required
for a sufficient number of notches, as well as depth required
in each notch, are often obstacles not easily overcome, and
the mechanical refinement necessary to ensure accuracy of
measurement is often difficult of attainment.
318. Obstacles to Accurate Measures. A correct
measurement of the depth of water upon a weir is not so
easily obtained as might be supposed by those unpractised
in hydraulic experiments.
If the weir is truly level and the shoulders truly vertical,
which are results only of good workmanship, and the
length intended to be some given number of even feet, the
chances are that only a skilled workman will have brought
the length within one, two, or even three-thousandths of a
foot of the desired length. Again, when the weir is truly
adjusted and its length accurately ascertained, it is not
easy to measure the depth upon the crest within one or two
thousandths of a foot, without excellent mechanical devices
for the purpose.
The errors due to agitation or ripple upon the water and
296 MEASURING WEIRS, AND WEIR GAUGING.
the capillary attraction of the measuring-rod have to "be
eliminated.
If the graduated measuring-rod is of clean wood, glass,
steel, copper, or any metal for which water has an affin-
ity, and its surface is moist, or is wetted Iby ripple, the
water will, in consequence of capillarity, rise upon it above
the true water level ; or if, on the other hand, the rod is
greasy, the water may, in consequence of molecular repul-
sion, not rise upon it to the true surface level.
These sources of error may not be of much consequence
in gaugings of mountain streams, when the only object is
to ascertain approximately the flow from a given watershed ;
but in measurements of power, and in tests of motors, tur-
bines, and pumps, they are of consequence.
Upon a weir ten feet long, with one foot depth of water
flowing over, an error of one-thousandth of a foot in meas-
urement of depth will affect the computation of flow about
two cubic feet per minute, and an error of one-thousandth
of a foot (about -^ of an inch) in length will affect the com-
putation about two-tenths of a cubic foot per minute.
These amounts of water upon a twenty-five or thirty foot
fall would have quite appreciable effects and value.
319. Hook Gauge. A very ingenious and valuable
instrument for accurately ascertaining the true level of the
water surface, and depth upon a weir to still water, was
invented by Uriah Boy den, C.E., of Boston, and used by
him in hydraulic experiments as early as the year 1840.
This, shown in one of its forms, in Fig. 48, is commonly
termed a hook gauge.
This gauge renders capillary attraction a useful aid to
detect error, instead of being a troublesome source of error.
The instrument is firmly secured to solid substantial
beams or a masonry abutment, so that it will be suspended
HOOK GAUGE.
297
FIG. 48.
HOOK GAUGE.
over the water channel a few feet up-
stream from the weir, and where the
water surface is protected, naturally
or artificially, from the influence of
wind and eddies. The gauge is here
adjusted at such a height that when it
reads zero the point of the hook shall
accurately conform to the level of the
crest of the weir ; or the vernier reading
is to be taken, with the hook at the
exact weir level, for a correction of
future readings.
This correction is to be verified as
occasion requires between successive ex-
periments.
When the full flow of water over the
weir has become uniform, the hook is
to be carefully raised by the screw mo-
tion, until the point just reaches the
surface of the water. If the point is
lifted at all above the water surface, the
water is lifted with it by capillary at-
traction, and the reflection of light from
the water surface is distorted and reveals
the fact. The screw is then to be re-
versed and the point slightly lowered
to the true surface.
In ordinary lights, differences of
0.001 of a foot in level of the water are
easily detected by aid of the hook,
and even 0.0001 of a foot by an expe-
rienced observer in a favorable light.
Such gauges are ordinarily gradu-
298 MEASURING WEIRS, AND WEIR GAUGES.
ated to hundredths of a foot and are provided with a ver-
nier indicating thousandths of a foot, and fractions of this
last measure may be estimated with reliability.
320. Rule Gauge. For rougher and approximate
measures a post is set at an accessible point on one side of
the channel, above the weir, and its top cut off level at the
exact level of the weir crest.
The depth of the water is measured by a rule placed
vertically on the top of this post and observed with care.
321. Tube and Scale Gauge. For summer meas-
ures, a pipe, say three-fourth inch lead, is passed from the
dead water a little above the weir, through or around the
weir, and connected to a vertical glass water tube set below
the weir at a convenient point of observation. In such case
a scale with fine graduations is fastened against the glass
with its zero level with the weir. With such an arrange-
ment quite accurate observations can be taken, as the
water in a three-quarter inch tube will rise to the level of
the water above the weir over the open mouth of the tube,
due precautions being taken to keep sediment out of the
tube.
CHAPTER XV.
FLOW OF WATER IN OPEN CHANNELS.
322. Gravity the Origin of Flow. Gravity tends to
cause motion in all bodies of water. Its effects upon the
flow of water under pressure have been already discussed
(Chap. XIII), as have also the effects of the reactions and
cohesive attractions that retard its flow.
The same influences control the flow of water in open
channels.
The fluid particles are attracted toward the earth's
centre along that path where the least resistance is op-
posed.
An inclination of water surface of one-thousandth of a
foot in one foot distance leaves many thousand molecules
of water, but partially supported upon the lower side, and
they fall freely in that direction, and by virtue of their
weight press forward the advanced particles in lower planes.
FIG. 49.
If water is admitted from the reservoir -4, into the open
canal B (Fig. 49), until it rises to the level W, it will there
stand at rest, although the bottom of the channel is in-
clined, for its surface will be in a horizontal plane. The
300 FLOW OF WATER IN OPEN CHANNELS.
resistances to motion upon opposite inclosing sides, and
also upon opposite ends, balance each other. The alge-
braic sum of horizontal reactions from the vertical end bd,
is exactly equal to the sum of the horizontal reactions from
the inclined bottom db', for the vertical projection, or trace
of the inclined area, db', exactly equals the vertical area bd.
The same equilibrium would have resulted if the bot-
tom had been horizontal or inclined downward from d to/,
and a vertical weir placed at fb', for the horizontal reaction
from/ b' would have been balanced by the sum of the hori-
zontal reactions from bd and df.
A destruction of equilibrium permits gravity to generate
motion.
If a constant volume of water is permitted to flow from
the reservoir A into the channel B, the water surface will
rise above the level bb', when there will be less resistance at
the end b' than at &, and the fluid particles, impelled by the
force of gravity, will flow toward b'. When motion of the
water is fully established, and the flow past b' has become
uniform, there will result an inclination of the surface from
a toward a'. This inclination, being a resultant of a con-
stant force, gravity may be used as a measure of the por-
tion of that force that is consumed in maintaining the
velocity of flow.
323. Resistances to Flow. Let the channel be ex-
tended from b' (Fig. 49) indefinitely, and with uniform in-
clination, as from a' to 7c (Fig. 50). Some resistance to flow
will be presented by the roughness and attraction of the
sides and bottom of the channel.
If the sides and bottom are of uniform quality, as re-
spects smoothness or roughness, the amount of their resist-
ance in each unit of length will be proportional to the sum
of their areas, plus the water surface in contact with the
EQUATIONS OF RESISTANCE AND vLCKY. /01
/ ' j
air reduced by an experimental fractional coefficient jr,nd }
to the square of the velocity of flow past them ; and' iji| -
versely to the section of the stream flowing past them. ' </
The exact resistance due to the air perimeter, has yet to
be separated and classified by a series of careful experi-
ments, but we may assume that the resistance of calm air
for each unit of free surface will not exceed ten per cent, of
that for like units of the bottom and sides of smooth chan-
nels, and will bear a less ratio for rough channels.
The air perimeter resistance will be increased by oppos-
ing and lessened by following winds.
Let H be the sum of resistances from the sides, bottom,
and surface, in foot pounds per second ; C, the contour, or
wetted area of sides and bottom, and c, the width, or sur-
face perimeter, in square feet ; &, the sectional area of the
stream, in square feet ; and v, the mean velocity of flow of
the stream, in feet per second ; then we have for equation
of resistance to flow, from sides, bottom, and surface, for
one unit of length :
and for any length, Z, in lineal feet,
E = + s ' lC ' x I x mtf. (2)
324:. Equations of Resistance and Velocity.
When the surface of the water is level the entire force of
gravity acts through it as pressure, but when the surface is
inclined, a portion of the pressure is converted into motion.
Motion is measured by its rate or distance passed through
in the given unit of time, and the rate is expressed by the
term velocity.
302
FLOW OF WATER IN OPEN CHANNELS.
In Fig. 50, let a'Jc be the inclination of the water surface
in a unit of length of the stream, then a"Jc will be its ver-
tical distance and Jc'Jc its horizontal distance.
The effective action of gravity g to maintain motion, or
velocity of the water, is dependent on this slope, and the
slope is usually indicated by a ratio of the vertical distance
to the horizontal distance.
FIG. 50.
Let 7i" be the vertical distance, a"Jc and I be the hori-
zontal distance Jc'Jc, and i the slope, or sine of the inclina-
tion, then the ratio of slope is i = -y-.
If the sides and bottom of the channel opposed no resist-
ance to flow, then the velocity v should be accelerated in
the length Jc'Jc an amount equal to the V%gh"-, but the flow
being uniform, the sum of the resistances in I just balance
the accelerating force of gravity <?, and the velocity v con-
tinues from a' to Jc at the same rate that had already been
established when the stream reached a', which was due to
some height aa' = Ji = ~ .
By transposition, we have v = V2gh.
If the sum of the resistances in the length Jc'Jc balance
the accelerating force due to the head a"Jc = Ji", then we
have
h , l= tf_ x a + .ic, x M .
m
(4)
EQUATIONS OF RESISTANCE AND VELOCITY. 303
8 Section
The inverted fractional term eT^. = C5ntou^ ls
termed in open channels the hydraulic mean deptJi^ and
the letter r is used to express it. Since i expresses the
h"
value of the sine of tJie slope = -=-, we have
*. (5)
h" = . (6)
The total head H equals the heights aa' + a"Tc = 7i + h",
and
" 2# 2gr " ( r ) * 2^"
f_?fflH
V:t 1+I 4j' (8)
In long canals and rivers, with slopes not exceeding
three feet per mile, the velocity head 7i is usually insig-
nificant compared with the frictional head 7^", and may be
neglected in the equation.
When the rate of flow is uniform, 7i is a constant quan-
tity, independent of the length, and when the mean velocity
is known may be taken, by inspection, from the table of
" Heads (h) due to given Velocities," page 264.
The frictional head h" increases with the length, hence
the term I in the equation of h".
nr
* In full pipes equals the sectional area divided by the full circumfer-
L/
ence, and is termed the hydraulic mean radius ( 268), but in open channels
the contour is the wetted perimeter ; that is, the sum of the sides and bottom
and air surface in contact with the water.
304 FLOW OF WATER IN OPEN CHANNELS.
The mean velocity, which multiplied into the sectional
area of the stream will give the volume of discharge, is a
quantity often sought.
v 2
Neglecting the value of 7i = , which has given the
*9
stream its resultant motion, and taking the formula for A",
the head balancing the resistance to flow,
7 _ Imv*
:
and we have by transposition,
(9)
in which v = mean velocity of all the films, in feet per sec.
8f
r = hydraulic mean depth = Y in feet.
O ~f~ (J'iCg
i = sine of inclination = -j- in feet.
L
g = 32.2.
m a comprehensive variable coefficient.
C = wetted earth perimeter.
c s = surface (air) perimeter, taken at O.lc s for
smooth channels, or 0.05c s for rough channels.
I = length, referred to a horizontal plane.
7i = vertical fall in the given length.
325. Equation of Inclination. If the flow is to be
at some predetermined rate, and it is .desired to find the
inclination, or slope to which the given velocity, for the
given hydraulic mean radius, is due, then we have, by
transposing again,
COEFFICIENTS OF FLOW IN CHANNELS. 305
The member v, refers to the mean motion of all the fluid
threads, or the rate which, multiplied into the section of the
stream, gives the volume of flow.
326. Coefficients of Flow for Channels, The value
of the coefficient of flow m, is very variable under the influ-
ences of
(a.) Velocity of flow, or inclination of water surface ;
(b.) Hydraulic mean depth ;
(c.) Mean depth ;
(d.) Smoothness or roughness of the solid perimeter;
(e.) Direction and force of wind upon the water surface.
A complete theoretical formula for flow in a straight,
smooth, symmetrical channel should have an independent
coefficient for each of these influences, and other coefficients
for influences of bends, convergence or divergence of banks,
and eddy influences ; but such mathematical refinement
belongs oftener to the recitation room than to expert field
practice.
The comprehensive coefficient m, for open channels,
which includes all these minor modifiers, is inconstant in a
degree even greater than the coefficient m for full pipes,
which we have already discussed ( 27O. Peculiarities of
the Coefficient of Flow), to which the reader is here referred.
Experience teaches that m is less for large or deep, than
for small or shallow streams ; for high velocities, than for
low velocities ; and for smooth, than for rough channels.
Kutter adopted,* for open channels, the simple formula
r> = c Vfi, and divided the values of c into twelve classes,
to meet the varying conditions, from small to great velocities
and sections of streams, and from smooth to rough sides
* Vide " Hydraulic Tables," trans, by L. D. A. Jackson. London, 1876.
306
FLOW OF WATER IN OPEN CHANNELS.
and beds of channels. His c corresponds to y -^, as herein
employed, and a portion of its values are :
r.
I.
II.
III.
IV.
V.
VI.
VII.
VIII.
IX.
X.
XI.
XII.
5
S3
82.5
8^.8
77-9
79-5
72.4
74.2
66.9
68.9
61.1
63.3
55,8
49-5
51.8
43-2
45.5
36.7
38.9
29.7
22.5
24.1
;|
&
84.8
8 S .6
80.7
81.7
Jlis
70-5
71.9
65.1
66.5
59-9
61.5
53-8
55-4
47-4
49.0
40.7
42.3
33-4
34-9
25-5
26.8
9
88.8
86.4
82.6
77-9
73-o
62.9
56.9
5'5
43-8
36.2
28.0
89-3
87.0
83-3
78.7
74.0
69.0
64.1
58.2
57-8
60 i
37-5
29.1
J
58 7
68 3
62 I
64 8
45-o
f
66*8
68 K
I?'"*
I
f '3
2
2.9
9
55- 1
co
IOO
IOO
IOO
IOO
IOO
IOO
IOO
IOO
IOO
IOO
IOO
IOO
327. Observed Data of Flow in Channels. Let us
deduce the several values of m from various actual meas-
urements of streams, and seek its curve of mean values, so
that when it is a divisor of the simple fundamental equation
= V2gri y we shall have some degree of confidence in the
use of this simple equation for channels and small streams.
For this purpose we will select at random from data given
by Messrs. Humphreys and Abbott, 1861 ; M.M. Darcy
and Bazin, 1865 ; M. Heinr Gerbenau, 1867 ; and sundry
reports of U. S. Engineer Corps, and compute the experi-
mental value of m for each case.*
It will be observed that the data cover ranges as follows :
Of sectional area, from 9.5 to 15911 sq. feet ; of hydraulic
mean depth, from .96 to 15.9 feet; and of velocity, from
.817 to 4.689 feet per second, or from three-quarters to about
three and one-quarter miles per hour.
* The same, with additional data for large rivers, has been used by General
H. L. Abbott, in a paper upon Gauging of Rivers, for the purpose of testing
the new (Humphreys and Abbott) formula for flow of rivers, vide Jour. Frank-
lin Institute, May, 1873.
TABLE OF COEFFICIENTS FOR CHANNELS.
307
TABLE No. 74.
OBSERVED AND COMPUTED FLOWS IN CANALS AND RIVERS,
( 2 gri
AND m =
A.
B.
C.
D.
E.
F.
G.
NAME OF STREAM.
t*j
II
8
53
Wetted
Perimeter
= C.
in
s-a
*f
EQ
Inclination
= /.
Observed
Velocity
Value of
Coefficient
= tn.
Computed
Velocity
= V.
Feeder Chazilly
Sq.ft.
9-5
Feet.
O.Q
Feet.
0.96
Feet.
0.000792
Feet.
1.234
.03215
Feet.
10.8
1.04
0.962
.03227
o 966
tt <t
14.0
12.3
1. 21
.000808
1.667
.02265
it u
18.1
13-1
1.38
.000450
1.296
.02381
1.275
a it
18.8
13.3
I.4I
1.798
.02789
1.926
44 14
13.8
I.4I
0008 58
1.815
.02363
U It
000086
11 il
22.9
14.7
IJ6
000842
1.998
.02118
a n
15.9
I 71
Feeder Grobois . .
IO.2
0.98
.000555
0.984
.03617
n.8
xi. 3
1.05
.000310
0.817
.03155
0.852
U it
17.2
12.5
1.38
.000450
1.326
.02274
I 278
it 41
14.1
1.63
It U
25.0
14.1
1.71
.000515
1.746
.01860
1.617
it it
26.8
30.8
15.7
17.3
?*
.000493
.000275
1.683
1.467
.01917
1.585
1.231
It tt
02 ,O
17.3
is
I 781
Speyerbach . . ....
3O.2
19.7
1.54
.000467
1.814
.01408
I 422
Canal
20. 6
2.40
Lauter Canal
56.4
31.0
1.82
.000664
2.^06
.01754
Saalach
86.9
61.2
1.38
01082
96.7
71.8
1.34
.001136
1.970
.02585
ligio
1C
119 O
32.5
3-7
.000698
C. and O C. Feeder
121.
32.7
3-7
.000699
3.032
.01811
0. C27
River Haine
248.5
50.5
4.90
00836
Isaa
3OO.I
161.6
1.85
.002500
.01864
7.8l2
006.4
53-4
5 7
2 s<;8
00869
2 328
Seine . . .
1978
B. La Fourche
2868
230
2* C 8o
Z
tt
3708
238
3 145
Seine
3 8lO
*
.007
tt
8O34
4.232
4 682
6 126
(i
cxo
18 40
A 680
Rhine ...
I45 8
00828
Upper Mississippi
icgll
1612
9.87
.000074
2.554
328. Table of Coefficients for Channels. From
the experimental results we deduce the following values of
m for the given hydraulic mean depths. Since 2g is a con-
stant, we have also the corresponding values A /%?.
V m
308
FLOW OF WATER IN OPEN CHANNELS.
TABLE No. 75.
VALUES OF m FOR OPEN CHANNELS, AND VALUES OF A / M.
FOR GIVEN HYDRAULIC MEAN DEPTHS.
.9
= c.
T.
4/^
r
r-- 9 -
C
m.
4/.
V m
25
.0500
35-89
7
.0096
81.90
3
.0478
36.70
7-5
.0092
83.66
4
.0440
38.25
8
.0088
85-54
5
.0408
39-73
8-5
.0085
87.04
.6
.0378
41.27
9
.008I
89.16
7
353
42.71
9-5
.0077
9J-45
.8
0332
44.04
10
.0074
93-28
-9
.0312
45-43
ii
.0068
97.3i
1.0
.0298
46.49
12
.0064
100.30
1.25
.0260
49-77
13
.0058
105.36
i-5
.0234
52.46
14
.0054
109.21
2
.0197
57-17
15
.0049
. 114.65
2-5
.0172
61 . 19
16
.0043
122.37
3
OI 53
64.87
17
.0040
126.88
3-5
.0137
68.56
18
.0036
133.77
4
.0127
71.21
J 9
.0033
139.69
4-5
.0118
73-87
20
.0030
146.53
5
.0112
75-83
21
.OO29
149.04
5-5
.0107
77.58
22
.OO27
154-44
6
.0102
79.46
23
.OO25
160.49
6.5
.0099
80.65
25
.O02O
179.44
These values of m and of
were inserted in the
m
were used for a
simple formula, v = \\/ -2 Vri[ , and
test to compute the velocities in the column G, of the above
table of experimental data. The computed velocities may
there be compared with the observed velocities. The results
are satisfactory, if the exceeding difficulty of securing an
accurate measurement of mean velocity of the stream and.
the probability of small errors are considered.
VARIOUS FORMULAS OF FLOW COMPARED. 309
The velocities in the experimental table albove, cover the
range in ordinary practice, excepting the extremes of floods
and droughts. The values of m are for the mean range of
velocities there given. A considerable increase of velocity
would reduce, or of roughness of channel would increase,
the value of m for its given hydraulic mean depth. The
influences of bends and eddies are to be eliminated from the
formula, since the formula applies to a straight, smooth,
symmetrical channel.
Jackson gives,* from Darcy, Bazin, Gauguillet, and
Kutter, variable coefficients for the channel surfaces named,
as follows. (These appear to be applicable to a constant
value of v, equal to about 2.5.) :
.018, Well-planed plank.
.020, Glazed pipes, or smooth cement lining.
.022, Smooth cement and sand mortar lining.
.024, Unplaned plank.
.026, Brickwork and cut-stone lining.
.034, Rubble masonry lining.
.040, Canals, in very firm gravel.
.050, Rivers in earth, free from stones and weeds.
.070,, " with stones and weeds in great quantities.
329. Various Formulas of Flow Compared. To
compare this simple formula, having its variable w, with
some of the more complex formulas, in the forms in which
they are generally quoted in text-books and cyclopedias,
four experiments are taken from the table, having their
hydraulic mean depths and sectional areas of mean, mini-
mum, and maximum values, and their velocities are com-
puted by it. The velocities are then computed by well-
known formulas upon the same data. The results are given
in the following table :
* Hydraulic Manual. London, 1875.
310
FLOW OF WATER IN OPEN CHANNELS.
TABLE No. 76.
FORMULAS FOR FLOW OF WATER IN CHANNELS, TO FIND THE VELOCITY.
Comparing results given by the several formulas.
AUTHORITY.
FORMULAS.
FEEDER
CHAZILLY.*
LAUTER
CANAL.!
1
i
Cfl
4
"I
Eq. (9), 324
Du Buat
Eytelwein . . .
Girard
..JJt.rfU...
Com-
puted
veloc.
in ft.
Per
sec.
0.966
1.929
1.932
1.109
1.962
1.932
2.161
2.151
2.151
Com-
puted
veloc.
in ft.
Per
sec.
1-934
3.627
3.184
2.289
3-352
3.184
S'fyS
3.338
3-438
3.438
2.086
1-747
2.078
Com-
puted
veloc.
in ft.
Per
sec.
2.107
2.411
2.442
1-572
2-545
2-435
2.778
2.691
2.691
2.691
2.166
2.350
2.642
Com-
puted
veloc.
in ft.
per
sec.
3-145
2.143
2.382
1-517
2.479.
2418
2.706
2.627;
2.627
2.627
2.582;
3.268
4-582
( m )
88.51 (r*-. 03) _ ^ Q3)
(_L)i_hyp.log. Q-+X.6)*
v = (10567.8?? + 2.67)^ 1.64
D'Aubuisson.
Neville
T f c i:/
ioo 4/r"
Pole
*/?
( AS) i
Beardmore. . .
Darcy and I
Bazin. f
M. Hagen....
Humphreys )
and Abbott, f
r ** ic \
\ IOOOZ J 1.
1.047
1.237
1.372
{ .o8 534 r + .35 J
w = 4-39^(0*
i./ - /-^fTV .^-1* 2-4^
^ ~\ \/ .0081^+1 5 ' I .09 \b r ,.
(r W+w^/ ) 1+ ^
* FEEDER CHAZILLY. Area, 11.3 sq. ft. Hydraulic mean depth, 1.04 ft Inclination, .000445.
Observed velocity, 0.962 ft.
t LAUTER CANAL. Area, 564 sq.ft. Hydraulic mean depth, 1.82 ft. Inclination, 000664.
Observed velocity, 2.106 ft.
$ SEINE. Area, 1978 sq. ft. Hydraulic mean depth, 5. 70 ft. Inclination, .000127. Ob-
served velocity, 2.094 ft. ,
B. LA FOURCHE. Area, 3738 sq. ft. Hydraulic mean depth, 15.7 ft. Inclination, .000044-
Observed velocity, 3.076 It.
VELOCITIES OF GIVEN FILMS. 311
In the preceding table, the symbols in the formulas have
values as follows :
r = hydraulic mean depth, in feet.
i = inclination of surface in straight channel, in feet.
I = length, in feet.
7i = head, or fall in the given length, in feet.
S = sectional area of stream, in square feet.
O = wetted solid perimeter, in feet.
v = mean velocity of stream, in feet per second.
In the Humphreys and Abbotts' formula, the symbols
have values as follows :
a = sectional area of stream, in square feet.
1 69
5 = a function of depth =
Vr + 1.5
p = wetted perimeter.
r = mean hydraulic depth.
i inclination of surface of stream, corrected for bends.
W = width of stream.
v' = value of first term in the expression for v.
v = mean velocity of stream.
33O. Velocities of Given Films. Since the chief
source of resistance to flow arises from the reactions at the
perimeter of the stream, along the bottom and sides, A, B,
B', A', Fig. 51, and in a small degree along the surface
A, A, in contact with the air, it is evident that the points
of minimum velocity will be along the solid perimeter, and
the point of maximum velocity will be that least influenced
by the resultant of all retarding influences. In a channel
of symmetrical section, the point of maximum velocity
should be, according to the above hypothesis, on a vertical
line passing through the centre of the section and a little
below the water surface, provided the surface was unin-
312
FLOW OF WATER IN OPEN CHANNELS.
fluenced "by wind. The velocity measurements of Darcy
and Bazin*with an improved "Pitot" Tube, locate the
thread of maximum velocity in a trapezoidal channel, at a,
Fig. 51 ; a nearly concentric film of lesser velocity at &, and
other films, decreasing regularly in velocity, at c, d, e, f,
and g.
If the velocities, at the depths at which the given films
cross a vertical centre line, are plotted as ordinates from a
vertical line, as at a, &, c, etc., Fig. 52, their extremities will
lie in a parabolic curve, and the degree of curvature will be
less or greater as the velocity is less or greater, and as the
bottom is smoother or rougher, for the given section.
Velocity ordinates, plotted in the same manner for any
horizontal section, as in the surface, or through , a, &, c,
etc., Fig. 51, will also have their extremities from shore
FIG. 51.
FIG. 52.
nearly to the centre in parabolic curves, the longest ordi-
nate being near the centre of breadth of the canal, and the
two side parabolas being connected by a curve more or less
flat, according to breadth of canal. In Fig. 51, d indicates
the film of mean velocity, and it cuts the central vertical line
at nearly three-fourths the depth from the surface. In
deep streams, or channels in earth, it is usually a little
below the centre of depth.
* Tome XIX des Memoires presentes par divers Savants a 1'Institut Impe-
rial de France, Planche 4.
SURFACE VELOCITIES. 313
331. Surface Velocities. The velocity of the centre
of the surface, in symmetrical channels, or of the mid-
channel in unsymmetrical sections, is that most readily
obtainable by simple experiment.
For such velocity observations a given length, say one
hundred feet of the smoothest and most symmetrical
straight channel accessible is marked off by stations on
both banks, and a wire stretched across at each end at
right angles to the axis of the channel. Thin cylindrical
floats are then put in the centre of the stream a short dis-
tance above the upper wire, by an assistant, and the time
of their passing each wire accurately noted.
A transit instrument at each end station is requisite for
very close observations. A small gong-bell, on a stand or
post beside the transit, is to be struck by the observer the
instant the centre of the float passes the cross-hair, or a
signal is to be transmitted by an electric current, and the
time, noted to the nearest quarter-second by a skillful
assistant, is to be recorded.
The floats are sometimes of wax, weighted until its
specific gravity is near unity ; sometimes a short, thick vial,
corked, and containing a few shot or pebbles ; and some-
times a thin slice of wood cut from a turned cylinder, which
for small channels may be two inches diameter. For large
rivers, the float may be a short keg, with both heads in
place, and weighted with gravel stones. The float is to be
loaded so its top end will be just above the surface of the
water. In broad streams, a small flag may be placed in the
centre of the float.
If a number of floats are started simultaneously at
known distances on each side of the axis of the channel,
they should have each a special color-mark or conspicuous
flag number, so that the time and distance from axis, at
314 FLOW OF WATER IN OPEN CHANNELS.
each station, may be correctly noted for each individual
float.
Du Buat made experiments with small rectangular and
trapezoidal channels of plank, 141 feet long and about
18 inches wide, with depths from .17 to .895 feet, and veloc-
ities from .524 to 4.26 feet, to determine the ratio of the
mean velocity v of the channel section to its central surface
velocity, V. From the mean results he deduced the empi-
rical formula,
v = (A/T .15) 2 + .02233. (11)
This gives, when Fis taken as unity,
v = .545 V.
Prony afterwards, reviewing the same experimental re-
sults, proposed the formula,
_ F /F+ 7.782\ .
\ V + 10.345/ "
Ximenes' experiments upon the River Arno, Raucort's
upon the Neva, Funk's upon the Wesser, Defontaines and
Brunning's upon the Rhine, on larger scales, gave mean
velocities in a vertical line at the centre equal to .915 F,
which being the maximum velocity in its horizontal plane,
indicates, if the reduction of velocity toward the shore is
considered, an approximate mean velocity,
v = .915 (.915 F) = .837 F. (13)
Mr. Francis' experiments in a smooth, rectangular chan-
nel, with section about 10 feet broad and 8 feet deep, and
velocity of 4 feet per second, indicates
<y = .911F. (14)
In the Mississippi River, with depths exceeding one
RATIOS OF SURFACE TO MEAN VELOCITIES. 315
hundred feet, Messrs. Humphreys and Abbott occasionally
found v greater than V.
The Ganges Canal experiments at Roorkee, in 1875, by
Capt. Cunningham, R. E., in a rectangular section 9 feet
deep and 85 feet wide, gave the mean surface velocity
equal to. 927 V.
In any series of rectangular channels of like constant
sectional areas or of like constant borders, it is seen, by
simple mathematical demonstrations, that the hydraulic
Sf
mean depth = -~, is at its maximum when the breadth
equals twice the depth.* Since the velocity of flow in a
series of rectangular channels is nearly proportional to the
square roots of their hydraulic mean depths, it follows that
the proportions of such channels most favorable for high
velocities is breadth equal twice depth.
These proportions of breadth to depth being adopted
again for another series of rectangular channels of varying
section, the velocities will again be sensibly proportional to
the square roots of their hydraulic mean depths.
The ratio of v to V should be at its maximum when
breadth equals twice the depth, and when the section is the
maximum of the given series. .
332. Ratios of Surface to Mean Velocities. Let
d depth and b = breadth of rectangular channels, then
letting depth be unity for a depth of 8 feet and approxi-
mately between 6 and 12 feet, and we shall have, according
to the various recorded experiments, approximate values
of the mean velocity v of flow in the channel, as compared
with the central surface velocity V, as follows, for smooth
channels :
* The influence of sectional profile upon flow is elaborately discussed by
Downing, in Elements of Practical Hydraulics, p. 204, et seq. (London, 1875.)
316
FLOW OF WATER IN OPEN CHANNELS.
When
b = 2d
b = 3d
b = 4d
b = 5d
b = 6d
b = 7d
b = 8d
b = 9d
b = lOd
then
V =
V
V =
V =
V =
= .920F
= .910 F
= .896F
= .882F
= .864F
= .847F
.826F
.804F
.780F
(15)
The values of v should be slightly less for trapezoidal
canals of equal sections, decreasing as the side slopes are
flattened. The values of v will decrease also as the bottom
and sides increase in roughness. The wind may enhance
or retard the surface motion, and thus affect the mean
velocity.
Since inclination of water surface, section of stream,
hydraulic mean depth, and roughness of bottom and side,
all affect the final result of flow, it is evident that experi-
ence and good judgment will aid materially in the selection
of the proper ratio of v to F. A misapplication of formulae
that are valuable when judiciously used, may lead to gross
errors; as, for instance, Prony's formula, deduced from
experiments with Du Buat's small canal, gave result fifteen
per cent, too small when tested by the flow in the Lowell
flume, 10 feet wide and 8 feet deep, where the volume was
proved by tube floats and weir measurements at the same
time.
333. Hydrometer Gaugings. When opportunity
offers, the mean velocity for the whole depth should be
measured, and thus some of the uncertainties accompany-
ing surface measures be eliminated. Among the most
reliable hydrometers that have been used for this purpose
TUBE GAUGE. 317
in canals and the smaller rivers may be mentioned, tin tubes
of length nearly equal to the depth of the stream ; improved
" Pitot tubes ; " and " Woltmann tachometers"
334. Tube Gauge. When the velocity measurements
are to be taken with Francis' tubes or Krayenhoff poles,
Fig. 53, a straight section of the stream is chosen, with
smooth symmetrical channel, clear of weeds and obstruc-
tions. A length of one hundred or more feet, according to
circumstances, is marked off by stations at each end on
each bank, located so as to mark lines at right angles to the
axis of the stream. A steel measuring chain, or wire with
marks at equal intervals, is then to be stretched across at
each end. The depths are then to be taken across the stream
at each end, and at the centre if the banks are warped, at
known intervals of a few feet, accord-
ing to the formation of the banks and
bottom of the stream, so that the sec-
tional area of the stream shall be
accurately known, and may be plot-
ted. The soundings are all to refer
to the same datum previously estab-
lished, and referred to a permanent
bench mark on the shore, which will greatly facilitate
future observations or verifications at the same point.
The requisite number of tight tin tubes, of say two
inches diameter,* are then to be prepared, one for the axis
of the stream, and others for short successive intervals on
each side of the axis, all to be duly numbered for their
respective positions. The length of each is to be such that
it will float just clear of the bottom, and extend to a little
above the water surface. The tube is to be loaded at one
'./, /. ,-... ,/,,/ .,/, ,
* Tubes 40 feet long, 3 inches diameter, made up in sections, have been,
used by the United States Coast Survey Staff.
318 FLOW OF WATER IN OPEN CHANNELS.
end with fine shot or sand, until it has the proper sub-
mergence in a vertical position.
The several tubes are to be started by signal, simultane-
ously if possible, from a short distance above the upper end
station, so that they may cross the upper station as nearly
as possible at the same instant. Their arrivals at the lower
stations are to be carefully noted, and the time of transit of
each recorded.
When the experiment has been several times repeated,
the central and other tubes may be passed down singly, if
the volume of the stream still remains constant, to verify the
first observations. In the last observations, transits may
conveniently be used to observe the passage by the stations,
as suggested above for observing surface floats.
Suppose the stream to be divided transversely into seven
sections, as in Fig. 54, then tubes 1, 2, 3, etc., may be started
FIG. 54.
in the centres of their respective sections. The degree of
accuracy with which they will move along their intended
courses will depend upon the symmetrical regularity of
flow, and very much upon the regularity of the side banks,
and several trials may be necessary to get satisfactory
side and even central measurements, since a slight obstruc-
iion, or a stray boulder upon the bottom, may distort the
Huid threads in an unaccountable manner. The side floats
have also a tendency away from shore.
The mean area of each of the sub-sections being known,
,and the mean velocity through each being ascertained,
GAUGE FOKMULAS. 319
their product gives the volume flowing through, and the
sum of volumes of the sub-section gives the volume for the
whole section.
When streams are in the least liable to fluctuations from
the opening or closing of sluices above, or the opening or
closing of turbine gates when the stream is used for hy-
draulic power, a hook-gauge (Fig. 48), should be placed
over the axis of the stream where the usual vibration of
surface is least, to watch for such fluctuations, since a vari-
ation in the mean level of the water surface one-hundredth
of a foot will appreciably affect the velocity and volume of
flow. If the tubes have much clearance they will not be
influenced by the films of slowest velocity next the bottom.
A clearance of six inches in a rectangular flume eight feet
deep, may give an excess of three per cent, of velocity.
The cross-section depths, in canals and shallow streams,
may be taken with a graduated sounding-rod having a flat
disk of three or four inches diameter at its foot, and in deep
streams by a measuring-chain with a sufficient weight upon
its foot to maintain it straight and vertical in the current.
A good level instrument and level staff are requisite, how-
ever, for accurate work.
In broad streams the transverse stations may be located
trigonometrically by two transits placed at the extremities
of a carefully measured base line upon the shore.
335. Gauge Formulas. The volume of flow through
the mean transverse section (Fig. 64) is required.
Let s be the established length, or distance between the
longitudinal end stations, and A 4 4 4 the times occu-
pied by the several tubes in passing along their respective
courses between end stations ; then the mean velocities in
the respective sub-sections will be
s s s s
320
FLOW OF WATER IN OPEN CHANNELS.
Let the transverse breadths of the sub-sections be, a l a z a 3 . . . . a,^
" " mean depths " " " d t d a d 3 . . . . d n .
" " mean velocities in " " " v t a v 3 . . . . v n .
" " " volumes of flow in " q 1 q 2 q 3 . . . . q n .
Then the whole sectional area in square feet, $, of the
stream is,
8 = i . d l + a 2 . d 2 + a 3 . d B + . . . . a n . d n ; (16)
and the whole volume in cubic feet, <2, is
Q = fa. d { ) Vt + (a 2 . d 2 ) v 2 + ( 3 .^3)^3 + ... (a n d,>) v n ; (17)
and the mean velocity in feet per second, v, of the whole
section is,
|- . (18)
The summary of field notes, beginning at a on the left
shore, is :
Breadths of sub-sections
Mean depths of
Mean velocities in the I
sub-sections f
Feet,
a ! 16.45
</i 4-85
Z>! 2.25
Cu. //.
fi J 79-5
Feet.
a, 2 20,00
d* 9.74
v z 3.80
Cu.ft.
q* 740.2
Feet.
a 3 24.85
d a 12.37
v 3 4.62
Cu.ft.
q 3 1420.2
Feet.
a 32.00
di 15.68
v* 5-oo
Cu.ft.
? 4 2508.8
Feet.
a* 29.50
d 6 12.52
v s 4-65
Cu.ft.
g s 1717-4
Feet.
a 26.80
d 9.71
3'7S
Cu.ft.
fo 975-8
Feet.
a 7 18.24
^7 4-79
t/ 7 2.00
Cu.ft.
q-, 174.7
f.*
[ = c.
Volume in the sub-sec- j
The sum of the several products of breadth into depth is
S = 1800.675 square feet.
The sum of the several volumes is Q = 7716.73
Q 7716 73
The mean velocity for the whole section is ^ ^ Q( ^^ a ^ K
o loOU.bTo
= v = 4.285 feet per second.
If the tubes have several inches clearance at the bot-
tom, a slight reduction, say two and a half per cent., from
the computed velocity and volume are to be made, to com-
pensate therefor.
336. Pitot Tube Gauge. The Pitot tube has been
used with a tolerable degree of success in many experi-
ments upon a small scale. In its best simple form it has
PITOT'S TUBE.
321
FIG. 55.
been constructed of glass tubing swelled into a bulb near
one end, and with tube of smaller diameter below the bulb
bent at a right angle, and terminated with an expanded
trumpet-mouth, as in Fig. 55.
For deep measures the mouth and bulb and a con-
venient part of the tube may be of copper, that part which
is to project above the surface
of the water being of glass, and
the whole instrument may be at-
tached to a vertical rod, which
rests on the bottom, so as to be
slid up and down on the rod to
the heights of the several films
whose velocities are required.
When in use, the bulb and
tube are to be held vertically, ^^
and the small trumpet-mouthed
section exposed horizontally to the current so as to receive
its maximum force into the mouth.
The object of the expanded bulb and contraction below
the bulb is to reduce oscillation of the water within the tube
to a minimum.
Theoretically the impulse of the current, acting as pres-
sure on the water within the tube, should raise the surface
v 2
of the water within, a height, 7i = ~-, above the normal
f *9
surface.
But owing to reactions from several parts of the tube,
the entire force of the current does not act upon the column
of water in the vertical section of the tube, hence the eleva-
tion of the water in the tube is cji and
PITOT S TUBE.
- = cji and v =
(19)
21
322 FLOW OF WATER IN OPEN CHANNELS.
The coefficient c , for the given tube and the different
velocities, must be determined by experiment before it can
be used for practical measures.
The stream is cross-sectioned, as before described for
the leading station when long tin tubes are used, and
the mean velocity is ascertained from the mean velocity of
the various superposed films taken in a vertical line at the
centre of each sub-section.
The computations of volume are made in a manner sim-
ilar to those when tubes are used.
Pitot introduced a plain tube bent at right angles as
early as 1730, and by his measurements with it in the Seine
and other streams, overthrew some of the hypotheses of the
older hydraulicians.
It has since received a variety of forms and entered into
a variety of combinations, among which may be mentioned
the " Darcy-Pitot " tube, which, after an instantaneous
closing of a stop-cock, can be lifted up for an observation,
and the Darcy double tube, but there is still difficulty in
reading by its graduations measures of small velocities, with
sufficient accuracy, and the capillarity may be a source of
error in un skillful hands.
The almost exclusive use of this instrument in improved
forms by Darcy and Bazin in their valuable series of ex-
perimental observations, has given to it prominent rank
among hydrometers.
337. Woltmann's Tachometer. The most success-
ful of all the simple mechanical hydrometers, not requiring
the assistance of an electric battery, has been the revolving
mill introduced by Woltmann in 1790, and known as
" Woltmanrts Tachometer" or moulinet. This current
meter has from two to five blades, either flat or like marine
propeller blades, set upon a horizontal shaft as shown in
WOLTMANN'S TACHOMETER.
323
Fig. 56, which represents the entire instrument * in its actual
magnitude, for small canal and flume measures.
Upon the main axle, which carries the propeller, is a
worm-screw, G. A series of toothed wheels and pinions,
with pointers and dials similar to the registering apparatus
FIG. 56.
WOLTMANN'S TACHOMETER.
of a water or gas meter, are hung in a light frame, (?, imme-
diately beneath the main axle. One end of the frame is
movable upward and downward, but when out of use is
held down by a spring, F.
The whole instrument is secured by a set-screw upon an
Iron rod, Z>, on which it may be set at any desired height.
* Another form with two blades is illustrated in Stevenson's Canal and
River Engineering. Edinburgh, 1872, p. 101.
324 FLOW OF WATEE IN OPEN CHANNELS.
When brought into practical use, the instrument is
adjusted upon the rod,* so that when the staff rests upon
the bottom, the main axle will be at the height of the film
to be first measured. It is then placed in position with the
propeller toward the approaching current and the main axle
parallel \frith the direction of the current. The propeller
will soon acquire its due velocity of revolution from the
moving current, when the movable end of the frame carry-
ing the recording train is lifted by the wire E, and the first
toothed wheel brought into mesh with the worm-screw. If
the train does not stand at zero, its reading is to be taken
before the instrument is brought into position. The times
when the train is brought into mesh with the worm-screw,
and when disengaged, are both to be accurately noted and
recorded.
Upon the slackening of the wire E, the spring F, in-
stantly throws the train out of mesh, and it is held fast by
the stud A^ which engages between two teeth of the wheel.
The instrument may then be raised and the revolutipns in
the observed time read off. In waters exceeding a few feet
in depth there are usually pulsations of about one minute,
more or less, intervals, and the instrument should be held
in position until several of these have passed.
The velocities are thus measured at several heights on
vertical centre lines in the several sub-sections, and the com-
putations for mean velocity and volume completed as in the
above described case when long tin tubes are used.
The blades of the propeller are usually set at an angle
of about 70, or with an equivalent pitch if warped as a pro-
peller blade.
* Several moulinets upon the same staff, at known heights between bottom-
and surface, expedite the work and tend to greater accuracy.
HYDROMETER COEFFICIENTS. 325
338. Hydrometer Coefficients. The number of revo-
lutions of the main axle is nearly proportional to the velocity
of the impinging current ; but there is some frictional resist-
ance offered by the mechanism, hence it is necessary that
the coefficients for the given instrument and for given veloci-
ties be established by experiment, and tabled for convenient
reference before it is put to practical use. These coefficients,
which decrease in value as the velocity increases, may be
ascertained, or verified, by placing the instrument sub-
merged in currents of known velocity, or by causing it to
move, submerged, through still water at known velocities.
An apparatus adapted to the last purpose is described
by L' Abbe Bossut, and illustrated in Plates I and II, in
" Experts * De Bossut,"
If the instrument is to be tested in a reservoir of still
water, by moving it with different known velocities through
a given distance, let s be that distance, t the time consumed
in passing the instrument from end to end stations, n the
number of revolutions of the main axle in the given time ,
c the coefficient of revolutions for the given velocity, and v
the given velocity.
Then -^ = v ; and = c ; and c n = s ; and ~ = v.
v 7b t
Now if the instrument is placed in a current, and n is
the observed number of revolutions in the given time, c may
be taken from the table, or an approximate value of c as-
sumed and nearer values determined by the formula
= c, when the velocity will be, v = . (20)
* Nouvelles Experiences sur la Resistance des Fluids ; M. 1'Abbe Bossut,
Rapporteur. Paris. '
Vide, also, Annales des Fonts et Chaussees, Nov. et Dec., 1847, and Journal
of Franklin Institute, May, 1869, and Beaufoy's Hydraulic Experiments.
326 FLOW OF WATER IN OPEN CHANNELS.
339. Henry's Telegraphic Moulinet. An ingenious
indicating current meter * has been invented by D. Farrand
Henry, C. E., late assistant of the U. S. Lake Survey, and
was tested by him with very satisfactory results in the sur-'
veys of the large streams joining and flowing from the great
lakes of North America. The recording apparatus of this
meter may be retained above the water surface in a position
convenient for observation, while the revolving propeller is
submerged at any desired depth. The two portions of the
instrument are connected by flexible wires with an electric
battery so that the circuit passes through the axle of the
propeller. The electric circuit is closed for an instant during
each revolution, when the lever of the register moves the
first of the train of registering wheels forward one cog.
This meter gives promise of especial value for gaugings
of deep waters and tidal estuaries.
340. Earlier Hydrometers. Castelli's quadrant, or
hydrometric pendulum, Boileau's horizontal gauge glass,
Gauthey's and Brunning's pressure plates, Brewster's long
screw-meter, and Lapointe's beveled gear-meter, have now
all been superseded by the more perfect modern current
meters.
341. Double Floats. Various double-float combina-
tions, having one float at the surface and a second near the
bottom, connected with the first by a cord or fine wire rope,
have been used both in Europe and America. The liability
of erroneous deductions from the movements of such com-
binations has been ably discussed f by Prof. S. W. Rob-
inson.
342. Mid-depth Floats. The mid-depth float proves
* This meter is illustrated in the Jour, of the Franklin Inst., May,
and Sept. 1871.
f Vide Van Nostrand's Eclectic Engineering Magazine, Aug., 1875.
MID-DEPTH FLOATS. 327
most generally satisfactory of all float apparatus, excepting
full-depth tubes, for gauging artificial channels and the
smaller rivers.
This may consist of a hollow metal globe of say six
inches diameter, with a cork-stopper or pet-cock at its
lower vertical pole, which permits the partial filling of the
globe with water until its specific gravity, submerged, is
slightly in excess of unity. This globe is connected by a
fine flexible wire with the smallest and lightest circular
disk-float upon the surface that can retain the globe in its
proper mid-depth position.
It is desirable that the float be controlled as fully as
possible by the mid-depth velocity, where, in artificial
channels and deep streams, the film of most constant
velocity is found. The reactions and eddies that continually
agitate all the particles that flow near the bottom and sides
of the stream, and the wind pressure and motion along the
surface, make the motions of all perimeter (so called) films
very complex, and continually cause the parabolic velocity
values in the central vertical plane to change between
flatter and sharper curves, or to straighten out and double
up, hinged, as it were, upon a mid-depth point ; hence the
bottom, side, and surface velocities are liable to great irreg-
ularities, and these irregularities are projected to some
extent through the whole body of the water. These effects
may be readily observed in a stream carrying fine quartz
sand, upon a sunshiny day, if a position is taken so that
the sunlight is reflected from the sand-grains to the eye. If
in such case the eye and body is moved along with the cur-
rent, the whole mass of water appears in violent agitation
and the particles appear to move upward, downward, back-
ward, forward, and across, with writhing motions, illus-
trating the method by which the water tosses up and bears
328 FLOW OF WATER IN OPEN CHANNELS.
forward its load of sediment. In the midst of this agitation,
the film having a velocity nearest to the mean resultant of
onward progress is usually over the mid-channel of a
straight course, and near to, or a little below, the centre of
depth. The suspended float that takes this mean velocity
is more certain to give a reliable velocity measure than that
controlled by any other point of the stream section.
343. Maximum Velocity Floats. If it is desired to
place the submerged float in the film of maximum velocity
in artificial channels, then this may be sought over the
mid-channel, and between the surface and one-third the
depth, according to the cross-section of the stream and
velocity of flow. In a smooth rectangular section with
depth equal to width, or with depth one-half width, it will
probably be near one-third the depth, and higher as the
depth of stream is proportionately less, until depth is only
one-fourth breadth, when it will have quite, or nearly,
reached the surface.
The film of maximum velocity may reacn the surface in
trapezoidal canals when depth of stream is only one- third
mean breadth. It is at one-fourth depth in the trapezoidal
channel, Fig. 51 , in which bottom breadth equals twice depth.
In shallow streams, the maximum velocity is at or near
the surface.
344. Relative Velocities and Volumes due to
Different Depths. When the mean velocity has been
reliably determined in a channel, or small stream, at some
given section, and for some particular depth, it is often
desirable to construct a table of velocities and volumes of
flow, for other depths in the same section, so that, if a read-
ing of depth is taken at any time from a gauge established
at that section, the velocity and volume due to the observed
depth at that time may be read off from the table.
RELATIVE VELOCITIES AND VOLUMES. 329
The inclination, or surface slope, i = ~ , and the value
of the coefficient of friction, m -~ , may be observed
within the ordinary extremes of depth at the time of the
experimental measurement, if opportunity offers, or other-
wise for the given experimental depth, and computed for
the remaining depths.
Theory indicates that the variation of velocity , with
varying depth, is nearly as the variation of the square root
/a
o*f the hydraulic mean radius, = y -^, and the variation of
G
volume of flow is nearly as the variation of the product of
sectional area into the square root of hydraulic mean radius,
These terms are readily obtained for the several depths,
from measurement of the channel.
To compare new depths, velocities, and volumes, with
the depth, velocity, and volume accurately measured by
experiment, as unity,
let the
imental depth be
d, and the
new depth b
e d,;
hy. mean rad. "
r, " "
" hy. mean rad. '
?i
slope "
i, "
" slope
h
coef. of friction "
m, " "
" coef. of friction
m l
sectional area "
8, " "
" sectional area
&i
velocity "
v, " "
" velocity '
i
volume "
q. " "
" volume
<?!
The relative values of new depths, velocities, volumes,
etc., will be
* ^- gi etc
d ' v 9 q'
and v : Vi :: 1 : :
330 FLOW OF WATER IN OPEN CHANNELS.
q : q, : : 1 : ^ ; etc.
The ratio of Vi to v is
_^i^ J2gyA|>_._ J2grt(i = (Wftli
-0 " " I /#! f I w I ' ~ ( Ti?^ ) '
*
*>,. (22)
In long straight .channels of uniform section, ^ will be
less than for increased depths, and greater than i for
reduced depths ; but ordinarily (except with great velocities)
their values will be so nearly equal to each other that they
may be omitted from the equation without serious error,
when the equation of velocity will become,
The variations in m cannot be neglected in relatively
shallow channels.
For illustration of the equations, let Fig. 57 be a smooth
FIG. 57.
s/^X^sjjiUsE
/reet. >
trapezoidal channel, 6 feet broad at the bottom, = e, and
with side slopes inclined thirty degrees from the horizon,
RELATIVE VELOCITIES AND VOLUMES.
331
During the experimental measurement, let the depth be
4 feet ; the slope, one foot in one mile = i = .000189 ; the
experimental velocity, 1.201 feet per second ; and the ex-
perimental volume, 62.128 cubic feet per second.
The velocities and volumes are to be computed when the
depths are 2 feet and 6 feet, respectively.
Let d be any given depth;
e " the bottom breadth, = 6 feet ;
5 " the mean breadth ;
</> " the slope of the sides, = 30 ;
6 " the sectional area ;
C " the wetted earth perimeter.
Then we have for the given values of d:
ASSUMED VALUES OF d.
2 FEET.
4 FEET.
6 FEET.
tan '
S = -\- de . . =
tan !>
2d sec
r / 4
12.93
18.93
14.00
.OOO2
.02396
19.86
22.00
.OOOlSg
.0187
26.79
98.35
30.00
3.28
.000185
.0146
tan</>
S
C"
i
w .>...........
7;. . .
.836
I.2OI
62.128
1. 606
<7i .
With increase of depth, there is also increase of velocity ;
hence there are two factors to increase of volume.
Some practical considerations relating to open canals
are given in Chap. XVII, following.
SECTION III.
PRACTICAL CONSTRUCTION OF WATERWORKS,
CHAPTER XYI.
RESERVOIR EMBANKMENTS AND CHAMBERS.
345. Ultimate Economy of Skillful Construction.
An earthwork embankment appears to the uninitiated
the most simple of all engineering constructions, the one
feature that demands least of educated judgment an A expe-
rience. Possibly from such delusion has, in part, resulted
the fact, which is patent and undeniable, that failures of
reservoir embankments have exacted more terrible and
appalling penalties of human sacrifice, and sacrifice of cap-
ital, than the weaknesses of all other hydraulic works
together.
Each generation in succession has had its notable flood
catastrophes, when its broken dams have poured deluges
into the valleys, which have swept away houses and mills
and bridges and crops, and too often twenty, fifty, or a
hundred human beings at once.
Such devastations are scarcely paralleled by, though
more easily averted by forethought, than those historical
inundations when the sea has broken over the embanked
shores of Holland and England, and when great rivers
334 RESERVOIR EMBANKMENTS AND CHAMBERS.
have poured over their populous leveed plains, yet they
seem to be quickly forgotten, except by the immediate
sufferers who survived them.
The earliest authenticated historical records of the East-
ern tropical nations describe existing storage reservoirs and
embankments, and more than fifty thousand such reser-
voirs have been built in the Indian Madras Presidency
Districts alone. Arthur Jacobs, B. A., says* of these
Madras embankments, that they will average a half mile in
length each, and the longest has a length of not less than
thirty miles.
Two thousand years of practice seems to have developed
but a slight advance of skill in the construction of earth-
works, while their apparent simplicity seems to have dis-
tracted modern attention from their minute details, and to
have led builders to the practice of false economy in some in-
stances, and to the neglect of necessary precautions in others.
Among the recent disastrous failures may be mentioned
the Bradfield or Dale Dyke embankment of the Sheffield,
England, water- works, in 1864 ; the Danbury, Conn., water,
works embankment, in 1866 ; the Hartford, Conn., water-
works embankment, in 1867 ; the New Bedford, Mass.,
water-works embankment, in 1868; the Mill Eiver, or
Williamsburgh, Mass., embankment, in 1875 ; and Worces-
ter, Mass., water-works embankment, in 1876. More than
one hundred other breakages of dams are upon record for
New England alone for the same short period.
The practical utility of streams is dependent largely
upon the storage of their surplus waters in the seasons of
their abundant flow, that they may be used when droughts
would otherwise reduce their volume.
* Vide Paper read before the Society of Engineers, London.
EMBANKMENT FOUNDATIONS. 335
Their waters are usually stored in elevated basins,
whether stored for power, for domestic consumption, for
compensation, or to regulate floods ; and frequently single
embankments toward the head-waters of streams suspends
millions of tons of water above the villages and towns of
the lower valleys. In other instances, embanked distrib-
uting reservoirs crown high summits in the midst of popu-
lous cities. These are good angels of health, comfort, and
protection, when performing their appointed duties, but
very demons of destruction when their waters break loose
upon the hillsides.
Every consideration demands that a storage reservoir
embankment shall be as durable as the hills upon which it
rests. To this end, no water is to be permitted to percolate
and gather in a rill beneath the embankment ; its core must
be so solid, heavy and impervious that no water shall push
it aside, lift it up or flow through it, or follow along its dis-
charge pipes or waste culvert ; its core must be protected
from abrasions and disintegrations ; and its waste overfall
must be ample in length and strength to pass the most
extraordinary flood without the embankment being over-
topped.
346. Embankment Foundations. The foundation
upon which the structure rests is the first vital point requir-
ing attention, and may contain an element of weakness that
shall ultimately lead to the destruction of the structure
placed upon it.
The superposed drift strata beneath the surface layer of
muck or vegetable soil may consist of various combinations
of loam, gravel, sand, quicksand, clay, shale and demoral-
ized rock, resting upon the solid impervious rock, or above
an impervious stratum of sufficient thickness to resist the
penetration of water under pressure. If the water is raised
336 RESERVOIR EMBANKMENTS AND CHAMBERS.
fifty feet above the surface and there are thirty feet of per-
vious earth in the bed of the valley, then the pressure upon
the bed stratum will be five thousand pounds, or two and
one-half tons per square foot, which will tend to force the
water toward an outlet in the valley below. That much of
the natural earth is porous is well demonstrated by the
freedom with which water enters on the plains and courses
through the strata to the springs in the valleys, even with-
out a head of water to force its entrance. Such porous
strata must be cut off or sealed over, or the permanency and
efficiency of the structure, however well executed above,
cannot be assured.
If the valley across which the embankment is thrown is
a valley of denudation, or if the embankment stretches
across one or more ridges to cover several minor valleys
with a broad lake, the waters in rising may cover the
outcropping edges of coarse porous strata that shall lead
the flowage by subterranean paths to distant springs where
water had not flowed before. Hence the necessity of a
thorough examination of the geological substructure of
the valley, and of tests by trial shafts, supplemented by
deep borings, of the site of the embankment and the hill-
sides upon which it abuts. The test borings should cover
some distance above and below the site of the embankment,
lest a mere pocket filled with impervious soil be mistaken
for a thick strata supposed to underlie the whole vicinity.
The trial shafts only, permit a proper examination of the
covered rock, which may be so shattered, or fissured, as to
be able to conduct away a considerable quantity of water,
or to lead water from the adjoining hills to form springs
under the foundations.
Several deep reservoirs constructed within a few years
past have demanded excavations for cut-off walls, to a
SURFACE SOILS. 337
depth of a hundred feet at certain points along their lines,
but the porosity and the firmness of the strata in such cases
are points demanding the exercise of the most mature judg-
ment, that the work may be made sure, and at the same
time labor be not wasted by unnecessarily deep cutting.
Thoroughness in the preliminary examination of the
substrata of a proposed site may frequently result in the
avoidance of a great deal of vexatious labor and enhanced
cost that would otherwise follow from the location of an
embankment over a treacherous sub-foundation.
347. Springs under Foundations. If the excava-
tion shall cut off or expose a spring that, when confined,
will produce an hydrostatic pressure liable to endanger the
outside slope of the embankment, it must be followed back
by a drift or open cutting to a point from whence it may
be safely led out in a small pipe below the site of the
embankment.
348. Surface Soils. Dependence cannot be placed
upon the vegetable soil lying upon the site of an embank-
ment to hold water under pressure, for it is always porous
in a state of nature, as is also the subsoil to the depth pene-
trated by frost. The vegetable soil should be cleared from
beneath the core of the embankment, and the subsoil rolled
and compacted.
The vegetable soil will be valuable for covering the top
and outside slope of the embankment.
If good hard-pan underlies the surface soil to a depth
sufficient to make a strong foundation for the embankment,
then its surface should be broken up to the depth it has
been made porous by frost expansion, and the material
rolled down anew in thin layers with a grooved roller of
not less than two tons gross weight, or of one-half ton per
lineal foot.
22
338 RESERVOIR EMBANKMENTS AND CHAMBERS.
If next to the surface soil there is a layer of hard-pan
within the basin to be flowed, and this hard-pan covers open
and porous strata that extend below the dam, caution
should be used in disturbing the hard-pan, lest the water
be admitted freely to the porous strata, when it will escape,
perhaps by long detour around the dam.
349. Concrete Cut-off Walls. If the trench for the
cut-off wall is deep and very irregular, it is well to level up
in the cuts with a water-proof concrete well settled in place,
and this may prove more economical than to cut the deep
trench of sufficient width to receive a reliable puddle wall ;
also, the greater reliability of the concrete under great pres-
sure should not be overlooked.
350. Treacherous Strata. In one instance the writer
had occasion to construct a low embankment, not exceed-
ing twenty feet height at the centre, across an abraided cut
through a plain. The embankment was to retain a storage
of water for a city water supply, and the enclosed lake was
to have an area of 200 acres.
The test pits and soundings developed the fact that the
abraided valley and adjacent plains were underlaid with a
stratum of fine sand twelve feet in thickness, which, when
disturbed, became a quicksand, and if water was admitted
to it, would flow almost as freely as water.
The sand lay in a compact mass, and would not pass
water freely until disturbed. Above the sand was a layer
of about three feet of fine hard-pan, and above this about
three feet of good meadow soil had formed.
For this case the decision was, not to uncover the quick-
sand, but to seal it over in the vicinity of the embankment.
The foundation of the embankment, and of the waste over-
fall which necessarily came in the centre of length of the
embankment, was made of concrete of such thickness as to
EMBANKMENT CORE MATERIALS. 339
properly distribute the weight of the earthwork and over-
fall masonry. Above the embankment, after a careful
cleaning of the soil to the depth penetrated by the grass
roots, the valley was covered with a layer of gravel and
clay puddle for a distance of one hundred feet.
Beneath the toe of the inside slope, where the bottom
puddle joined the concrete foundation, a trench was cut
across the valley into the quicksand, as deep as could be
excavated in sections, with the aid of the light pumping
power on hand, and sheet piling placed therein and driven
through the quicksand, and then the trench was filled
around the piling with puddle, thus forming a puddle and
plank curtain under the inside edge of the embankment.
Such expedients are never entirely free from risks,
especially if a faithful and competent inspector is not re-
tained constantly on the work to observe that orders are
obeyed in the minutest detail.
In the case in question many thousands of dollars were
saved, and the work has at present writing successfully
stood the test of seven years use, during which time the
most fearful flood storm recorded in the present century has
swept over the section of Connecticut where the storage lake
is situated.
351. Embankment Core Materials. Rarely are
good materials found ready mixed and close at hand for
the construction of the core of the embankment. It is
essential that this portion be so compounded as to be im-
pervious.
If we fill a box of known cubical capacity, say one cubic
yard, with shingle or screened coarse gravel, we shall then
find that we can pour into the full box with the gravel a
volume of water equal to twenty-eight or thirty per cent,
of the capacity of the box, according to the volume of voids ;
340 RESERVOIR EMBANKMENTS AND CHAMBERS.
or if we attempt to stop water with the same thickness (one
yard) of gravel, we shall find that water will flow through
it very freely. Then let the same gravel be dumped out
upon a platform and twenty-eight per cent, nearly of fine
gravel "be mixed with it, so as to fill the voids equally, and
the whole be put into the measuring-box. We now find
that we can again pour in water equal to about thirty per
cent, of the cubical measure of the fine gravel. Then let fine
sand, equal to this last volume of water, be mixed with the
coarse and fine gravel, and the whole returned to the meas-
ure. We now find that we can pour in water, though not
so rapidly as before, equal to thirty-three per cent, approx-
imately of the cubical measure of the sand, and we resort
to fine clay equal to the last volume of the water to again
fill the voids. The voids are now reduced to microscopic
dimensions.
If we could in practice secure this strict theoretical pro-
portion and thorough admixture of the material, we should
introduce into one yard volume quantities as follows : Coarse
gravel, 1 cubic yard ; fine gravel, 0.28 cubic yard ; sand,
0.08 cubic yard ; and clay, 0.03 cubic yard, or a total of
the separate materials of 1.39 cubic yards.
In practice, with a reasonable amount of labor applied
to thoroughly mix the materials so as to fill the voids, we
shall use, approximately, the following proportion of ma-
terials :
Coarse gravel 1.00 cubic yard.
Finegravel 0.35 "
Sand 0.15 "
Clay 0.20 "
Total 1.70 "
which, when mixed loosely or spread in thin layers, will
make about one and three-tenths yards bulk, and when.
WEIGHT OF EMBANKMENT MATERIALS.
341
thoroughly compacted in the embankment, will make about
one and one quarter cubic yards bulk.
The voids now remaining in the mass may each be a
thousand times broader than a molecule of water, yet they
are sufficiently minute, so that molecular attraction exerts
a strong force in each and resists flow of the molecules,
even under considerable head pressure of water.
It will be interesting here to compare the weights of a
solid block of granite with its disintegrated products of
gravel and sand, taking for illustration a cubic foot volume.
TABLE No. 77.
WEIGHTS OF EMBANKMENT MATERIALS.
MATERIAL.
Av. WEIGHT.
SPECIFIC GRAVITY.
Av. VOIDS.
Granite
166
I2O
116
no
I2 5
62.1
Ibs.
u
tt
u
, tt
>
2662
I 925
i. 86 1
1.440
I.OOO
.28 per cent.
.30 " "
,,
.12 " "
Coarse Gravel
Gravel .
Sharp Sand
Clay
Water. .
If the shingle is omitted and common gravel is the bulk
to receive the finer materials, then the proportions in prac-
tice may be :
Common gravel 1 .00 cubic yard.
Sand 0.36 "
Clay 0.25 "
1.61
which, when loosely spread, will make about one and one-
sixth yards bulk ; and compacted, some less than one and
one-tenth yards bulk.
Gravel is usually found with portions of sand, or sand
and clay, already mixed with it, though rarely with a suf-
342 RESERVOIR EMBANKMENTS AND CHAMBERS.
ficiency of fine material to fill the voids. The lacking ma-
terial should be supplied in its due proportion, whether it
be fine gravel sand, fine sand, or clay. The voids must be
filled, at all events, with some durable fine material, to
ensure imperviousness.
It is sometimes found expedient to substitute for a por-
tion of the fine sand or clay, portions of loam or selected
soil from old ground, and on rare occasions peat, but
neither peat nor loam should be introduced in bulk into
the core of an embankment.
There is a general prejudice against the use of peat or
surface soils in embankments, and the objections hold good
when they are exposed to atmospheric influences. Mr.
Wiggin remarks,* howeve.r, that a peat sea-bank which was
opened after being built for seventeen years, exhibited the
material as fibrous and undecayed as when first deposited.
Weight is a valuable property in embankment material,
when placed upon a firm foundation, since, for a given bulk,
the heavier material is able to resist the greater pressure.
Peat and loam are very deficient in the weight property,
and therefore need the support of heavier materials. Clay
is heavier than sand or fine gravel ; shingle is heavier than
clay ; but the compound of shingle, gravel, sand, and clay,
above described, is heavier than either alone, and weighs
when compacted, for a given volume, nearly as much as
solid granite.
CoTiesiveness and stability are valuable properties in
embankment materials, but sand and gravel lack perma-
nent cohesiveness, and clay alone, though quite cohesive,
is liable to slips and dangerous fissures, if unsupported ;
but a proper combination of gravel, sharp sand, and clay,
* Embanking Lands from the Sea, p. 20. London, 1852.
PECULIAR PRESSURES. 343
gives all the valuable properties of weight, cohesiveness,
stability, and iraperviousness.
352. Peculiar Pressures. There are peculiar pres-
sure influences in an earthwork structure that are not
identical with the theoretical hydrostatic pressures upon a
tight masonry, or fully impervious structure of the same
form. The hydrostatic pressure upon an impervious face,
whatever its inclination, might be resolved into its hori-
zontal resultant (171), and that resultant would be the
theoretical force tending to push the structure down the
valley, and would be equal to the pressure of the same
depth of water acting upon a vertical face. The pressure
would be, upon a vertical face, per square foot, at the given
depths, as follows :
Depth, in feet
Pressure, in Ibs
5
3".i
10
624.3
15
936.4
20
1249
25
1561
3
1873
35
2185
40
2497
2809
50 60
3121(3746
I
437
80
4994
90
5618
100
6243
The effective action of the theoretical horizontal resultant
is neutralized somewhat upon an impervious slope by the
weight of water upon the slope.
But all embankments are pervious to some extent. If
with the assistance of the pressure, the water penetrates to
the centre of the embankment, it presses there in all direc-
tions, upward, downward, forward and backward, and at a
depth of fifty feet the pressure will be a ton and a half per
square foot. Such pressure tends to lift the embankment,
and to soften its substance, as well as to press it forward,
and if in course of time the water penetrates past the centre
it may reach a point where the weight or the imperviousness
of the outside slope is not sufficient to resist the pressure,
when the embankment will crack open and be speedily
breached.
That portion of the embankment that is penetrated by
344 RESERVOIR EMBANKMENTS AND CHAMBERS.
the water has its weight neutralized to the extent of the
weight of the water, or at any depth, a total equal to the
water pressure at that depth ; thus, at fifty feet depth, that
portion penetrated is reduced in its total weight a total of
one and one-half tons per square foot.
Hence the value of imperviousness at the front as well
as in the centre of the embankment, so that the maximum
amount of its weight may be effective.
If water penetrates the subsoil beneath the embarikment,
as is frequently the case, it there exerts a lifting pressure
according to its depth.
353. Earthwork Slopes. If earth embankments of
the forms usually given to them, and their subsoils also,
were quite impervious, as a wall of good concrete would be,
the embankments would have a large surplus of weight,
and might be cut down vertically at the centre of their
breadth, and either half would sustain the pressure and
impact of waves with safety, but the vertical wall of earth
would not stand against the erosive actions of the waves
and storms. Surface slopes of earthwork are controlling
elements in their design, and govern their transverse profiles.
Different earths have different degrees of permanent
stability or of friction of their particles upon each other,
that enable them to maintain their respective natural sur-
face slopes, or angles of repose, against the effects of gravity,
ordinary storms, and alternate freezings and thawings, until
nature binds their surfaces together with the roots of weeds,
grasses and shrubs. The coefficient of friction of earth
equals the tangent of its angle of repose, or natural slope.
The amount or value of the slope is usually described by
stating the ratio of the horizontal base of the angle to its
vertical height, which is the reciprocal of the tangent of the
inclination.
EARTHWORK SLOPES.
345
The following data relating to these values are selected *
in part from Rankine, and to them are added the angles at
which certain earths sustain by friction other materials laid
upon their inclined surfaces.
TABLE No. 78.
ANGLES OF REPOSE, AND FRICTION OF EMBANKMENT MATERIALS.
MATERIAL.
ANGLE OF
REPOSE.
COEFFICIENT OF
FRICTION.
RATIO OF SLOPE.
Dry sand fine
28
c 22
f/ari. Vert.
1.88 tO
" " coarse
10
jo*
.C77
1.71 "
Damp clay
i!
'Oil
I OOO
I 00 "
Wet clay .
iS
268
171 "
Clayey gravel
I OOO
O" 1 O
1.00 "
Shingle
4*
.000
I. II "
Gravel
38
7 ^
.781
1.28 "
Firm loam
^6
727
i *8 "
Vegetable soil .
3S
/ */
7OO
*o**
1.41 "
Peat
35 o
20
/ ww
.^64.
A *tO
2.7C "
Masonry, on clayey gravel. .
" dry clay
" " moist clay. . .
Earth on moist clay ......
" " wet clay
1
18
577
.510
325
I. OOO
.106
*"/ J
1.73 "
1.96 "
3.08 "
1. 00 "
1.26 "
x /
Inclined earth surfaces are most frequently dressed to
the slopes, having ratios of bases to verticals, respectively
1 J to 1 ; 2 to 1 ; 2J to 1 ; and 3 to 1 ; corresponding respect-
ively to the coefficients of friction 0.67, 0.50, 0.40, and 0.33,
and to the angles of repose 33J, 26^, 21|, and 18J,
nearly.
Gravel, and mixtures of clay and gravel, will stand
ordinarily, and resist ordinary storms at an angle of 1 J to 1,
but the angle must be reduced if the slope is exposed to
accumulations of storm waters or to wave actions, and upon
* Civil Engineering, p. 316. London, 1872.
346 RESERVOIR EMBANKMENTS AND CHAMBERS.
broad lake shores the waves will reduce coarse gravel, if
unprotected, to a slope of 5 to 1, and finer materials to
lesser slopes. Complete saturation of clay, loam, and vege-
table soil, destroys the considerable cohesion they have
when merely moistened, and they become mud, and assume
slopes nearly horizontal ; hence the conditions to which the
above table refers may be entirely destroyed and the angles
be much flattened, unless the slopes are properly protected.
On the other hand, the table does not refer to the temporary
stability which some moist earths have in mass, for com-
pact clay, gravel, and even coarse sand may, when their
adhesion is at its maximum, or when their pores are par-
tially and nearly filled with water, be trenched through,
and the sides of the trench stand for a time, nearly vertical,
at heights of from 6 to 15 feet. In such cases, loss or
increase of moisture destroys the adhesion, and the sides of
the trench soon begin to crumble or cave, unless supported.
354. Reconiioissance for Site. Let us assume, for
illustration, that a storage reservoir is to be formed in an
elevated valley. The minimum allowable altitude being
fixed upon, and designated by reference to a permanent
bench mark in the outfall of the valley, the valley is then
explored from the given altitude upward for the most favor-
able site for the storage basin, and for the site for an
embankment, or dam, as the circumstances may require.
We may expect to find a good site for the storage at some
point where a broad meadow is flanked upon each side by
abrupt slopes, and where those slopes draw near to each
other at the outlet of the meadow, as is frequently the case.
Having found a site that appears favorable, a preliminary
reconnoissance with instruments is made to determine if the
basin has the required amount of watershed and storage
capacity, previously fixed upon ( 59), and to determine
DETAILED SURVEYS. 347
approximately the height the embankment or masonry
dam must have. If the preliminary reconnoissance gives
satisfactory results, then the site where the embankment
can be built most economically and substantially is care-
fully sought, and test pits and borings put down at the
point giving most promise upon the surface. It is import-
ant to know at the outset that the subsoil is firm enough to
carry the weight of the embankment without yielding, and if
there is an impervious substratum that will retain the pond-
ed water under pressure. It is important also to know that
suitable materials are obtainable in the immediate vicinity.
355. Detailed Surveys. The preliminary surveys all
giving satisfactory indications as respects extent of flowage,
volume of storage, depth of water, inclination and material
of shore slopes, soils of flowed basin, and the detailed sur-
veys confirming the first indications, and also establishing
that the drainage area and rainfall supplying the basin is
of ample extent and quantity to supply the required amount
of water ( 24) of suitable quality ( 1OO et seq.) ; then let
us suppose that the conditions governing the retaining em-
bankment may best be met by a construction similar to
that shown in Fig. 59, based upon actual practice.
356. Illustrative Case. Here the water was raised
fifty feet above the thread of the valley. The surface of the
impervious clay stratum, containing a small portion of fine
gravel, was at its lowest dip, thirty feet below the surface
of the valley, and was overlaid at this point, in the following
order of superposition, with stratas of sandy clay, coarse
sand, quicksand, sandy marl, gravel and sand, gravelly loam,
and vegetable surface soil, each of thickness as figured.
Gravel and sand and loam were obtainable readily in
the immediate vicinity, but clay was not so readily pro-
cured, and must therefore needs be economized.
348 RESERVOIR EMBANKMENTS AND CHAMBERS.
FIG. 59.
STORAGE RESERVOIR EMBANKMENT.
357. Cut-off Wall. A broad trench was cut, after the
clearing of the surface soil, down to the sandy marl, and
then a narrow trench cut down to eighteen inches depth in
the thick clay strata, finishing four feet wide at the bottom.
A wall of concrete, four feet thick, composed of machine-
broken stone, four parts ; coarse sand, one part ; fine sand,
one part ; and good hydraulic cement, one part, was built
up to eighteen inches above the top of the marl stratum.
The concrete was mixed with great care, and the materials
rammed into the interstices of the bank, to insure imper-
viousness in the wall, and to prevent water being forced
down its side and under its bottom. Puddle, of one part
mixed coarse and fine sharp gravel, one part fine sand, and
one part good clay then filled the broad trench up to the
surface of the embankment foundation.
358. Embankment Core. The core of the embank-
ment was composed of carefully mixed coarse and fine
gravel, sand, and clay, in the proportions given above
EMBANKMENT CORE. 349
(p. 340), requiring for one cubic yard of core in place, ap-
proximately :
Coarse gravel 74 cubic yard.
Fiife " 26 "
Sand II
Clay : ^15 "
L26 "
When measured by cart-loads, these quantities became
eight loads* of mixed gravels, one load of sand, and two
loads of clay, the cubic measure of each load of clay being
slightly less than that of the dry materials. The gravel
was spread in layers of two inches thickness, loose, the clay
evenly spread upon the gravel and lumps broken, and the
sand spread upon the clay. When the triple layer was
spread, a harrow was passed over it until it was thoroughly
mixed, and then it was thoroughly rolled with a two-ton
grooved roller, made up in sections, the layer having been
first moistened to just that consistency that would cause it
to knead like dough under the roller, and become a com-
pact solid mass.
Such a core packs down as solid, resists the penetration
or abrasion of water, nearly as well, and is nearly as diffi-
cult to cut through as ordinary concrete, while rats and eels
are unable to enter and tunnel it.
The proportions adopted for the core was a thickness
of five feet at the top at a level three feet above high-water
mark, and approximate slopes of 1 to 1 on each side.
For the maximum height of fifty-four feet this gave a
breadth of 113 feet base.
This core was abundantly able to resist the percolation
of the water through itself, and to resist the greatest pres-
* Seven loads of coarse and three loads of fine gravel make, when mixed,
about eight loads bulk.
350 RESERVOIR EMBANKMENTS AND CHAMBERS.
sure of the water, and had these been the only matters to
provide for, the embankment core would have been the
complete embankment.
359. Frost Covering. Frost would gradually pene-
trate deeper and deeper into that part of the work above
water and into the outside slope, and by expansions make
it porous and loose to a depth, at its given latitude, of from
four to five feet. A frost covering was therefore placed
upon it, and carried to a height on the inside of five feet
above high-water line, and of just sufficient thickness at
high- water line to protect it from frost.
The frost-covering was composed of such materials as
could be readily obtained in the vicinity of the embank-
ment. It was built up at the same time, in thin layers, with
the core, and the whole was moistened and rolled alike,
making the whole so compact as to allow no apparent
"after settlement." The wave slope was built eighteen
inches full, and then dressed back to insure solidity be-
neath the pavement.
The core of an embankment should be built up at least
to the highest flood level, which is dependent upon length
of overfall as well as height of its crest, and the frost-cover-
ing should be built of good materials to at least three feet
above maximum flood level.
360. Slope Paving. The exterior slope, when soiled,
was dressed to an inclination of 1 J to 1 ; the interior slope
was made 2 to 1 from one foot above high water down to a
level, three feet below proposed minimum low water, where
there was a berm five feet wide, and the remainder of the
slope to the bottom was made 1J to 1. The lower interior
slope was paved with large cobbles driven tightly, the berm
with a double layer of flat quarried stone, and the upper
slope, which was to be exposed to wave action, was covered
PUDDLE WALL. 351
with one foot thickness of machine-broken stone, like " road
metal" and then paved with split granite paving-blocks of
dimensions as follows : Thickness, 10 to 14 inches ; widths,
12, 14. or 16 inches ; and lengths, 24 to 48 inches.
A granite ledge, in sheets favorable for the splitting of
the above blocks, was near at hand, and supplied the most
economical slope paving, when labor of placing and future
maintenance was considered. From one foot above high
water to the underside of the coping, the paving had a slope
of 1 to 1 , and the face of the coping was vertical.
361. Puddle Wall. The policy might be considered
questionable of using clay in so large a section of the
embankment, when the haulage of the clay was greater
than of any of the other materials, and when the clay might
be confined to the lesser section of the usual form of puddle
wall. These methods of disposing the clay were compared
in a preliminary calculation, both upon the given basis, and
that of a puddle wall of minimum allowable dimensions,
viz., five feet thick at the top and increasing in thickness
on each side one foot in eight of height, which gave a maxi-
mum thickness of 18.6 feet at base with 54 feet height. (See
dotted lines in Fig. 59.)
The estimate of loose materials for each cubic yard of
complete core was coarse gravel, .74 cu. yard ; fine gravel,
.26 cu. yd. ; sand, .07 cu. yd. ; and clay, .15 cu. yd. ; and
for puddle wall of equal parts of gravel and clay gravel
.59 cu. yd., and clay .59 cu. yd.
This calculation gave the excess of clay in the maximum
depth of embankment, less than 4 cubic yards per lineal
foot of embankment, and the excess at the mean depth of
thirty feet, about three-fourths yard per lineal foot of
embankment.
The difference in estimated first cost was slightly against
352 RESERVOIR EMBANKMENTS AND CHAMBERS.
the mixed core, but in that particular case this was consid-
ered to be decidedly overbalanced by more certainly in-
sured stability, more probable freedom from slips and
cracks in a vital part of the work, and by the additional
safety with which the waste and draught pipes could be
passed through the core.
The value of puddle in competent hands has, however,
been demonstrated in many noble embankments. It is
usually placed in the centre of the embankment, as in
Fig. 61, and occasionally near the slope paving, as in
Fig. 62, from a design by Moses Lane, C. E.
363. Kubble Priming Wall. The drift formation
presents a great variety of materials ; but not always such
as are desired for a storage embankment, in the immediate
vicinity of its site. The selection of proper materials often
demands the best judgment and continued attention of the
engineer. Clay, which is often considered indispensable in
an embankment, may not be found within many miles.
Fig. 60 (p. 84) gives a section of an embankment con-
structed where the best materials were a sandy gravel and
a moderate amount of loam, but abundance of gneiss rock
and boulders were obtainable close at hand.
Here a priming wall of thin split stone was carried up
in the heart of the embankment from the bed-rock, which
was reached by trenching. Each stone was first dashed
clean with water, and then carefully floated to place in good
cement mortar, and pains taken to fill the end and side
joints, and exceeding care was taken not to move or in any
way disturb a stone about which the mortar had begun to
set. No stones were allowed to be broken, spalted, or
hammered upon the wall, neither were swing chains drawn
out through the bed mortar. The construction of a water-
tight wall of rubble-stone is a work of skill that can be
APPLICATION OF FINE SAND. 353
performed, but the ordinary layer of foundation masonry
in cement mortar seems no more to comprehend it than
would a fiddler at a country dance the enchanting strains
of a Vieuxtemps or Paganini.
Grouting such rubble-stone walls, according to the usual
method, will not accomplish the desired result, and is
destructive of the most valuable properties of the cement.
363. A Light Embankment. In this embankment
(Fig. 60), selected loam and gravel were mixed in due pro-
portions on the upper side of the priming wall, so as to
insure, as nearly as possible, imperviousness in the earth-
work. The entire embankment was built up in layers,
spread to not exceeding four or five inches thickness, and
moistened and rolled with a heavy grooved roller.
The cross-section of this work is much lighter than that
advised by several standard authorities, both slopes being
1-J to 1, but great bulk was modified by the application of
excellent and faithful workmanship. This embankment
retains a storage lake of sixty-six acres and thirty feet
maximum depth. It was completed in 1868, and has
proved a perfect success in all respects. This work fills the
offices of both an impounding and distributing reservoir, in
a gravitation water supply to a New England city.
364. Distribution Reservoirs. Distributing reser-
voirs are frequently located over porous sub-soils and
require puddling over their entire bottoms and beneath
considerable portions of their embankments, and puddle
walls are usually carried up in the centres of their embank-
ments or near their inner slopes. .
The same general principles are applicable to distrib-
uting as to storage reservoir embankments.
365. Application of Fine Sand. Fig. 58 (p. 333) illus-
trates a case where the bottom was puddled with clay, but a
354
RESERVOIR EMBANKMENTS AND CHAMBERS.
sufficiency of clay to puddle the embankments was not ob-
tainable. The embankment is here constructed of gravel,
coarse sand, very fine sand, and a moderate amount of
loam. The materials were selected and mixed so as to
secure imperviousness to the greatest possible extent, and
were put together in the most compact manner possible, and
have proved successful. This has demonstrated to the sat-
isfaction of the writer that very fine sand may replace to a
considerable extent the clay that is usually demanded, and
his experience includes several examples, among which, on
a single work, is more than three-fourths of a mile of suc-
cessful embankment entirely destitute of clay, but sand
was used with the gravel, of all grades, from microscopic
grains to coarse mortar sand, and a sufficiency of loam was
used to give the required adhesion. The outside slopes
were heavily soiled and grassed as soon as possible.
FIG. 61.
REVETTED RESERVOIR EMBANKMENT.
366. Masonry-faced Embankment. When there
is a necessity for economizing space, one or both sides of an
embankment may be faced with masonry.
An example of such construction is selected from the
practice of a successful engineer in one of the Atlantic
EMBANKMENT SLUICES AND PIPES. 355
States, and is shown in Fig. 61. A method of introducing
clay puddle into a central wall in the embankment, beneath
the embankment, and on the reservoir bottom, is also here
shown. The puddle of the reservoir bottom is usually
covered with a layer of sand.
367. Concrete Paving. The lower section of the
slope paving of the distributing reservoir, Fig. 58, was built
up of concrete, composed of broken stone 4 parts ; coarse
sand 1 part ; fine sand I part ; and hydraulic cement 1 part.
The cement and sand were measured and mixed dry, then
moistened, and then the stone added and the whole thor-
oughly worked together. The concrete was then deposited
and rammed in place, building up from the base to the top,
in sections of about forty feet length. A very small quan-
tity of water sufficed to give the concrete the proper con-
sistency, and if more was added the concrete inclined to
quake under the rammer, which was an indication of too
much water.
The general thickness of the concrete sheet is ten inches,
and there is in addition four ribs upon the back side to give
it bond with the embankment, and to give it stiffness, and
also to check the liability of the sheet being lifted or cracked
by back pressure from water in the embankment, when the
water in the reservoir may be suddenly drawn down.
The upper part of the slope that is exposed to frost is
of granite blocks laid upon broken stone. The layer of
broken stone at the wave line is fifteen inches thick, which
is none too great a thickness to prevent the waves from
sucking out earth and allowing the paving to settle.
368. Embankment Sluices and Pipes. Arched
sluices have been in many cases built through the founda-
tion of the embankment and the discharge pipes laid therein,
and then a masonry stop-wall built around the pipes near
356 RESERVOIR EMBANKMENTS AND CHAMBERS.
the upper end of the sluice. By this plan the pipes are
open for inspection from the outside of the embankment up
to the stop wall. If the sluice is not circular or elliptical,
its floor should be counter-arched, and its sides made strong,
to resist the great pressure of the water that may saturate
the earth foundation.
FIG. 62.
SLOPE PUDDLED RESERVOIR EMBANKMENT.
Such a sluice is sometimes built in a tunnel through the
hillside at one end of the embankment. The latter plan,
when the upper end of the tunnel is through rock, is the
safer of the two, otherwise there is no place where it can be
more safely founded, constructed, and puddled around,
than when it is built upon the uncovered foundation of the
embankment, either at the lowest point in, or upon, one
side of the valley, since every facility is then offered for
thorough work, which cannot so easily be attained in an
earth tunnel obstructed by timber supports.
A circular or rectangular well rising above the water
surface, is usually built over the upper end of the sluice,
and contains the valves of the discharge pipes, and inlet
sluices at different heights, admitting water to the pipes
from different points below the surface of the reservoir.
When the sluice is used for a waste-sluice, also, the
stop-wall is omitted, and the sluice well rises only to the
weir crest level, or has openings at that level and an addi-
tional opening at a lower level controlled by a valve.
GATE CHAMBERS. 357
Sometimes heavy cast-iron pipes, for both delivery and
waste purposes, are laid in the earthwork instead of in
sluices, in which case the puddle should be rammed around
them with thoroughness. In this latter case they should be
tested, in place, under water pressure before being covered.
A "suitable hand force-pump may be used to give the
requisite pressure if not otherwise obtainable. Bell and
socket pipes with driven lead joints are used in such
cases, and projecting flanges are cast around the pipes at
intervals.
The method of laying and protecting discharge pipes, as
shown in Fig. 60 (p. 84), has been adopted by the writer in sev-
eral instances with very sati sfactory results. A foundation of
masonry is built up from a firm earth stratum to receive the
pipes, and then when the pipes have been laid and tested,
they are covered with masonry or concrete. In such case
the sides of the masonry are not faced, and pointed, or plas-
tered, but the stones are purposely left projecting and
recessed, and the covering stones are of unequal heights,
making irregular surfaces. This method is more economi-
cal in construction, and attains its object more successfully
than the faced break-walls sometimes projected from the
sides of gate-chambers and sluices.
The puddle or core material is rammed against the ma-
sonry in all cases, so as to fill all interstices solid. This
portion of the work demands the utmost thoroughness and
faithfulness ; and with such, the structure will be so far
reliable, and otherwise may be uncertain.
369. Gate Chambers. When an impounding reser-
Toir is deep, requiring a high embankment, it is advisable
to place the effluent chamber upon one side of the valley
toward the end of the embankment, with the effluent pipes
for ordinary use only as low as may be necessary to draw
358
RESERVOIR EMBANKMENTS AND CHAMBERS.
the lake down to the assumed low water level, as in Fig. 63 r
showing the inside slope of an embankment.
A waste-pipe for drawing off the lowest water is, in such
case, extended from the front of the effluent chamber, side-
ways down the slope and side of the valley to the bed of
its old channel, and is fitted with all details necessary for it
FIG. 63.
EFFLUENT CHAMBER AND SIPHON WASTE.
to perform the office of a siphon when there shall be occa-
sion to draw the reservoir lower than the level of the gate
chamber floor. By such arrangement the pipes may pass
through the embankment, or through a sluice or tunnel in
the side of a hill at a level twenty or twenty-five feet above
the bed of the valley.
When a valve-chamber is built up from the inner toe of
the embankment, so that the water surrounds it at a higher
level, provision must be made for the ice-thrust, lest it crowd
back toward the embankment the upper portion sufficiently
to make a crack in the wall ; and precaution must also be
taken to prevent the ice lifting bodily the whole top of the
GATE CHAMBERS. 359
chamber when the water rises in winter, as it usually does
in large storage reservoirs.
The writer has usually connected the gate-house with
the embankment by a solid pier, when there would other-
wise be opportunity for the ice to yield behind the chamber
by slipping up the paving, as it expanded, and thus en-
danger the gate-chamber masonry.
There are inlets through the front of the effluent chamber
shown in Fig. 63, at different depths, permitting the water
to be drawn at different levels.
These, when the volume of water to be delivered is small,
may be pieces of flanged cast-iron pipe built into the
masonry, with stop-valves bolted thereon, but usually are
rectangular openings with cast-iron sluice - valves and
frames (Fig. 64) secured at their inside ends. The seat and
bearing of the valves are faced with a bronze composition,
which is planed and scraped so as to make water-tight
joints. The screw-stem of the valve is also of composition,
or aluminum or manganese bronze.
If such a valve exceeds 2'-3" x 2'-9" in area, or is
under a pressure of more than twenty feet head, some form
of geared motion is usually necessary to enable a single
man to start it with ease.
It is usually advisable to increase the number of valves
rather than to make any one so large as to be unwieldy in
the hands of a single attendant, even at the expense of some
frictional head.
The stem of the small valves usually passes up through
a pedestal resting on the floor of the chamber, and through
a nut in the centre of a hand- wheel that revolves upon the
pedestal.
The outside edge of each valve-frame should be so formed
that a temporary wood stop-gate might be easily fitted
360
RESERVOIR EMBANKMENTS AND CHAMBERS.
FIG. 64.
against it by a diver, in case accident required the removal
of the valve for repairs. The chamber might then be readily
emptied and the valve removed, without drawing down the
lake.
Upon the back of the valve (Fig. 64) are lugs faced with
bronze, and upon the frame corresponding lugs, both being
arranged as inclined planes, and their office is to confine the
valve snug to its seat when closed.
If the valve is secured to the side of the opening opposite
to that which the current approaches, or to the pressure, its
bolts must enter deep into or pass
through the masonry.
A slight flare is usually given to the
sluice-jambs, from the sluice-frame out-
ward.
370. Sluice-Valve Areas. When
the head is to be rigidly economized,
the submerged sluice-valve area must
be sufficient to pass the required vol-
ume of water at a velocity not exceeding
about five lineal feet per second; when
the loss of head due to passage of the
valve will not exceed about one-half
foot.
If Q is the maximum volume, in cu.
ft. per second ; S, the area of the sluice
in square feet ; , the assumed maxi-
mum velocity ; then
(1)
IRON SLUICE-VALVE.
in which c is a coefficient of contraction,
that may be taken, for a mean, as equal
to .70 for ordinary chamber-sluices.
STOP-VALVE INDICATOR. 361
From this equation of Q, we derive that of area,
CD
(2)
Let Q = 70 cubic feet per second ; v = 5 lineal feet
per second ; then we have - L = 20 square feet area, and we
(?D
may make the valve opening, say 4' x 5'.
If there are a number of valves, whose respective areas
are ^, s 2 s s . . . . s then
i- =
Cc/
(3)
advisedly we should give a slight excess to the sum of
. Q
or
areas and make
+ s 2 +
FIG. 65.
371. Stop-Valve Indicator. When a stop-valve is
used, instead of a sluice-valve whose screw rises through
the hand- wheel, it is usually desir-
able to have some kind of an indi-
cator to show how nearly the stop-
valve is to full open.
Fig. 65 illustrates such an indi-
cator attached to. the hand -wheel
standard, as manufactured by the
Ludlow Valve Co., at Troy, N. Y.
A worm-screw upon the valve-stem
revolves the indicator-wheel at the
side of the standard, and indicates
the various lifts of the valve between
shut and full open.
372. Power Required to Open
a Valve. The theoretical computa-
tion of the power required to start a
362 RESERVOIR EMBANKMENTS AND CHAMBERS.
closed valve, when it is pressed to its seat by a head of water
upon one side and subject only to atmospheric pressure on
the other side, is 'attended with some uncertainties ; neverthe-
less this computation, subject to such coefficients as experi-
ence suggests, is a valuable aid when proportioning the parts
of new designs.
Take the case of the metal sluice-valve, Fig. 64, raised
by a screw, with its nut placed between collars in the top
of a pedestal, and revolved by a hand-wheel, and let the
centre of water pressure upon the valve be at a depth of
30 feet. Let the size of valve-opening be 2-6" x 2-9", the
pitch of the screw .75 inch, and the diameter of the hand-
wheel 30 inches.
The weight has to slide along the spiral inclined plane
of the screw, but its actual advance is in a vertical line, the
pitch distance, for each revolution of the screw.
The power is applied to the hand-wheel, which is equiva-
lent to a lever of length equal to its radius, moving through
a horizontal distance equal
FlG - 66. to the circumference of its
circle (= radius x 6.283*)
and a vertical distance
equal to the pitch of the
screw.
The distance d, moved through by the power in each
revolution, is the hypothenuse be, Fig. 66, of an angle
whose base, a&, equals the circumference of its circle, and
whose perpendicular, ac, equals the pitch of the screw =
'/circumference 2 + pitch 2 = d.
Let w be the weight in Ibs.; p the pitch, in inches ; d the
distance moved by the power per revolution, in inches, and
P, the power, in foot-pounds..
According to a theory of mechanics, the
POWER REQUIRED TO OPEN A VALVE. 363
Vel. of Power : Yel. of Weight :: Weight : Power; or,
d : p :: w : P.
The weight, in this case, includes the actual weight of
the iron valve and its stem ; its friction upon its seat due to
the pressure of water upon it ; the friction of the screw upon
its nut, and the friction of the nut upon its collar. These
we compute as follows :
Weight of valve, assumed = 300 Ibs.
Friction of valve (15469 Ibs. pres. x coef..20) = 3094 "
Friction of screw (300 + 3094) x coef. 20 = 679 "
Friction of nut (300 + 3094) x coef. 15 = 501 "
Total equivalent weight, w = 4574 "
Distance of power, d = \ circum. 2 -- pitch 8 fi = 94.25 inches.
Pitch = .75 "
In the form of equation,
Theoretically, this power applied at the circumference
of the hand- wheel would be just upon the point of inducing
motion, or if this power was in uniform motion around the
screw, it would just maintain motion of the weight. The
theory here admits that the screw and nut are cut truly to
their incline, and that there is no binding between them due
to mechanical imperfection.
When two metal faces remain pressed together an ap-
preciable length of time, the projections of each enter into
the opposite recesses of the other, to a certain extent. These
projections of the moving weight must be lifted out of lock,
and the inertia of the weight must be overcome before it
can proceed. Metal valves usually drop against an inclined
wedge at their back that presses them to their seat, and
there is also a fibre lock with this wedge, or "stick," as it
364 RESERVOIR EMBANKMENTS AND CHAMBERS.
is commonly called, according to the force with which the
valve is screwed home.
Hence, the power required to start A val^e is often double
i/( fasL-frC^
or treble, or even quadruple that Q&B& would theoretically
be required to maintain it in motion the instant after start-
ing. The equation for starting the valve in such case may
become,
The computed distance which the power moves per revo-
lution (94.25 inches) equals 7.854 feet, and the computed
power 36.4 Ibs. If twenty revolutions of the hand- wheel are
made per minute, then the power exerted is theoretically
7.854 ft. x 20 rev. x 36.4 Ib. = 5717.7 foot-pounds per minute.
This is a little more than one-sixth of a theoretical horse-
power.
If, for the hand- wheel, which revolves the nut, there is
substituted a spur-gear of equal pitch diameter, and into
this meshes a pinion of one-third this diameter, and the
same hand- wheel is placed upon the axle of the pinion, then
the new power required will be reduced proportionally, as
the square of diameter of the pinion is reduced from the
square of diameter of the spur, or in this case, one-ninth.
373. Adjustable Effluent Pipe. An adjustable
effluent pipe, capable of revolving in a vertical plane, and
connected directly to the main supply pipe,* is shown in
Fig. 60 (p. 84).
This adjustable pipe is constructed of heavy sheet cop-
per, and is sixteen inches in diameter. Upon its end is a
* Tliis ingenious form of flexible joint was suggested to the writer by Hon.
Alba F. Smith, one of our most able American mechanical engineers. Mr.
Smith designed this joint many years ago, and used it at watering stations
upon the Hudson River, and other railroads under his charge.
FISH SCREENS. 365
perforated bulb, through which the water enters the pipe.
The movable section of the pipe is counter- weighted within
the chamber, so the bulb can be set at any desired depth
in the water, or raised out of water to the platform upon the
chamber, for cleaning, expeditiously and easily by a single
attendant. This arrangement has operated most satisfac-
torily during the eight years since its completion, and de-
livers the water supply for about 18,000 inhabitants.
Equivalent devices have been adopted in several in-
stances in Europe and in India, and they are especially
applicable to cases where the impounding reservoirs are
also the distributing reservoirs, without the intervention of
filtering basins, and to cases where the surface fluctuates
frequently, rapidly, or to a considerable extent.
When a sudden or considerable decrease of the tem-
perature of the air chills the quiet reservoir water surface,
and thus induces a vertical motion in, or shifting of position
of the whole mass of water, the bulb may be made to fol-
low the most wholesome stratum.
If the impounded water is to be led to filter-beds or to
one or more distributing reservoirs, then the discharge-
pipes lead directly from the effluent chamber.
374. Fish Screens. In the chamber, Fig. 67, is shown
a set of fish-screens, arranged in panels so as to slide out
readily for cleaning. The finer ones of the double set are
of No. 15 copper wire, six meshes to the inch, and the
coarser ones of No. 12 copper wire, woven as closely as
possible.
Figs. 67 and 68 show a plan of and a vertical section
through an influent chamber of a distributing reservoir.
The pipes d d deliver water from the impounding reser-
voir, or may be force mains, leading from pumping engines
to the chamber A. The main chamber is divided in two
366 RESERtOIR EMBANKMENTS AND CHAMBERS.
FIG. 67.
PLAN OF INFLUENT CHAMBER.
parts, for convenience in management when there are sev-
eral delivery pipes. There are sluices 7c Tc, controlled by
valves, through which the water may be admitted to the
reservoir O. There is also a weir, i, over which water may
be passed, instead of through the sluices.
FIG. 68.
SECTION THROUGH INFLUENT CHAMBER.
Grooves are prepared in each section of the main cham-
ber for a double set of screens, ss.
V ^> * x '\ < bN
FOUNDATION^,/ 'V', 367 >T
</,^ ^ /';. \
>, a waste Dme. and ^a wast&^^ r
GATE-CHAMBER
B is a waste chamber, and e a waste pipe, an
overflow weir. C^
A frost curtain, w, is placed in front of the inflow weir/
to prevent the water surface in the chamber from freezing,
if the pumps are not in operation during winter nights.
There are drain pipes, p, leading from the sections of
the main chamber to the waste well.
In the dividing partition is a sluice, with valve so that
the whole chamber may be connected as occasion requires.
A distributing reservoir effluent chamber might be simi-
lar to the above, omitting the waste chamber, weirs, and
frost curtain ; the direction of the current would in this case
be reversed, of course.
In the effluent chamber of the reservoir shown in Fig. 58,
a check-valve is placed in the effluent pipe, so that when
the pumps are forcing water into the distribution pipes
around the reservoir, with direct pressure, the water will
not return into the reservoir by the supply main.
375. Gate-Chamber Foundations. Gate-chambers
built into the inner slope of an earthwork embankment will
introduce an element of weakness at that point, unless
intelligent care is exercised to prevent it.
Any after settlement along t]je sides of the foundation
or walls of the chamber separates the earth from the
masonry, leaving a void or loose materials along the side
of the masonry, which permits the water of the reservoir to
percolate along the side to the back of the chamber, under
the full head pressure.
The stratum of earth on which the foundation rests
should be not only impervious, but so firm,- or made so
firm, that no settlement of the foundation can take place.
If the chamber is high and heavy, the footing courses
should be extended on each side so as to distribute the
368 RESERVOIR EMBANKMENTS AND CHAMBERS.
weight on an area of earth larger than the section of the
chamber.
The foundation of the chamber is to be water-tight, and
capable of resisting successfully the upward pressure upon
its bottom due to the head of water in the reservoir, when
the chamber is empty.
376. Foundation Concrete. The use of belon, or
hydraulic concrete, is often advisable for the bed-course of
a valve-chamber foundation, to aid in distributing the
weight of the structure and in securing a water-tight floor.
The composition of the concrete is to be proportioned for
these especial objects. Concrete for a revetment, demands
weight as a special element ; for a lintel, tensile strength ;
for an arch, compressile strength ; but for the submerged
foundation of a gate-chamber, impermousness, which will
ensure sufficient strength.
The volume of cement should equal one and one-third
times the volume of voids in the sand. The volume of mor-
tar should equal one and one-third times the volume of
voids in the coarse gravel or broken stone. The cement
and sand should be first thoroughly mixed, then tempered
with the proper quantity of water equally worked in, and
then the mortar should be thoroughly mixed with the
coarse gravel or broken stone, which should be clean, and
evenly moistened or sprinkled before the mortar is intro-
duced. None of the inferior cement so often appearing in
the market should be admitted in this class of work. Good
hydraulic lime may in some cases be substituted for a
small portion of the cement, say one-third.
The concrete should be rammed in place, but never by
a process that will disturb or move concrete previously
rammed and partially set. A very moderate amount of
water in the concrete suffices when it is to be rammed.
CHAMBER WALLS. 369
377. Chamber Walls. Fine -cut beds and builds,
hammered end joints, and coursed work, in chamber ma-
sonry, make expensive structures, but even such work is
hardly made water-tight by a poor or careless mechanic.
A great deal of skill and care must be brought into requi-
sition to make a rubble wall water-tight.
Imperviousness is here, again, a special object sought.
That a wall may be impervious, its mortar must be imper-
vious ; its voids must be compactly tilled, every one ; its
stones must be cleaned of dust, moistened, laid with close
x joints, and well bedded and bonded ; and no stone must
be shaken or disturbed in the least after the mortar has
begun to set around it.
Stone must not be broken or hammered upon the laid
wall, or other stones will be loosened. Stones should be so
lewised or swung that the bed or joint mortar shall not be
disturbed when the stone is floated into place.
The plan occasionally adopted of grouting several courses
at the same time with thin liquid grout, might answer in a
cellar wall when the object was to prevent rats from peram-
bulating through its centre, but it is unreliable in a cham-
ber or tank-wall intended to resist percolation under pres-
sure. Skillful workmanship, in hydraulic masonry, is
cheaper than expensive stock.
24
CHAPTER XVII.
OPEN CANALS.
378. Canal Banks. The stored waters of an impound-
ing reservoir are sometimes conveyed in an open canal
toward the distributing reservoir, or the city where they are
to be consumed, or for the purposes of irrigation. "The
theory of flow in such cases has been already discussed
(Chap. XY).
The subsoils over which the canal leads require careful
examination, and if they are at any point so open and
porous as to conduct away water from the bed of the canal,
the bed and sides must be lined with a layer of puddle
protected from frost, as in Fig. 69, showing a section of a
puddled channel in a side-hill cut.
FIG. 69.
The retaining channel bank on the down-hill side is con-
structed upon the same principles as a reservoir embank-
ment ( 351), the chief objects being to secure solidity,,
imperviousness, and permanence.
INCLINATIONS AND VELOCITIES.
371
A longitudinal drain along the upper slope of side-hill
sections will prevent the washing of soil into the canal.
The water slopes will require revetments or paving from
three feet below low-water to two feet above high-water
line, and paving or rubbling down the entire slope at their
concave curves.
Substantial revetments or pavings of sound stone are the
most economical in the end.
Kevetments, built up of bundles of fascines laid with
ends to the water and each layer in height falling back
with the slope line, have been used to some extent on the
banks of canals of transport, and on dykes.*
If the slopes are rip-rapped, or pitched with loose stone,
the slopes must be sufficiently flat, so the waves and the
frost will not work the stones down into the water, and de-
mand constant repairs.
The retaining canal banks of the head races of water-
powers have sometimes
a longitudinal row of
jointed-edged sheet-piles
through their centre. The
selected mixed earth is
compactly settled on both
sides of this piling, as
shown in Fig. 70. Such
piling tends to insure im-
perviousness, prevent vermin from burrowing through the
bank, and lasts a long time in compact earth.
379. Inclinations and Velocities in Practice.
The unrevetted trapezoidal canals in earthwork, for water-
* Vide illustration of Foss Dyke in Stevenson's Canal and River Engineer-
ing, p. 18, Edinburgh, 1872 ; and Mississippi River Dyke at Sawyer's Bend.
Report Chief of U. S. Engineers, June 30, 1873.
FIG. 70.
SHEET-PILED CHANNEL BANK.
372 OPEN CANALS.
supplies, irrigation, and for hydraulic power, except in
water -powers of great magnitude, have sectional areas,
respectively, between 500 and 50 square feet limits, and
hydraulic mean radii between 7 and 2.5.
In such canals the surface velocities range between
5 feet and 2 feet per second, and the inclinations of surface
between .75 feet (= .000104) and 3.5 feet (= .000663) per
mile.
Practice indicates that the favorite surface velocity of
flow, in such straight canals, is about 2.5 feet per second,
in canals of ^about five feet depth, being less in shallower
canals, and increased to 3.5 feet per second in canals of
nine feet depth.
Only very firm earths, if unprotected by paving or rub-
ble, will bear greater velocities without such considerable
erosions as to demand frequent repairs.
Burnell states* that the inclinations given to the re-
cently constructed irrigation canals in Piedmont and Lom-
bardy, varies from y^ (= .000625) to ^^ (= .000278) ;
but that inclinations frequently given to main conductors
in the mountainous districts of the Alps, Tyrol, Savoy,
Dauphine, and Pyrenees, is ^ (= .002).
380. Ice Coverings. The maximum winter flow hav-
ing been determined upon, the sectional area, beneath the
thickest formation of ice at the lowest winter stage of water,
must be made ample to deliver this maximum quantity of
water, and the influence of the increase of friction on the ice
perimeter over that on the equal air perimeter must be duly
considered.
381. Table of Dimensions of Supply Canals.
The dimensions and inclinations of a few well-known canals
* Rudiments of Hydraulic Engineering, p. 127. London, 1858.
CAN'AL GATES.
373
are given as illustrative of the general practice in various
parts of the world, relating especially to water supply and
irrigation.
TABLE No. 79.
DIMENSIONS OF WATER SUPPLY AND IRRIGATION CANALS.
ij
"I
1
&
|
ITIO OF
-INATION.
EAN
OCITY.
1$
Q
c/5
|
"J
s
Henares Canal, Spain
Trapezoidal.
8.27
1 5 tO
4.02
i in 3067
.000326
2 2Q6
Roqueiavour Canal, France . . .
9.84
4-9*
n 3333
.0003
Marseilles
Q.8 4
i to
5.58
in 3000
.000333
2.72
Ourcq "
Montreal W. W. (old), Canada.
11.48
20
Jto
itO
4.92
in 9470
in 25000
.0001056
.00004
" (new), "
78
to
M
in 25000
.00004
....
Manchester, N.H., W.W., U.S.
6
to
14
in 5280
.000189
Ganges Canal, India -<
and part
Twin Rect.
8=
... . .
9
::::::l
3-7
Glasgow W. W., Scotland
Rectangular.
8
8
i in 6325
.000158
1.478
Cavour Canal, Italy
" \
131
6.1
i in 2800
.000357 i
2.6
}
11.15
.00025 j
In the numerous shallow irrigation canals of Spain,
Italy, and northern India, a mean velocity as great as three
feet per second is necessary to prevent a luxuriant growth
of weeds on the bottoms and side slopes, which reduce the
effective sectional area of the canal, and consequently the
volume of water delivered.
382. Canal Gates. Fig. 71 is a half elevation of the
gates in the Manchester, N. H., water- works canal, showing
also a profile of the canal beyond the wing walls of the
gate abutments.
This canal leads the water from Lake Massabesic to the
turbines and pumps at the pumping station.
The water surface rises and falls with the lake, which
has a maximum range of five feet, so that the turbines are
constantly under the full head of the lake. The canal is
sixteen hundred feet long, and has similar gates at its
374
OPEN CANALS.
entrance and at the head of the turbine penstock. The
entrance gates are provided witli a set of iron racks to inter-
cept floating matters that might approach from the lake,
and the penstock gates are provided with a set of fine mesh
copper- wire fish-screens.
There are four gates in each set, each 3 feet wide and
5 feet high. On the top of each gate is secured a cast-iron
FIG. 71.
CANAL SLUICE-GATES.
tube containing a nut at its top. Over each tube is fastened,
to a lintel, a composition screw, working in its nut, which
raises or lowers its gate.
Two gates in each set have their screws provided with
gears and pinions. The pinions, or screws, are turned by a
ratchet wrench, so the operator may turn them either way,
to raise or lower the gate, by walking around the screw, or
by a forward and backward motion of the arms.
The floor covering the gate-chamber is of tar-concrete
resting upon brick arches.
MINERS' CANALS. 375
When large sluices are necessary, a system of worm
gearing is usually applied for hoisting and lowering the
gates. These gears may be operated by hand-power, or
may be driven by the belts or gears upon a counter-shaft,
which is driven by a turbine or an engine.
Canals leading from ponds subject to floods or sudden,
rise above normal level, are to be provided with waste- weirs
near their head gates, and with waste-gates, so their banks
will not be overtopped or their waters rise above the pre-
determined height.
Stop-gates are placed at intervals in long water-supply
and irrigation canals, with waste-gates immediately above
them for drawing off their waters, to permit repairs, or for
flushing, if the waters deposit sediment.
Culverts are sometimes required to pass the drainage of
the upper adjoining lands beneath the canal, and these may
be classed among the treacherous details that require ex-
ceeding care in their construction to guard against settle-
ments, and leakage of the canal about them.
383. Miners' Canals. The sharp necessities of the
gold-mining regions of California and Nevada have led to
some of the most brilliant hydraulic achievements of the
present generation. The miners intercept the torrents of
the Sierras where occasion demands, and contour them in
open canals, along the rugged slopes, hang them in flumes
along the steep rock faces, syphon them across deep can-
yons, and tunnel them through great ridges, in bold defi-
ance of natural obstacles, though constant always to laws
of gravity and equilibrium.
The force of water is an indispensable auxiliary in sur-
face mining, and capital hesitates not at thirty, fifty, or a
hundred miles distance, or almost impassable routes, when
the torrent's power can be brought into requisition. A
376 OPEN CANALS.
hundred ditches, as the miners term them, now skirt the
mountains, where but a few years ago there was no evi-
dence that the civilization or energy of man had ever been
present.
The Big Canyon Ditch, near North Bloomfield, Nevada,
for instance, is forty miles long and delivers 54,000,000
gallons of water per day. The sectional area of the stream
is about 33 square feet, and the inclination 16 feet to the
mile. Its flumes are 6 feet wide with grade of one-half
inch in twelve feet, or about 18 feet to the mile. The con-
tour line of the canal is from 200 to 270 feet above the
diggings, to which its waters are led down in wrought-
iron pipes.
With a terrible power, fascinating to observe, its jets
dash into the high banks of gravel, rapidly under-cutting
their bases, and razing them in huge slides that flow down
the sluice-boxes with the stream.
Thus, in a single mine, 30,000 cubic yards of gravel melt
away in a single day, under the mighty hydraulic influence
that has been gathered in the torrent and canaled along the
eternal hills.
The Eureka Ditch, in El Dorado County, is forty miles
long, and there are many others of great length, whose
magnitude and mechanical effect entitle them to considera-
tion, as valuable hydraulic works, and monuments of
hardy enterprise.
The Eureka embankment is seventy feet in height, flows
two hundred and ninety-six acres, and is located six thou-
sand five hundred and sixty feet above the level of the sea.
CHAPTER XVIII.
WASTE-WEIRS.
384. The Office and Influence of a Waste- Weir.
An ample waste-weir is the safety-valve of a reservoir
embankment.
The outside slope of an earth embankment is its weakest
part, and if a flood overtops the embankment and reaches
the outer slope, it will be cut away like a bank of snow
before a jet of steam.
The overfall should be maintained always open and
ready for use, independent of all waste sluices that are
closed by valves to be opened mechanically, for a furious
storm may rage at midnight, or a waterspout burst in the
valley when the gate-keeper is asleep.
Data relating to the maximum flood flow is to be dili-
gently sought for in the valley, and the freshet marks
along the watercourse to be studied. The overfall is to be
proportioned, in both dimensions and strength, for the
extraordinary freshets, which double the volume of ordi-
nary floods, and if there are existing or there is a proba-
bility of other reservoirs being built in the valley above, it
may be wise to anticipate the event of their bursting, espe-
cially if an existing reservoir dam is of doubtful stability.
A short overfall may increase or affect the damage by
flood flowage to an important extent, and makes necessary
the building of the embankment to a considerable height
above its crest level ; while, on the other hand, a long over-
fall, if exposed to the direct action of the wind, may permit
378 WASTE-WEIRS.
too great a volume of water to be rolled over its crest in
waves just at the commencement of a drought, when it is
important to save, to the uttermost gallon. Such wave
action, under strong winds, might draw down a small reser-
voir several inches, or even a foot below its crest, unless
such contingency is anticipated and guarded against.
Strong winds blowing down a lake often heap up its waters
materially at the outlet, and increase the volume of waste
flowing over its weir or outfall.
An injudicious use of flash-boards upon waste- weirs has
in many instances led to disastrous results. In all cases, a
maximum flood height of water should be determined upon,
and then the weir dimensions be so proportioned that no
contingency possible to provide for shall raise the water
above the predetermined height. The length of the overfall
and volume of maximum flood-flow govern the distance
the highest crest-level must be placed below the maximum
flood-level. Flash-boards may in certain cases, and in cer-
tain seasons, be serviceable in governing the level of water
below or just at the crest line, especially when there are low
lands, or lands awash, as they are termed, bordering upon
the reservoir, with their surfaces not exceeding three feet
above the crest line.
Several English writers mention that a general rule for
length of waste-weir, accepted in English practice, is to
make the waste-weir three feet long for every 100 acres of
watershed. This rule will apply for watersheds not exceed-
ing three square miles area, but for larger areas gives an
inconvenient length.
385. Discharges over Waste-Weirs. Having de-
termined, or assumed from the best data available, the
maximum flood-flow which the overfall may have to dis-
charge, if a very heavy storm takes place when the reservoir
DISCHARGES OVER WASTE- WEIRS. 379
is full, the overfall is then to be proportioned upon the
basis of this flow.
For the calculation of discharge, the overfall may be
considered to be a species of measuring- weir ( 3O3), and
subject to certain weir formulas.
If there are flash-boards, with square edges, forming the
crest, then, for depths of from nine inches to three feet, Mr.
Francis' formula may be applied with approximate results,
and we have the discharge :
Q = 3.33 (I - O.lTi/7) H^ (I)
in which Q is the volume of discharge, in cubic feet per
second ; ZT, the depth of water upon the crest, measured to
the lake surface level ; Z, the clear length of overfall ; and
n the number of end contractions.
We have seen ( 3O9) that the velocities of the parti-
cles flowing over the crest are proportionate to the ordinates
of a parabola, and that the mean velocity is equal to two-
thirds the velocity of the lowest particles ; hence we have
the mean velocity, v, of flow over the crest,
= 5.35V Tl. (2)
Multiplying the depth of water H upon the weir, into
the length I of the weir, and into the mean velocity 0, we
have the volume of discharge, when there are no interme-
diate flash-board posts :
Q = mlH x l^ZgH= 6.96ml ff* 9 (3)
in which m is a coefficient of contraction ( 312), with
mean value about .622 for sharp-edged thin crests.
By transposition, we have :
If the overfall has a wide crest similar to that usually
given to masonry dams, Fig. 47, then we may apply more
380
WASTE-WEIRS.
accurately the formula suggested by Mr. Francis for such
cases, viz. : *
Q = 3.0121H 1SB . (5)
If we desire to know the depth of discharge for a given
volume and weir length, then, by a transposition of this
last formula, we have :
ff-
-
--
3M2l
L.M
(6)
A few approximate values of Q, for given values of H,
are given in the following table, to facilitate preliminary
calculations.
TABLE No. SO.
WASTE-WEIR VOLUMES PER LINEAL FOOT FOR GIVEI
DEPTHS.
H.
6=5.35^.
C =30i^>-. ^
In feet.
In cu. ft. per sec.
In cu. ft. per sec.*
5
1.043
I.I77
75
J-939
2.167
1. 00
3.012
3-339
1.25
4.238
4.670
1.50
5.602
6.134
1.75
7-93
7.625
2.OO
8.699
9.430
2.25
10.415
11.244
2.50
12.238
13.167
2-75
14-159
I 5- I 93
3.00
16.171
17.309
3 CO
21.2
"0
4 .OO
,\j\j
26 c.
w *o
4.50
T.2.7,
5 .OO
O 'O
38.6
O '
C.CQ
45.0
00
6.00
C2.O
6. co
O
60.0
^'O
7.00
68.3
/ * w
w O
78.0
8.00
/
87.0
* In this column m increases from .563 for 1 foot depth to .670 for 8 feet
depth, but the values of m for depths exceeding 3 feet have not been de-
termined by experiment, and their results are subject to some uncertainty.
REQUIRED LENGTH OF WASTE -WEIRS.
381
386. Required Length of Waste- Weirs. The fol-
lowing table, prepared to facilitate preliminary calculations,
gives estimated flood volumes of waste from small impound-
ing reservoirs, in ordinary Atlantic slope basins, for water-
sheds of given areas ; also the length of waste- weir required,
and approximate depth of water on the crest of the given
length :
TA BLE No. 81.
LENGTHS AND DISCHARGES OF WASTE-WEIRS.
Area of Water-
shed.
Required length
of overfall tor
given watershed.
Approx. depth of
water on overfall
of given length.
Approx. discharge
per lin. ft. of given
overfall, for given
depth.
Flood volume from
whole area,
Q=*<x>(M)$.
Square miles.
Feet.
Feet.
Cubicfeet.
Cubic feet per sec.
I
2 5
1.89
8 00
2OO
2
3 2
2-35
11.13
356
3
39
2. 5 6
12.82
500
4
44
2. 7 6
14-43
635
6
54
3.01
16.56
890
8
61
3.22
18-54
II 3 I
10
68
3-46
2O.O4
T363
15
83
3-70
23.01
1910
20
95
3-90
25-5 6
2428
2 5
!5
4.14
27.85
2925
30
116
4.28
29-35
3404
40
133
4-58
32.53
4326
50
149
4.71
34.95
5208
75
183
5-14
39-92
7304
100
212
5-34
43.78
9282
20O
2 95
6.28
56.08
16542
300
360
6.65
64.42
23190
40O
40O
7.36
73-70
29480
500
440
7.81
80.70
35500
6OO
480
7.98
86.08
41320
800
530
8.86
99.09
52520
IOOO
580
9-32
109.07
63260
The maximum flood, and consequently the required
length of overfall, or depth upon it, varies with the maxi-
mum periodic rainfall ; the inclination and porosity of
382
WASTE -WEIRS.
soils; the sum of pondage surfaces; and to some extent
with temperatures.
The above estimated flood volumes refer to ordinary
American Atlantic slopes, and forty to fifty inch mean an-
nual rainfalls, and to streams with comparatively small
pondage areas.
The above tabled lengths of overfalls or range of depths
upon crests of waste-weirs, are to be increased for flashy
streams, and may be reduced for steady streams with large
or many small ponds.
The increase of pressure upon all portions of the em-
bankment and foundation, and upon the waste-weir, by the
flood rise, must be fully anticipated in the original design
of the structure.
387. Forms of Wastfe-Weirs. Fig. 72 illustrates a
waste-weir placed in the centre of length of an earthwork
embankment, retaining a storage lake of twenty-four hun-
dred acres, and the drainage of forty square miles of water-
shed.
FIG. 72.
n
The down-stream face of the weir is constructed in a
series of steps of decreasing height and increasing projec-
tion, from the crest downward, so that the edges of the steps
nearly touch an inverted parabolic curve.
ISOLATED WEIRS. 383
The apron receiving the fall of waste water from the
crest of the weir is of rubble masonry, and contains two
upright courses intended to check any scour from the
"undertoe" during freshets, and also to lock the founda-
tion courses that receive the heaviest shocks of the falling
water.
The projection of the steps was arranged to break up
the force of the falling water as much as possible.
The fall from crest to apron is twenty-five feet, and the
flood depth upon the weir twenty inches ; yet the force of
the falling water is so thoroughly destroyed that it has not
been sufficient to remove, in three years service, the coarser
stones of some gravel carted upon the apron during con-
struction of the upper courses of the weir.
There is a 3 by 5 feet waste-sluice through the weir at
one end, discharging upon the apron. In front of the sluice
the apron consists of two eighteen-inch courses of jointed
granite upon a rubble foundation, doweled and clamped
together in a thorough manner.
A carriage-bridge spans the weir, and rests upon the
wing walls and three intermediate piers built upon the weir.
388. Isolated Weirs. Where the topography of the
valley admits of the waste- weir being separated from the
embankment, it should be so placed at a distance, and it
is often conveniently made to discharge into a side valley
where the flowage nearly, or quite, reaches a depression in
the dividing ridge.
But it is not always admissible to so divert the water, as
riparian rights may be affected, or flood damages be created
on the side stream.
When possible, it is advisable to locate the waste-weir
upon a ledge at one end of the embankment, so that the
fall from the crest will not exceed three or four feet.
384
WASTE -WEIRS.
There should be a fall of at least three feet from the crest,
as in such case a less length of weir will be required than if
it slopes gently away as a channel.
FIG. 73
TIMBER CRIB-WEIR.
389. Timber Weirs. In those localities where sound
and durable building-stones are scarce, and timber is plenty
and cheap, the waste- weir may be substantially constructed
of timber in crib form. Fig. 73 represents such a weir
placed upon a gravel foundation. The fall is twenty feet,
and the face of the weir is divided into three benches so as
to neutralize the force of the fell that in freshets, if vertical,
would tend to excavate a hole in the gravel in front of the
dam at least two-thirds as deep below the lower water sur-
face as the height of the fall.
The timbers are faced upon two sides to twelve inches
thickness and entirely divested of bark. The bed-sills are
TIMBER WEIRS. 385
sunk in trenches in the firm earth, and two rows of jointed
sheet-piling are sunk, as shown, to a depth that will prevent
the possibility of water working under them. Upon the
bed-sills longitudinal timbers are laid five feet apart, then
cross timbers as shown, and so alternately to the top. As
each tier is put upon another it is thoroughly fastened to
the lower tier by trenails or f -inch round iron bolts. The
bolts should pass entirely through two timbers depth and
one-half the depth of the next tier, requiring for twelve-inch
timbers 30-inch bolts.
As each tier is laid it should be filled with stone ballast
and sufficient coarse and fine gravel puddled in to make the
work solid, leaving no interstices by the side of or under
timbers. The gravel should be rammed under the timbers
so as to give them all a solid bearing.
A tier of plank is placed under each bench capping, and
a tier of close-laid timbers is placed under the crest capping.
The bench and crest cappings are of timbers jointed upon
their sides and laid close. The upper and lower faces are
planked tight with jointed plank.
A weir thus solidly and tiglitly constructed will prove
nearly as durable as the best masonry structures. The
capping and face plankings will be the only parts requiring
renewal, and these only at intervals of a number of years
if they are at first of proper thickness.
Similar forms of crib-work have been used with com-
plete success on rock bottoms, on impetuous mountain
streams, where they were subject to the shocks of ice at the
breaking up of winter, and to great runs of logs in the
spring. In such cases the bed-sills are bolted to the rocks.
Similar crib foundations may be used to carry masonry
weirs upon gravel bottoms, but the crib-work should in
such case be placed so low as to be always submerged.
25
386 WASTE-WEIRS.
Fig. 73 was designed for a case where the watershed is
of about one hundred square miles area. Its crest-length is
two hundred feet, and six feet is the estimated maximum
flood-depth upon its crest.
390. Ice-thrust upon Storage Reservoir Weirs.
Those weirs that are located in Northern climates upon
storage ponds, such as are drawn down in summer and do
not rise to the crest-level until past mid-winter, should be
backed with gravel to the level of the backs of their caps,
and the gravel should be substantially paved, as in Fig. 72.
Otherwise the expansion of the thick ice against the verti-
cal backs of the weirs may act with such powerful thrust as
to displace or seriously injure its upper portion.
391. Breadth of Weir- Caps. The cap-stones of weirs
in running streams should incline downward toward the
pond side at least two inches for each foot of breadth, so
that the floating ice and logs will not strike against their
back ends when the water is flowing rapidly.
There is a lack of uniformity, in practice, in breadths of
tops of waste-weirs, and the unsatisfactory working of the
quarry from which the caps are supplied often controls
this dimension so far as to reduce it to an unsubstantial
measure.
The breadth of cap required depends somewhat on the
pond behind the weir. If the pond is relatively broad and
deep, water and whatever floating debris it carries, will
approach the weir with a relatively low velocity. If the
pond is small and the stream torrential, with liability of
great depth upon the weir, then the cap-stones must have
length and weight to resist the force of the current and im-
pact of the floating bodies. Overfalls upon logging streams
rising in the lumber regions, require particularly heavy
caps, and the force of the logs or ice upon the caps will
THICKNESS OF WASTE -WEIRS AND DAMS.
387
usually be greater when the depth upon the weir is from
one and one-half to two feet, than when deeper.
392. Thickness of Waste-Weirs and Dams. If
the back, or pond side of the dam, is vertical, and the thick-
ness at cap constant, then the thicknesses at given depths
may be found, for plotting a trial section, by the following
equation :
Let b be the assumed top breadth, and t the thickness
at any given depth, d, then
t = b + .ld*. (7)
For illustration, let the assumed cap breadth, or length
of cap stones, for a long straight dam, be eight feet, then
for the following given depths, the ordinates or thicknesses
are as follows :
TABLE No. 82.
THICKNESS FOR MASONRY WEIRS AND DAMS.
DEPTHS FROM TOP
OF CAP.
THICKNESS.
Feet.
(6.)
(.*!.)
Feet.
O
8 +
o.o ==
8.00
4
8 +
.8 =
8.80
6
8 +
1.47 =
9-47
8
8 +
2.26 =
10.26
10
8 +
3.16 =
ii. 16
12
8 +
4. 16 =
12. l6
15
x 8 +
5-81 =
13.81
20
8 +
8.94 =
16.94
25
8 +
12.50 =
20.50
30
8 +
16.43 =
24.43
35
8 +
20.71 =
28.71
40
8 +
25-30 =
33.30
45
8 +
30.19 =
38 19
50
8 +
35-36 =
43.36
If the face curve is resolved into steps, as is advisable
over gravel bottoms or tertiary rock, then the masonry of
388 WASTE-WEIRS.
the steps must be very heavy and substantial, in the high
dams, to withstand for a long term of years the shock of the
falling water.
393. Force of the Overflowing Water. It is of
the utmost importance that the water passing over the lip
of a high dam shall reach the bed of the stream below the
dam with the least possible shock to the foundation, even
though it is of a tolerably hard rock, and especially if the
apron be of concrete or crib- work.
The "life" of numerous upright -face dams has been
materially shortened by the tremor due to the flood falls
upon their foundations.
In the case of an overfall twenty-five feet high, with six
feet depth of water above the crest, for instance, there is a
force of nearly 80,000 pounds per second pounding upon
each lineal foot of its apron, tending to shake the structure
into granular disintegration, and making the earth tremble
under the shock.
394, Heights of Waves. Stevenson gives, in his
treatise on Harbors, the following formula for computing
the height of waves coming from a given exposure, or
" fetch" of clear deep water :
H = 1.6 *SD + (2.5 - tfU), (8)
in which His, the height of waves in feet, and D is the length
of exposure or fetch in miles.
The numerical values of height of wave, according to
this formula, for given exposures, are as follows :
TABLE No. 83.
HEIGHTS OF RESERVOIR AND LAKE WAVES.
Exposure in miles . . .
25
.50
75
i
T5
g
3
5
10.
Height of wave, in feet..
2-543
2.756
2.868
3
3-031
3.332
3.782
4.437
5.466
HEIGHTS OF WAVES. 389
When waves meet a paved slope their vertical longi-
tudinal section is suddenly reduced and their velocity en-
hanced in inverse proportion. They will therefore rise up
the slope to a vertical height much greater than the height
of the approaching wave, which height will depend on both
the initial velocity of the wave and the suddenness with
which its sectional area is reduced.
CHAPTER XIX.
PARTITIONS, AND RETAINING WALLS.
395. Design. The hydraulic engineer finds necessary-
exercise for his skill on every hand to adapt a variety of
constructions in masonry to their several ends, in methods
at once substantial and economical.
Designs are required for reservoir partitions and gate
chambers that are to sustain pressures of water upon both
sides, and either side alone ; revetments for reservoirs,
canals, and lake and river fronts that are to sustain pres-
sures of water and earth upon opposite sides, and earth
alone upon one side; coal-shed walls that are to sustain
the pressure of coal, whose horizontal thrust nearly equals
that of a liquid of equal specific gravity ; conduit and filter
gallery walls, that are to sustain pressures of earth and
water and thrusts of loaded arches ; basement walls and
bridge abutments that are to sustain thrusts of earth and
carry weight ; wing walls of triangular elevations and vary-
ing heights, that are to sustain varying thrusts ; and waste-
weirs, that are to sustain pressures of water higher than
their summits and moving with velocity.
Rule of thumb practice in such structures has led to
many failures, when the amounts and directions of thrusts
were not understood ; and such failures have, on the other
hand, led to the piling up of superfluous quantities of
masonry, often in those parts of section where it did not
increase the stability of position, but did endanger the
stability of the foundations.
THEORY OF WATER PRESSURE. 391
*
Good design only, unites economy with stability in
masonry subjected to lateral thrusts.
396. Theory of Water Pressure upon a Vertical
Surface. The theory of pressure of water upon a plane
surface, and of the stability of a vertical rectangular retain-
ing wall, is quite simple, and is easily exemplified by
graphic illustration, and by simple algebraic equations.
Let BD, Fig. 74, be a vertical plane, receiving the
pressure of water.
The pressure, p, at any depth is proportional to that
depth into the density of the fluid.
Let w l be the weight of one cubic foot of waters
62.5 Ibs. ; then the pressure upon any square foot of the
vertical plane, whose depth of centre of gravity is represent-
ed by d, is p dwi.
Let the depth of the water B 2 D be 12 feet = h. Plot in
horizontal lines from B 2 D, at several given depths, the
magnitudes of the pressures at those depths = dw, as at ssi ;
then the extremities of those lines will lie in a straight line
passing through B, and cutting the horizontal line CDf, in
/, Df being equal to the magnitude of the pressure at D.
The total pressure upon the plane B 2 D, and its horizon-
tal effects at all depths are graphically represented by the
area and ordinates of the figure BJD.
In theoretical statics, the effect of a pressure upon a
solid body is treated as a force acting through the centre of
gravity of the body.
Consider the pressure of BfD to be gathered into its
resultant, passing through its centre of gravity,* g. The
* To find the centre of gravity of a triangle BfD, draw a broken line from
D, bisecting the opposite side in *,, and from/, bisecting the opposite side in
8 : the centre of gravity will then lie in the intersection of those lines. Or,
draw a line from any angle B 2 , bisecting the opposite side, and the centre of
392 PARTITIONS, AND RETAINING WALLS.
FIG. 74
horizontal resultant through g will meet B 2 D in N, at two-
thirds the depth 2 D.
Let DCB be a section of wall one foot long. Let BJ)
gravity will lie in this line, at one-third the height from the side bisected.
The centre of gravity is at two-thirds the vertical depth B 2 D = f A from B z .
WATER PRESSURE UPON AN INCLINED SURFACE. 393
= n = 12 ft. The centre of gravity of the submerged wall
surface BzD is at one-half its height, = - The total
<e
pressure of water p upon the wall-surface B 2 D equals the
product of the surface area, B 2 D = A^ into the weight of
one cubic foot of water, w^ into one-half the height, =
j> = 4n-} = k- (i)
19
= (12 x 1) x 62.5 x ~
= 4500 pounds = 2.25 tons.
Draw this total pressure to scale, in the resultant gN,
meeting B 2 D in N.
The effect of a pressure, when applied to a solid body,
is the same at whatever point in the line of its direction it
is applied ; so we may consider gN as acting upon the wall
either at N or at x, in the vertical through the centre of
gravity of the wall.
The force tending to push the wall along horizontally
isgN.
397. Water Pressure upon an Inclined Surface.
The maximum resultant of pressure of water upon the
inclined plane JO has a direction perpendicular to the
plane, and meets the plane in P l9 at two-thirds the vertical
depth of the water.
The entire weight of the triangular body of water CiJ is
supported by the masonry surface JO. Its vertical pressure
resultant upon JC passes through its centre of gravity in g^
and meets JC in P 1? at two-thirds the vertical depth iC or
JC. Its horizontal pressure resultant also meets JC in PI.
Let #q be the symbol of its horizontal resultant.
" e " " " vertical "
" y " " " maximum "
394 PARTITIONS, AND RETAINING WALLS.
The horizontal effect of the pressure, a? l5 may be com-
puted as acting upon the plane of its vertical projection or
trace, iC, and will equal,
= 2.25 tons, when 7i = 12 ft.
Draw x l 2.25 tons to scale in XiP^ . Let fall a perpen-
dicular upon JC, meeting it in P l ; then will the angle
equal the angle JCi = 0, and yP t will equal *
( 7i 2 )
y = <zv sec = j w i -Q- r sec angle x^P^y (3)
= 2.515 tons ;
and ePi will equal
i ft?)
e x^ tan = \ w l \ - tan angle XiP^ (4)
( * )
= 1.125 tons.
The horizontal force tends to displace the wall horizon-
tally. The vertical downward force tends to hold the wall
in place, by friction due to its equivalent weight.
If water penetrates under the base of the wall, it -will
there exert an upward pressure upon the base, opposed to
the downward pressure upon JC, and to the weight of the
wall, with maximum theoretical effect equal to area CD
into depth of its centre of gravity into the weight of one
cubical foot of water.
Let ^be the symbol of the maximum upward pressure,
and let GI be the ratio of the effective upward pressure in
any case to the maximum.
Draw ctfi in the vertical line through the centre of gravity
of the masonry, in Gzi.
When computing the resultant weight of the masonry,
* Vide trigonometrical diagram and table in the Appendix.
FRICTIONAL STABILITY
opposed to the horizontal water pressure, deduct from'th^
weight of wall the excess of upward, c^, over downward
pressure, e, G& e.
398. Frictional Stability of Masonry. The weight,
W, in pounds, of the wall (of one foot length) equals its
sectional area DCB = A, in square feet, into the weight of
one cubical foot w of its material :
W = Aw. (5)
The downward resultant of weight is
W r = (Aw) + e- (c&). (6)
The upward pressure of the water upon the base will rare-
ly exceed .50 per cent, of the theoretical maximum, even
though the wall is founded upon a coarse porous gravel, or
upon rip-rap, without a like upward relief of backfilling.
The frictional stability, S, of the wall, equals its result-
ant weight into its coefficient, c, of friction,
8 = \W+e-(c^\ x c. (7)
Foundations of masonry upon earth are usually placed
in a trench, by which means the frictional stability upon
the foundation is aided by the resistance of the earth side
of the trench, and the coefficient thus made at least equal to
unity. In such case the measure of resistance to horizontal
displacement is the friction of some horizontal or inclined
joint.
The value of the adhesion of the mortar in bed-joints is
usually neglected in computations of horizontal stability,
and sufficient frictional stability should in all cases be given
by weight, so that the resistance of the mortar may be
neglected in the theoretical investigation.
If, however, the mortar is worthless, or its adhesion is
396
PARTITIONS AND RETAINING WALLS.
destroyed by frost or careless workmanship, or otherwise,
then the mortar becomes equivalent to a layer of sand as a
lubricant, and the coefficient of friction may thus be reduced
very low.
399. Coefficients of Masonry Friction. The fol-
lowing table of coefficients of masonry frictions will be found
useful.* They are selected from several authorities, and
have been generally accepted as mean values.
TAB L E No. 84.
COEFFICIENTS OF MASONRY FRICTIONS (DRY).
COEF.
ANGLE
OF
REPOSE.
Point dressed granite
(medium) on dry clay . .
27 O
.3-3
.58
^O
" ' like granite . . .
7O
qe
" ' common brickwork ......
6-J
32 2
Fine cut granite
" ' smooth concrete
.62
"3,0
Very fine cut granite
.61
( U
' pressed Beton Coignet. . .
(medium) ' like limestone
.61
18
30.30
2O 48
11
" * brickwork
60
31
Beton blocks
(pressed) ' like Beton blocks
66
3 -3. 1C
Polished marble
.44
2-3.41;
1C ((
' fine cut granite . . .
6l
3O.3O
" common bricks
64
" dressed hard limestone.. .
.60
31
When S and x^ are equal to each other, the wall is just
upon the point of motion, and x l must be increased ; that
is, more weight must be given to the wall to ensure frictional
stability.
Let the water be withdrawn from the side B D, Fig. 74,
and let the upward pressure attain to one-half the maxi-
mum, and the coefficient be that of a horizontal bed-joint
upon a concrete foundation, assumed to be .62, then S =
* Vide 353, pp. 344, 345.
LEVERAGE STABILITY OF MASONRY. 397
(w + e .50^) x c = 2.79 tons, and x l 2.25 tons, and the
wall has a \ small margin of frictional stability.
The weight of the wall should be increased until it is
able to resist a horizontal thrust of at least 1.5^, or until
S= 1.5#i, when the equation of frictional stability becomes
S = (w 4- e C&) x c = 1.5#i, (8)
in which
w is the weight of masonry above any given plane.
e " vertical downward water pressure resultant.
2\ " maximum upward water pressure resultant.
d " ratio of effective upward water pressure to the
maximum.
c " coefficient of friction of the given section upon
its bed.
fy " horizontal water pressure resultant.
8 " symbol of frictional stability.
4OO. Pressure Leverage of Water. Since the hori-
zontal resultant of the water-pressure has its point of appli-
cation above the level of Z>, in N, its moment of pressure
leverage, L, has a magnitude equal to DN^ or Kx = \7i,
into the horizontal resultant.
(9)
4O1. Leverage Stability of Masonry. The moment
of pressure-leverage of the water tends to overturn the wall
about its toe, D or C, Fig. 74, opposite to the side receiving
the pressure alone, or the maximum pressure.
Let the weight of DCB, per cubical foot, be assumed
140 pounds, an approximate weight for a mortared rubble
wall of gneiss, or mica-slate ; then the total weight above
the bed-joint CD, is 140A = 5.25 tons, which we may con-
398 PARTITIONS, AND RETAINING WALLS.
sider as acting vertically downward through (7, the centre
of gravity of DOR
Plot to scale this vertical resultant of weight in xe 2 =
5.25 tons (neglecting for the present the upward and down-
ward pressures of the water), and the horizontal resultant
of water pressure in xN z = 2.25 tons, and complete the
parallelogram xJV 2 Me 2 ; then the diagonal xM, is in mag-
nitude and direction the final resultant of the two forces.
The resultant arising from the horizontal pressure on
JC, and weight of the masonry, is in magnitude and direc-
tion xO.
If the directions of xM and xO cut the base DC, then the
wall has, theoretically, leverage stability, but if the direc-
tions of these diagonals are outside of DC, then the wall
lacks leverage stability and will be overturned.
For safety, the direction of xM should cut the base at a
distance from K not exceeding one-half KC, and the direc-
tion of xO cut the base at a distance from K not exceeding
one-half KD.
4O2. Moment of Weight Leverage of Masonry.
Since the vertical resultant of weight of masonry takes its
direction through 6r, and cuts DC at a distance from (7,
the point or fulcrum over or around which the weight must
revolve, the moment of weight leverage of the wall has a
magnitude, when resisting revolution to the right, equal to
the distance KD into the vertical weight resultant ; and
when resisting revolution to the left, equal to the distance
KC into the vertical weight resultant.
Let the symbol of distance of K from the fulcrum, on
either side, be d, and its value be computed or taken by
scale, at will ; and let the symbol of moment of weight
leverage be JS 9 then
M= Awd. (10)
MOMENTS OF SECTIONS. 399
For double stability, or a coefficient of safety equal to 2,
A.wd
must, at least, be equal to A^ , or
D
4O3. Thickness of a Vertical Rectangular Wall
for Water Pressure.
Let 7i be the height of the wall and of the water.
" w " weight of a cubic foot of the masonry.
" M! " " " " " water.
" z " required thickness of the wall.
Then h x z x - t '- x w = leverage moment of weight of
T, T -, Ti 7i ,
wall, = s - ; and 7ix^xWiX- = leverage moment of
^ o
pressure of water = for double effect, ^
The equation for a vertical rectangular wall, Fig. 75,
that is to sustain quiet water level with its top, and that
just balances a double effect of the water is :
from which we deduce the equation of thickness,
3 7iw
4O4. Moments of Rectangular and Trapezoidal
Sections. Let DCEB, Fig. 75, be a vertical rectangular
wall of masonry, of sectional area exactly equal to the tri-
angular section of wall in Fig. 74, viz., 15 feet in height and
6 feet in breadth, and weighing, also, 140 pounds per
cubical foot. Let the depth of water which it is to sustain
upon either side, at will, be 12 feet.
400 PARTITIONS, AND RETAINING WALLS.
The horizontal resultant of water pressure is
w -|- = 2.25 tons,
and the vertical resultant of weight of wall into the coef-
ficient (.62) of friction is
[ w (.25s,)] x c = 2.96 tons.
This leaves a small margin of Motional stability.
The vertical weight resultant is
(Aw) - (.26s,) = 4.78 tons,
or, if there is no upward pressure,
Aw = 5.25 tons.
Plot to scale the horizontal and vertical resultants from
their intersection in x, and complete the parallelogram
xPMe 2 ; then will the diagonal
xM be the final resultant of the
two forces.
The direction of the diagonal
now cuts the base very near
the toe (7, and the given wall
with vertical rectangular sec-
tion lacks the usual coefficient
of leverage stability, though it
was found to have ample lever-
age stability in the equal tri-
angular section.
If we now give to this same
wall a slight batter upon each
side, as indicated by the dotted lines, its final resultant,
arising from the horizontal water pressure, will lie in x0 2y
FIG. 75.
MOMENTS OF SECTIONS.
401
and its direction will cut the base farther from the toe, and
the leverage stability of the wall will be increased.
Let DCEB, Fig. 76, be a section of a partition wall in a
reservoir, subject to a pressure of water whose surface coin-
cides with its top, on either side, at will. Let the height be
12 feet, and the thickness at top 4 feet.
The side EC is vertical and the side BD has a batter of
three inches to the foot.
The maximum pressure resultants meet the respective
sides in P and PI, in directions perpendicular to their sides,
and at depths equal to two-thirds the vertical depth EC.
26
402 PARTITIONS, AND RETAINING WALLS.
Plot to scale the horizontal pressure resultants in their
respective directions through P and P 15 and the weight
resultant in its vertical direction through the centre of grav-
ity,* (7, and complete the parallelograms. The diagonals
then give the directions and magnitudes of the maximum
leverage effects.
The diagonal xO cuts the base CD at a distance from K
less than half KD ; the diagonal xM cuts the base at a
distance from ./f more than half the distance KG.
The leverage stability of the wall is therefore satisfactory
to resist pressure from the left, but has not the desired
factor of safety to resist pressure from the right.
405. Graphical Method of Finding the Leverage
Resistance. The ratio of leverage resistance may be
obtained from the sketch by scale, as follows : Extend the
base, JO, of the parallelogram upon the right, indefinitely ;
draw a broken line from x through Z>, cutting J0r l in r x ;
then the ratio of leverage stability against the waiter pressure
upon EC is to unity as Jr^ is to JO.
Also extend K0 2 indefinitely ; draw a broken line from
y 2 through the toe C, cutting K0 2 r 2 in r 2 ; then the ratio of
leverage stability against the maximum water pressure
upon BD is to unity as Kr 2 is to K0 2 .
The ratio of r 2 2 to r 2 K exceeds .5, but the ratio of r M
to rJ is less than .5 ; therefore the effect of the horizontal
pressure xP to overturn the wall exceeds the effect of the
maximum pressure yP to overturn the wall.
406. Granular Stability. We have found the maxi-
* The centre of gravity of a rectangular symmetrical plane, Fig. 75, lies in
the intersection of its diagonals.
The centre of gravity of a trapezoidal plane DCEB, Fig. 76, may be found
graphically, thus : Prolong CD to t, and make Ci EB. Also prolong EB to
&, and make Bk = CD. Join ki. Bisect CD and EB, in d and b, and join db.
The centre of gravity G lies in the intersection of the lines db and ik.
COMPUTED PRESSURE IN MASONRY.
403
mum water pressure resultant upon the inclined side, JO
{Fig. 74), to Ibe yP l = y 2.515 tons ; its direction to be
perpendicular to JC, and its point of application to Ibe at
two-thirds the vertical depth JO, or iC.
Plot this inclined resultant, in the prolongation of the
line yP^ from a vertical through G, in y 2 P 2 = 2.515 tons ;
and plot the vertical weight resultant of the wall from the
intersection y in y 2 K 2 = 5.25 tons ; complete the parallelo-
gram y 2 P 2 2 K 2 , then the diagonal y 2 2 is in magnitude
and direction the maximum pressure resultant of the two
forces tending to crush the granular structure of the wall
and its foundation.
The following table of data relating to computed pres-
sures in masonries of existing structures, is condensed and
tabulated from memoranda* given by Stoney and from
other sources :
TABLE No. 85.
COMPUTED PRESSURES IN MASONRY.
KIND OF MASONRY.
LOCATION.
MATERIAL.
PRESSURE
IN LBS. PER
SQ. FOOT.
Piers, All Saints Church . .
Angers
Forneaux stone
86 016
Pillar, Chapter House
Pillars, dome St. Paul's Church
" St. Peter's Church
Aqueduct, pier
London.
Rome.
Marseilles.
Portland limestone.
Calcareous tufa.
Stone
40,096
39424
33,376
Arch bricks, bridge, Charing )
Cross . I
London.
London paviors.
26,880
Pier bricks, Suspension Bridge.
Bridge pier
Clifton.
Saltash
Staffordshire blue bricks.
Granite
22,400
21 280
Arch concrete, bridge, Char-)
ing Cross. y
London.
Port. Cement, i ; gravel, 7.
17,920
Arch bricks, viaduct
Birmingham
Red bricks
15 68O
Brick chimney
Glasgow
Rrirt
2O 1 60
Bricks, estimated pressure on )
leeward side in a gale f
33,600
Long span bridges have sometimes pressures at their springing exceeding
125,000 pounds per square foot.
* The Theory of Strains in Girders and Similar Structures. New York, 1873.
404
PARTITIONS, AND RETAINING WALLS.
Experimental data of the ultimate strength of masonry
in large masses has not been obtained in a sufficient number
of instances to determine a limit generally applicable for
safe practice.
Failure first shows itself by the spalting off of the angles
or edges of the stones, or by the breaking across of stones
subjected to a transverse strain, and next by the crushing
of the mortar.
4O7. Limiting Pressures. From experiments of sev-
eral engineers upon the ultimate crushing strength of small
cubes of dressed stones (1 inch and 1J inch square), and
from computations of pressures upon the lower courses of
tall stacks and spires, the data of the following table has
been prepared :
TABLE No. 86.
APPROXIMATE LIMITING PPESSURES UPON MASONRY.
Av. weight laid
in mortar, per
cubic foot.
Approx. ulti-
mate resistance
of dry, dressed,
one-inch cubes.
Est. safe static
pressure per
sq. ft. on thick
blocks, unlaid.
Est. safe pres-
sure per sq. ft.
in coursed rub-
ble masonry, at
2 ft. from edge,
when laid in
strong mortar.
Limestone
152 Ibs.
4,000 Ibs.
115,000 Ibs.
50,000 Ibs.
1*2 "
6,000 "
I7O,OOO "
<O OOO "
Granite
i"U "
10,000 "
280 ooo ft
6o,OOO "
Brick
120 "
2,^00 "
72,000 "
3^,000 "
McMaster mentions* that in Spain, and in some instances
in France, the limit of pressure in stone masonry has been
taken in practice as high as 14 kilogrammes per square
centimeter (= 28678 Ibs. per square foot) ; but in the ma-
jority of cases the limit is taken at from 6 kilometers to 8.50
kilometers per square centimeter.
* Profiles of High Masonry Dams. New York, 1876.
WALLS FOR QUIET WATER. 405
The ultimate granular resistance of the masonry is
largely dependent upon the strength of the mortar, and
upon the skill applied to the dressing and laying of the
stones. *
It is not advisable to allow either a direct or resultant
pressure exceeding 140 pounds per square inch within one
foot of the face of rubble masonry, or 225 pounds per square
inch in the heart of the work ; and these limits should be
approached only when both materials and workmanship
are of a superior class.
The resultant of the horizontal pressure is seen to cut
the base-line nearer to the toe, or fulcrum, over which the
resultant tends to revolve the wall, than does the resultant
of maximum pressure ; the crushing strain is therefore
greater near the face of the masonry from the horizontal
than the maximum resultant.
Care must be exercised, in high structures, that the safe
pressure limit near the edge is not exceeded, lest the edge
spalt off, and the fulcrum be changed to a position nearer
the centre of the wall, and the leverage stability thus re-
duced.
4O8. Table of Walls for Quiet Water The fol-
lowing table gives dimensions for walls to sustain quiet
water on either side, and also on the back only, with a
limiting face batter of two inches per foot rise :
406
PARTITIONS, AND RETAINING WALLS.
TABLE No. 87.
APPROXIMATE DIMENSIONS OF WALLS TO RETAIN WATER.
For granite rubble walls, in mortar, of specific gravity 2.25, ovyiveight, 140 pounds
per cubic foot ; to retain quiet water level with the top of the wall.
VERTICAL
RECTANGULAR
WALL.
PRESSURE ON EITHER SIDE.
SYMMETRICAL PARTITIONS.
PRESSURE ON BACK ONLY.
Height of
water and
wall, in feet.
Breadth in
Top
breadth in
Bottom
breadth in
Top
breadth in
Face batter
in inches
Bottom
breadth in
feet.
feet.
feet.
feet.
per ft. rise.
feet.
4
3-5
3-5
3-5
3-5
3-5
5
3-5
3-5
3-5
3-5
3-5
6
3-5
3-5
3-5
3-5
O
3-5
7
4.0
3-5
4.25
3-5
^
4.0
8
4-5
3-5
5-25
3-5
*i
5-o
9
S-o
3-5
6.00
3-5
2
5-75
10
5-5
3-5
6.50
3-5
2
6.75
ii
6.0
3-5
7-25
3-5
2
7-25
12
6-75
4.0
7-75
4.0
2
7-83
13
7-25
4.0
8.50
4.0
2
8.67
14
7-75
4.0
9-25
4.0
2
9-5o
15
8.25
4.0
10.00
4.0
2
10.50
16
9.00
4.0
10.75
4.0
2
11.50
17
9-So
4.0
11.67
4.0
2
12. OO
18
10.00
5-o
11.75
5-0
2
I2.5O
19
10.50
5-0
12.67
5-0
2
13.67
20
II.OO
5-0
13-33
5-
2
14.50
21
11.50
5-o
14.00
5-o
2
15.25
22
12.25
5-o
14.83
5-0
2
16.25
2 3
12.75
S-o
15-75
5-o
2
I7.25
24
13-25
5-
16.50
5-o
2
18.25
The top thickness is to "be increased if the top of the
wall is exposed to ice-thrust ; and the whole thickness
must be increased if water is to flow over the crest, accord-
ing to the depth of the crest, and its initial velocity of ap-
proach.
Unless partition- walls rest on solid rock, or on impervi-
ous strata of earth, as they should, percolation under the
ECONOMIC PROFILES. 407
wall must be prevented by a concrete or puddle stop- wall,
or by sheet- piling ; or the previous strata must be effectu-
ally sealed over.
4O9. Economic Profiles. It is evident, from the
above investigations, that the profile has an important influ-
ence upon the leverage stability of a wall of given weight
of material, and therefore, for a given stability, upon econ-
omy of material.
The leverage stability against pressures of water upon
the vertical sides of triangular or trapezoidal sections of
masonry is greater than the leverage resistances to pressures
upon their inclined sides, as is graphically illustrated in the
above sketches ; hence there is an advantage in giving all
the batter to the side opposite to the pressure.
The vertical rectangular sections are least economic, and
the triangular sections most economic of material.
When some given thickness is assumed for the top of a
retaining wall, to give it stability against frost, or displace-
ment from any cause, then theory makes both sides vertical
from the top downward until the limiting ratio of leverage
stability is reached, and then gives to the side opposite to
the pressure a parabolic concave curve.
It may be necessary to widen the base of high walls
upon both sides beyond the breadth required for leverage
stability, to distribute the weight sufficiently upon a weak
foundation. Practical considerations, in opposition to
theory, tend to rectangular vertical sections.
The engineer who is familiar with both theory and prac-
tice, adjusts the profile for each given case, so as to attain
the requisite frictional, leverage, and granular stabilities, in
the most substantial and economical manner, having due
regard to the quality and cost of materials, and the skill
and cost of the required labor.
408 PARTITIONS, AND RETAINING WALLS.
41O. Theory of Earth Pressures. Earth filling of
the different varieties behind retaining walls, is met in all
conditions of cohesiveness between that of a fluid and that
of a solid.
The same filling, in place, is subject to constant changes
in its degree of cohesion, as its moisture is increased or
diminished, or as its pressure and condensation is increased,
or as it is subjected to the tremulous action of traffic over it.
The theory of earth pressure, therefore, leads to less certain
results than does the theory of water pressure.
We have seen ( 353) that different earths have dif-
ferent natural angles of repose when exposed to atmos-
pheric influences, and they also tend to assume their natural
frictional angle when deposited in a bank. If we make a
broad fill with earth, behind a vertical wall and then sud-
denly remove the wall, a portion of the earth, of triangular
section, will at once fall, and the slope will assume its natu-
ral frictional angle. If we make such a fill even with the
top of a vertical rectangular wall, whose thickness is only
equal to one-fourth of its height, then the earth will over-
turn the wall. This is evidence that a portion of the earth
produces a lateral pressure. If the earth is fully saturated
with water, its lateral pressure may be nearly like that of a
fluid of equal specific gravity. If the earth is compact like
a solid, its thrust may be nearly like that of a rigid wedge.
Let LDBJ, Fig. 77, be an earth-fill behind a vertical
retaining wall DB. Let LDVi be the natural frictional
angle = </>, of that earth filling. It is evident that the por-
tion of earth LD 7i will produce no thrust upon the ma-
sonry, because it would remain at rest if the wall was
removed. Suppose all the filling above D Vi to be divided
into an infinite number of laminae whose planes of cleavage
all meet at one edge in D, and radiate from D. Then the
THEORY OF EARTH PRESSURES.
409
thin lamina adjoining D V l will exert the minimum thrust
against the masonry and the maximum weight-pressure
upon D Vi. The thin lamina adjoining BD will exert the
FIG. 77.
maximum wedge-thrust against -the masonry and minimum
weight-pressure upon D Vi.
Suppose the mass ViDBJio be divided into two parts
410 PARTITIONS, AND RETAINING WALLS.
by the plane DJ, which bisects the angle BD V v . Let the
wedge BDJ, then be increased in dimensions by revolving
the side JD to the right, around D ; then its weight, as a
solid, will rest more upon FjZ>, and its lateral thrust will
not be increased. Let the wedge BDJ, then be reduced in
dimensions by revolving the side JD to the left ; then its
total weight and its ability to produce lateral thrust upon
the masonry will be reduced. We may therefore assume
that that portion of the mass ViDBJ, included in the upper
wedge formed by bisecting the angle V^DB will be the
maximum portion of the earth that will first fall if the wall
is suddenly removed, and that the thrust of the wedge BDJ,
if considered alone, and as devoid of friction upon the plane
7Z>, will give a safe theoretical maximum effect upon the
masonry of the whole mass V^DBJ.
The practical value of such assumption has been ably
demonstrated by Coloumb, Prony, Canon Moseley, Ean-
kine, Neville, and others.
411. Equation of Weight of Earth-Wedge. The
weight W 2 of the wedge of earth (considered as one foot
in length), in pounds, equals its surface area DBJ, in square
feet, AS, into the weight of one cubical foot of the mate-
rial = w 2 .
W 2 = A 2 w 2 . (12)
Let the symbol of the frictional angle LDV of the
earth filling be </> ; then will the angle
Let the height BD equal 12 feet, = h ; then the area of
DBJ will equal DB into one-half BJ
A 2 = 7i x \ tan 6 = ^ cotan (<j> + 0). (13)
PRESSURE OF EARTH-WEDGE. 411
Equation of Pressure of Earth-Wedge.
Assume the weight of the wedge DBJ= A 2 w 2 = W 2 to be
gathered into its vertical resultant passing through its cen-
tre of gravity, g ; then the thrust P of the wedge equals
its weight into its horizontal breadth BJ, divided by its
vertical height BD =
P = A 2 w 2 tan = W 2 cotan (<f> + 0). (14)
Draw the vertical resultant W 2 to scale in eP, meeting
the inclined plane JD, in P.
The thrust effect of W* will have its maximum action in
a line parallel to the line D Vi , since the mass V^DBJ, as
a whole, tends to move down the plane ViD.
The theoretical reaction from the wall, necessary to sus-
tain W 2 , will then be in a direction parallel to D V\ , cutting
the vertical resultant in P. Draw the reaction of the wall
to scale in nP. The reaction of the plane JD is in direc-
tion and magnitude equal to the diagonal Py, of the paral-
lelogram of which W 2 and P form two sides. Draw the
reaction of JD to scale in VP. Then, will the three result-
ants eP> nP y and VP be in equilibrium about the point P.
Let = 30.
Assume the filling to be of gravel, weighing 125 pounds
per cubic foot, and that after a storm, its drains being
obstructed, its voids are filled with water, increasing the
weight to 140 pounds per cubic foot, = w 2 ; then
7,2
= 12 feet x y feet x .57735 x 140 pounds
= 5,820 pounds = 2.91 tons.
The reaction from the wall necessary to sustain the
weight of the wedge JBD =
412 PARTITIONS, AND RETAINING WALLS.
P = W 2 tan e = ^ cotan 2 (0 + 6) w, (15)
4>
= 2.91 tons x .57735
= 1.68 tons.
The horizontal effect of P =
x = P cos = A 2 w 2 tan 6 cos (16)
= 1.68 tons x .86602 = 1.45 tons.
The thrust of the wedge tending to push away and to
overturn the wall is equal to the reaction from the wall
necessary to sustain the wedge in position. We find its
horizontal effect in this case to be 1.45 tons, and this is the
maximum effect, = #, tending to displace the wall hori-
zontally.
413. Equation of Moment of Pressure Leverage.
The maximum moment of pressure leverage, Z>, tending
to overturn the wall around its toe, equals x into the height,
in feet, above D at which x meets the wall.
When the wall is vertical and the surface of filling hori-
zontal, x always meets BD at one-third Ti from Z>, = ~ ;
therefore the equation of moment of pressure leverage
becomes
L, = x^ = (A 2 w 2 tan e cos 0) | (17)
-10 ff
= 1.45 tons x =^p = 5.80 tons.
o
414. Thickness of a Vertical Rectangular Wall
for Earth Pressure. The moment of weight leverage of
a vertical rectangular wall is 5, in which z is the thick-
tt
ness of the wall.
SURCHARGED EARTH-WEDGE. 413
The double moment of pressure leverage of earth level
with the top of the wall is
h h 3
(h 2 w* tan 2 d cos 0) x = w 2 tan 2 6 cos 0.
o o
When the wall just balances the theoretical double
pressure of the earth level with its top,
= w 2 tan 2 6 cos 0,
o
from which is deduced the equation of thickness for a ver-
tical rectangular wall,
( 2h 3 w 2 tan 2 e cos ) 1 _ ( h 2 w 2 tan 2 6 cos 1 i
B r ~sM^ "f B r "TM~ -j
415. Surcharged Earth-Wedge. When the earth-
fill behind a wall is carried up above the top level BJ of
the wall, and is sloped down against the top angle B, or
upon the top of the wall, the fill DBF is then termed a
surcharged fill.
Its weight W 2 is, as in the case of the level fill, per lineal
foot,
W 2 = A 2 w 2 . (19)
To compute the pressure of the surcharged fill, we may
divide the mass ViDBF into two wedges by a plane DF,
bisecting the angle V V DB^ and take the action of the wedge
FDE as equivalent to the effective action of the whole mass
VDBF.
Let the natural Motional angle of the earth-fill be
= 30.
The area A 2 of the wedge FDB may be computed by
any method of ascertaining the area of a triangular super-
414 PARTITIONS, AND RETAINING WALLS.
fices. If, with a given slope BF, the fill does not rise as
high as F, and its surface level cuts FB and FJ between
the levels of F and B, then its area is ascertained by any
method of ascertaining the superfices of a trapezium.
Let fall upon DF a perpendicular from B, meeting DF
in i ; then the distances Di and IF are equal, each, to the
QO <t\
cosine of the angle BDF = cos. ^?- = cos and the
tO
distance iB is equal to sin 5 ? = sin 6.
&
Let the height DB = 7i = l2 feet.
The area BDF equals the length DF into one-half IB =
A 2 = Ji x 2 cos x Ji \ sin 6 = 7i cos x h sin (20)
= (12 x .866) x (12 x .5) = 62.53 sq. ft.
Let the mean weight of the fill, which is quite sure to be
drained above the level BJ, be assumed 130 pounds per
cubical foot.
416. Pressure of a Surcharged Earth- Wedge.
Suppose the weight to be gathered into its vertical resultant
passing through the centre of gravity g^ of the mass DFB.
This vertical resultant will meet the plane FD in P l at a
level higher than P.
The wedge-thrust P 15 due to the weight W 2 , equals the
weight into the horizontal breadth BJ, divided by the
height DB =
P! = TF 2 tan = A 2 w 2 cotan (< + 0) = (21)
62.53 sq. ft. x 130 Ibs. x .577 = 4690.38 Ibs. = 2.345 tons.
The. maximum pressure-action of the weight upon the
wall is in a direction parallel to ViD, the natural fractional
angle 0, of the filling material. Its horizontal pressure
effect, #1, is therefore :
PRESSURE OF AN INFINITE SURCHARGE. 415
x l = PI x cos = A 2 w 2 tan cos = (22)
2.345 tons x .866 = 2.03 tons.
The maximum horizontal pressure resultant takes its
direction through P l and meets the wall at the altitude of
P,, which is greater than -^.
o
We may here observe that, even though the fill DBF
is of lighter material than the fill DBJ, so that the total
weight of one is exactly equal to the total weight of the
other, the pressure leverage effect from the surcharged fill
will exceed the pressure leverage effect from the level fill,
"because its centre of gravity g 2 will be higher than g, its
vertical resultant W 2 will meet the plane JD in PI at a point
higher than P, and its horizontal resultant x l will meet the
wall at a greater altitude from D than will the resultant x.
Let r h be the symbol of the ratio of *^ at which x l meets
the wall from D ; then if x l meets DB at J^, r h = .3333 ;
and if x { meet DB at &, r h = .5, etc.
417. Moment of a Surcharge Pressure Leverage.
The maximum moment of pressure leverage L^ of a sur-
charged fill, tending to overturn the wall around its toe,
equals x l into the height, in feet = (rji) above Z>, at which
XL meets the wall.
LI = X I x (rji) = A 2 w 2 tan cos </> (r h h) = (23)
2.03 tons x 5.98 = 12.14 tons.
418. Pressure of an Infinite Surcharge. Let
Fig. 78, be the natural slope of the filling material, and
parallel with DI, which makes with DL the natural fric-
tional angle LDI </>. Let BF extend indefinitely.
If IDBF is a perfect solid it will be just upon the point
of motion down the slope ID ; on the other hand, if IDBF
416 PARTITIONS, AND RETAINING WALLS.
is liquid, of specific gravity equal to the specific gravity of
the filling material, it will then exert its maximum pressure
upon the wall-face DB.
Let the filling be considered liquid, resting upon the
equivalent horizontal "base DI, and having the equivalent
horizontal surface BF.
Let fall upon DI a perpendicular from B, meeting DI
iuj ; then will Bj be an equivalent vertical projection, or
trace, of BD. The angle DBj equals the angle LDI = 0.
The distance Bj = Ti^ equals the distance BD (=h) into the
cosine of the angle DBJ = 7i cos <f>.
7i 2
The direct liquid pressure P 1 upon Bj equals -~- w 2 =
, (24)
and the pressure upon BD in the same direction is
and its maximum resultant has a direction parallel with
ID, and meets Bj at one-third the height jB, in m, and BD
at one-third the height DB, in P^
The horizontal pressure effect x l upon the wall BD, is
h 2
Xi = P l cos </> = w 2 -^ cos 3 = (25)
&
19 2
130 Ibs. x - x .6495 = 6079.32 Ibs. = 3.036 tons.
<e
The maximum moment of liquid pressure leverage LI
of the infinite surcharged fill tending to overturn the wall
around its toe, equals x l into one-third the height BD.
L, = x^= (w 2 | cos 3 0) x A = (26)
jo -Ft-
3.036 tons x ^^ = 12.14 tons.
RESISTANCE OF MASONRY REVETMENTS. 417
419. Resistance of Masonry Revetments. The
elements of stability of a revetment that enables it to sus-
tain the thrust of an earth-filling behind it, are identical
with those we have already examined ( 4O1), that enable
it to sustain a pressure of water.
There must be sufficient weight, W, to give it fractional
stability, S, and the profile must be adjusted so that with
the given weight the mass shall have the requisite moment
M of weight leverage, with an ample coefficienty of safety,
to resist the thrust of the earth-filling, at its maximum.
The weight of wall above any given horizontal plane
between B and D (Fig. 77) equals the area of the section
above that plane in square feet, into the weight of a cubical
foot of the materials of the wall ( 398),
= W= Aw.
Thefrictional stability, S, of the wall at the given hori-
zontal plane, that has to resist the horizontal pressure of
the earth filling, equals the weight of masonry above that
plane, plus the vertical downward pressure of any water
that may rest upon its front batter (EC, Fig. 80), less the
vertical resultant of upward pressure beneath the plane or
in the bed-joints, and into the coefficient of friction of the
given section upon its bed ( 398),
S = (W+e - &)..
The moment of weight leverage of the wall that has to
resist the overturning tendency of the earth-thrust, equals
the weight of the masonry above the given plane into the
horizontal distance of the centre of gravity of the masonry
from the toe, or fulcrum, over which the thrust tends to
revolve it ( 4O2),
M Awd.
27
418 PARTITIONS, AND RETAINING WALLS.
In these equations :
TFis the weight above the given plane.
S " " frictional stability of the given section.
M " " moment of weight leverage of the given section.
e " " vertical downward water pressure resultant.
Zi " " vertical upward water pressure resultant.
GI " " ratio of effective vertical upward water pressure.
c " " coefficient of friction of the given section upon
its bed.
The moment of weight leverage of the wall must, for a
safe coefficient of stability, be equal to double the moment
of pressure leverage of the earth fill ; that is, for a level fill
we must at least make
Awd , Ji
^- = A 2 w 2 tan. 6 cos. -,
& d
and for a surcharged fill,
-^- = A 2 w 2 tan. cos. (/*),
40
and a like margin of frictional stability should be secured.
43O. Final Resultants in Revetments. The height
of the wall (Fig. 79) is the same, by scale, as the wall in
Fig. 77, whose reactions to sustain the level and surcharged
fills we have investigated.
The back of the wall (Fig. 79) is vertical, and the hori-
zontal earth-thrusts against it are as before computed viz.,
1.45 tons for the level fill, and 2.03 tons for the surcharged
fill. Draw these horizontal earth-thrust resultants to the
left from a vertical line passing through the centre of gravity
of the masonry, in their respective directions and at their
respective altitudes. Draw in the vertical line the vertical
weight resultant of the masonry in PK; complete the paral-
lelogram PKQ& ; then will the diagonal P0 2 represent, in
TRAPEZOIDAL REVETMENTS.
419
magnitude and direction, the resultant effect of the level fill
LDBJ.
Draw the vertical weight resultant of masonry, also, in
P 3 e. 2 , and complete the parallelogram P^Mx-^ ; then will the
diagonal PJtt represent, in magnitude and direction, the
resultant effect of the surcharged fill LDBF.
The comparative thrust effects of the level and sur-
charged fills upon the masonry are shown by the positions
of the respective final resultants, and the comparative re-
sistances of the wall against each, by the distances from
O, at which their directions cut the plane CD.
FIG. 79.
E
421. Table of Trapezoidal Revetments. The fol-
lowing table of dimensions of walls, to sustain earth, in
which the sections are trapezoidal, and face batters limited
to two inches per foot rise, is adapted for walls to sustain
gradings about pump-houses, reservoir-grounds, etc., and
will give approximate dimensions for plotting trial sections
when it is desired to resolve the profile into other forms.
420
PARTITIONS, AND RETAINING WALLS.
TABLE No. 88.
APPROXIMATE DIMENSIONS OF WALLS TO SUSTAIN EARTH.
For granite rubble walls, in mortar, of specific gravity 2.25, or weight 140 pounds
per cubic foot, to retain earth level with the top of the wall.
Height of wall,
in feet.
Top breadth of
wall, in feet.
Face batter of
wall, in inches
per foot rise.
Base breadth of
wall at lower earth
surface, in feet.
Thickness of a
vertical rectangular
wall, in feet.
4
3-0
O
3.0
3.0
5
3.0
O
3.0
3.0
6
3.0
3.0
3.0
7
3.0
3-25
3-5
8
3-
3.83
4.00
9
3-33
I
4-83
4-25
10
3-33
I
5.00
4-5
ii
3-5
I-
5-25
5.00
12
3-5
2
5.67
5-5
13
3-5
2
6-33
5-83
14
3-5
2
7.0O
6.25
15
3-5
2
7-50
6.75
16
4.0
2
8.00
7-25
17
4.0
2
8.67
7-75
18
5.0
2
9.00
8.25
19
5.0
2
9-5
8-75
20
5-o
2
9.87
9.00
21
5.0
2
10.50
9.50
22
5*
2
ii .00
10.25
23
5 -
2
u-33
10.50
24
5-
2
11.78
10.75
It will rarely be advisable to reduce the top thicknesses
given in the table, with a view only to economizing ma-
terial lest the top courses be too light to withstand the
variety of shocks to which they will be liable, and which
are not recognized in the common formulas.
Several eminent professors who have written upon the
theory of retaining walls, give formulas for determining their
proportions ; but such formulas usually give too small top
breadths, for practical adoption, for low walls, and objec-
tionably great top breadths for high walls.
CURVED FACE BATTER EQUATION. 421
Each class of wall has its own most convenient top
breadth, which remains nearly constant through a large
range of height.
Common uncoursed rubble walls of granite, laid dry,
should be increased from the above dimensions six inches
in the top breadth and thirty -three per cent, in the bottom
breadth. If the level earth-filling behind the wall is to be
loaded, or subject to traflic, the weight and leverage resist-
ance of the wall are to be increased accordingly.
The thrust of the filling material behind a retaining wall,
upon the wall, will be lessened if the filling next the wall
is spread in thin horizontal layers and well settled, instead
of being allowed to slope against it, as it falls at the head
of a dump.
422. Curved Face Batter Equation. When it is
desired to give to the face a curve, the back being perpen-
dicular, and the top breadth constant, the following equa-
tion will assist in determining ordinates at any given depths
for plotting a trial section.
Let 5 be the assumed top breadth, and t the thickness
at any given depth d, then 0?)r
t=b+-ttV&. (27)
For illustration, assume the top breadth not less than
3.5 feet ; then for several given depths, from 0.0 to 30 feet,
we have ordinates, or thicknesses, as given in Table No. 89.
Upon the curve thus^ obtained, steps may be laid off with
either vertical or battered risers.
Tests with the equation for moment of leverage stability,
will determine whether the risers may cut the curve, or if
the inner angle of tread and riser shall lie in the curve.
A slight increase or reduction of the top breadth, or of
the fractional multiplier, will increase or reduce the wall-
section, as desired.
422
PARTITIONS, AND RETAINING WALLS.
TABLE No. 89.
THICKNESS AT GIVEN DEPTHS OF A CURVED FACE WALL.
DEPTHS.
THICKNESS.
Feet.
(*.)
75 t'^
Feet.
O
3-5
H-
.O =
3-5
4
3-5
+
.6 =
4.10
6
3-5
+
1. 10 =
4.60
8
3-5
+
1.69 =
5.19
10
3-5
+
2-37 =
5^7
12
3-5
+
3.12 =
6.62
IS
3-5
+
4.36 =
7.86
2O
3-5
+
6.71 =
10.21
25
3-5
+
9.38 =
12.88
30
3-5
+
12.32
15.82
423. Back Batters, and their Equations. When
for practical or other reasons there is objection to giving all
the batter to the front of the wall, and a portion of it is
placed upon the back, then it is usually arranged in a
series of offsets or steps D l , Fig. 80.
In such case, the weight of the triangle of earth BJ)^E.
may be assumed to be supported entirely by the wall, and
as producing no lateral thrust upon the wall. This triangle
increases the weight leverage of the wall, and moves its
weight resultant farther back from the toe C.
Find the centre of gravity of the masonry, in g, and find
the centre of gravity of the triangle of earth, in g 2 ; then will
the centre of gravity of the two united bodies be in G.
Let Z>!/be the natural fractional angle of the material.
Bisect the angle IDiS 2 by the plane D^F ; then we may
assume the trapezium D<J$J?-J? to be that portion of the
earth-filling that, considered alone, will produce the maxi-
mum thrust effect upon the wall, and its horizontal and
leverage effects may be computed by equations 21 and 23.
INCLINATION OF FOUNDATION.
423
Prof. Moseley's equation* for the maximum pressure of
a surcharge similar to^this is
P l = %w 2 Jsec </> (hi 2 tan 2 </> + c 2 2 )^ 2 , (28)
In which c 2 is the height B 2 c 2 .
P L " maximum pressure of the earth.
W 2 " weight of one cubic foot of earth.
hi c vertical distance DiC 2 .
" frictional angle of the earth.
424. Inclination of Foundation. The frictional
stability of a wall upon its foundation is materially in-
Mechanics of Engineering, p. 426. Van Nostrand, New York, 1860.
?
4:24 PARTITIONS, AND RETAINING WALLS.
creased, and its pressure is more evenly distributed upon
the foundation stratum, if an inclination is given to the bed
nearly at right angles to the final thrust resultant, as in
Fig. 80. Bed-joints may often be similarly inclined with
advantage.
A sliding motion in such case involves the additional
work of lifting the whole weight up the inclined plane.
425. Front Batters and Steps. Masons experience
a very considerable difficulty in laying the face of rubble
walls with batters exceeding two inches to the foot, and
often with batters exceeding one and one-half inches to the
foot, unless with stones from a quarry where the transverse
cleavage varies several degrees from a perpendicular to
the rift.
The difficulty is increased when the bed-joints of the
work are level from front to rear, as the workmen prefer to
make them.
It is especially troublesome to the workmen, and expen-
sive as well, to make face-batters of high walls conform to
the theoretical curved batters deduced from the logarithmic
equations.
It is better, therefore, to transpose the curve into a series
of steps when its tangent inclination exceeds two inches to
the foot, in which case the steps may have equal heights
and varying projections, as in Fig. 81, which is a revetment
ujKm a navigable river, or may have both varying rise and
projection, with batter upon the rise, as in the weir, Fig. 72.
426. Top Breadths, The thickness at the top of a
revetment should in all cases be sufficient, so that its weight
will be able to resist the frost expansion thrust of the sur-
face layers of the earth. Sometimes a batter is given to the
back of the wall, three or four feet down from the top, to
enable the earth to expand readily in a vertical direction,
TOP BREADTHS.
425
and thus act with less force horizontally against the backs
of the cap-stones.
An increased thickness at the top of the wall, and at all
points of depth, is also necessary when the filling is liable
to be loaded with construction materials, fuel, merchandise,
FIG. 81.
or other weights, or if it is to sustain traffic of any kind.
The additional weight may in such case be considered
equivalent to a surcharge weight, and the centre of gravity
of the filling and of the additional weight will be resolved
into their united centre of gravity and the vertical resultant
426
PARTITIONS, AND RETAINING WALLS.
be considered as passing through this new centre of gravity.
The new horizontal thrust resultant will then act upon the
wall at a greater altitude, and with greater leverage than
the horizontal resultant of filling alone ( 416), as has
been already demonstrated.
In the cases of discharge weirs the floods are considered
as surcharge weights, and not only the depth of water
behind the weir and upon its crest is to be considered, but
FIG. 82.
the additional height to which the velocity of approach of
the water is due.
If there is but one or two feet depth of water flowing
over, then the cap-stones may be subject to the blows of
logs, cakes of ice, and such debris as the floods gather.
427. Wharf Walls. When a wall is to be generally
ELEMENTS OF FAILURE. 427
used for wharf purposes, its face should be protected by
fender piles, both for its own advantage and that of the
vessels that lie alongside.
Fig. 82 illustrates the method of piling and capping,
adopted by the writer, in an extensive wharf -pier of one-
half mile frontage in one of the deep harbors upon the New
England coast. The caps are, in this case, dressed dimen-
sion stones, three and one-half feet wide and one foot thick.
The wharf log is made up of 12" x 10" and 12" x 8" hard
pitch pine, placed one upon the other so as to break joints,
and tre-nailed together. The anchors of the pile-heads pass
through the cap-log, and their bolts pass through the cap-
stones into headers specially placed to receive them. The
piles are placed eight feet between centres, and each fourth
pile extends above the log for a belay pile. Waling
pieces of 6" x 12" hard pine are fitted between the pile-heads,
and spiked to the face of the cap-log to confine the pile-
heads rigidly in place. Midway between the belay piles
are belay rings, whose bolts pass through the cap-logs into
headers, and are also anchored by straps to cap-stones.
428. Counter-forted Walls. There is so rarely an
economic advantage in counter-forting a wall, except in
those cases of brick walls where the counter-fort may take
the form of a buttress upon the exterior face, that we shall
not here devote space to their special theoretical investiga-
tion, which, by graphical analysis, is a simple reapplication
of the principles already laid down.
429. Elements of Failure. In our theoretical inves-
tigation of the resistances of masonry to sliding or overturn-
ing we have supposed the walls to be laid in mortar and
solid, and well bonded, so that the mass was practically
one solid piece, considered as one foot long.
If any given foot of length, considered alone as a unit
428 PAKTITIONS, AND KETAINING WALLS.
of length, is found stable, and each other foot is equal to it,
then evidently the whole length will be stable.
The joints from front to rear in cut and first-class rubble
walls are usually laid level, and the workmen intend to give
a good bond of one course upon another. When consider-
ing the leverage stability of a high wall, at the respective
joints, working from top downward, we usually treat the
joints as horizontal planes. Let us turn again to the sketch
of the partition wall, Fig. 76, which has joints laid off upon
it showing an average class of rubble work. Suppose the
water to be drawn off from the side EC, and the full water
upon the opposite side to be freezing, and the ice exerting a
thrust upon the upper courses of the wall. We investigate
the leverage stabilty at the joint jj\, and find that it will
resist a considerable leverage strain, which for further illus-
tration we assume to be ample. Examining critically the
building of the wall, we find that jj\ is not the real joint,
and,/! the fulcrum to be considered in connection with
pressure upon Bj\ but in consequence of faulty workman-
ship, jjzjz is the zigzag joint and / 3 the fulcrum, and that
the joint, instead of being horizontal, is an equivalent in-
clined plane on which the wall is quite likely to yield by
slipping slightly with each extra lateral strain "put upon it.
If in a high and long wall such weaknesses are repeated
several times, the result will be a bulge upon the face of
the wall, ordinarily reaching its maximum at about one-
third the height of the wall, the portion above that level
appearing to have been moved bodily forward, and retain-
ing nearly its true batter.
When walls are so high as to require a thickness in a
considerable portion of their height exceeding seven or
eight feet, careless wall-layers, who are not entitled to the
honorable name mechanic, often pile up an outside and
f " !
FACED, AND CONCRETE REVETMENTS. 429
inside course, and fill in the middle with their refuse stone,
thus producing a miserable structure, especially if it is dry
rubble, that is almost destitute of leverage stability, unless
a great surplus of stone is put into the wall sufficient to
resist the thrust of an earth-backing by compounded weight
alone.
Short walls supported at each end may by such trans-
verse motion be brought into an arched form, concave to
the pressure, but at the same time into a state of longitudi-
nal tension that will assist in preventing further motion.
If there is the least transverse motion in a mortared wall
sustaining water, the masonry ceases from that instant to
be water-tight, and if the stones are in the least disturbed
on their bed after their mortar has begun to set, the wall
will never be tight.
430. End Supports. Well constructed short walls,
supported at each end, such as gate-chamber and wheel-pit
walls, have an appreciable amount of that transverse resist-
ance prominently recognized in a beam, which permits
their sections to be reduced, an amount dependent on the
effective value of such transverse support. The supported
ends of long walls transmit the influence of the support in a
decreasing ratio, out to some distance from the supports,
and walls whose ends abut upon inclines, as in the case of
stone weirs across valleys, may be reduced in thickness,
ordinarily, at the top and through their whole height, as
the height reduces.
431. Faced, and Concrete Revetments. Walls on
deep water-fronts, as in Fig. 81, for instance, when laid
within coffer-dams, are often faced with coursed ashler
having dressed beds and builds, and backed up with either
rubble- work laid in mortar, or with concrete, the headers of
the ashler being intended to give the requisite bond between
430 PARTITIONS, AND RETAINING] WALLS.
the two classes of work. Much care must be exercised in
such composite work, lest the unequal settlement of the
different classes of work entirely destroy the effective bond
between them and thus lead to failure.
Such walls have been constructed with perfect success
without coffer-dams, of heavy blocks of moulded beton, and
also successfully by depositing concrete in place in the wall,
under water, with the assistance of a caisson mould, or
sheet-pile mould, thus forming a monolithic revetment.
Foundations under water to receive masonry structures
have also been successfully placed by the last-mentioned
system.
Concrete structures under water laid without coffers,
however, demand the exercise of a great deal of good judg-
ment, educated both in theory and by practice, and admit
only of the most faithful workmanship.
FIG. 83.
FIG. 84.
FIG. 88.
FIG. 87.
FIG. 89.
n I 2 3 4- 5 6 7 Sf 9 10 II 12.
CONDUIT SECTIONS.
OHAPTEE XX.
MASONRY CONDUITS.
432. Protection of Channels for Domestic Water
Supplies. The observations, sound reasonings, and good
judgments that influence municipalities to seek and secure
the most wholesome and coolest waters for their domestic
uses, compel them also to guard the purity and maintain
the equable temperature of the waters as they flow to the
point of distribution.
The larger cities, with few exceptions, must lead their
waters in artificial conduits, from sources in distant hills,
where neither the soils nor atmosphere are tainted by
decompositions such as are always in progress in the midst
of large concourses of human beings and animals.
Such long water-courses ought to be paved or revetted,
or their currents will be impregnated with the minerals
over which they flow, and will cut away their banks where
the channels wind out and in among the hills. An arch of
masonry spanning from wall to wall is then the most sure
>rotection from inflowing drainage, the approach of cattle
id vermin, the heating action of the summer sun, and the
i-owth of aquatic plants in too luxuriant abundance.
433. Examples of Conduits. When proper grades
ire attainable to permit the waters to flow with free sur-
faces, such conduits, requiring more than six or eight square
feet sectional area are usually, and most economically, con-
structed of hydraulic masonry.
432 MASONRY CONDUITS.
Figures 83 to 89 illustrate some of the forms adopted in
American masonry conduits.
Fig. 87 is a section of the Croton conduit, at a point
where it is raised upon embankment. This conduit is 7'-5"
wide and 8-5J" high, and conveys from Croton River to the
distributing reservoir in Central Park, New York city,
about one hundred million gallons of water daily. The
combined length of conduit and of siphons between Croton
Dam and Central Park is about thirty-eight miles, and they
were completed in 1842.
Fig. 88 is a section of the Washington conduit, which is
circular, of 9 feet internal diameter. This leads water from
a point in the Potomac River about sixteen miles from the
capital, to a distributing reservoir in Georgetown, from
whence the water is led to the Government buildings and
grounds, and throughout the City of Washington, in iron
pipes. This conduit was constructed in 1859.
Fig. 84 is a section of the Brooklyn, L. I., conduit lead-
ing the waters of Jamaica and other ponds to the basin ad-
joining the well of the Ridge wood pumping-engines. This
conduit increases in dimensions at points where its volume
of flow is augmented from 8'-2" wide to lO'-O" wide, and to
a maximum height of 8'-8". It was constructed in 1859.
Fig. 86 is a section of the Charlestown, Mass., conduit,
leading the water of Mystic Lake to the well of the Mystic
pum ping-station. This conduit is 5-0" wide and 5-8" high,
and was constructed in 1864.
Fig. 85 is a section of the Lowell, Mass., conduit, of
4-3" diameter. This leads water from a subterranean
infiltration gallery along the margin of the Merrimack
River, a short distance above Lowell, a portion of the dis-
tance to the pumping-station. It was constructed in 1872.
Fig. 89 is a section of the second Chicago tunnel, extend-
FOUNDATIONS OF CONDUITS. 433
ing under Lake Michigan two miles from the shore to the
lake crib, and underneath the city to the side opposite to
the shore of the lake. It is 7'-0" wide and 7-2" high in the
clear. The masonry of this tunnel consists of three rings of
brickwork, the two inner of which have the sides of their
bricks in radial lines, and the outer having its sides of
brick at right angles to radial lines. This tunnel was com-
pleted in 1874.
Fig. 83 is a section of the Boston conduit, commenced in
1875, to lead an additional supply from Sudbury Eiver to
the Chestnut Hill reservoir. Its length is sixteen and one-
half miles, its width 9-0", and height 7-8".
The new Baltimore conduit, as in progress in 1876, is to
be 36,495 feet in length, entirely in tunnel, extending from
Gunpowder River to the receiving reservoir. The portions
lined with masonry are circular in section, of 12 feet clear
diameter. The inclination is 1 in 5000, and the anticipated
capacity about 170,000,000 gallons per 24 hours.
The Cochituate conduit of the Boston water supply is
5 feet wide, 6'-4" high, of oviform section, and has an incli-
nation of 3 inches to the mile. Its capacity is 16,500,000
gallons per 24 hours.
434i Foundations of Conduits. The foundations of
masonry conduits must be positively rigid, since the super-
structures are practically inelastic, and any movement is
certain to produce rupture. A crack below the water-line
admits water into the foundation, and tends to soften or
undermine the foundation, and to further settlement, and
to additional leakage. So long as the foundation yields,
the conduit cannot be maintained water-tight, for the set-
tling away of the support at any point results in an undue
transverse strain upon the shell, and the adhesion of the
mortar to the masonry is overcome and the work cracks.
28
434
MASONRY CONDUITS.
435. Conduit Shells. A perfect shell should have
considerable tensile strength in the direction of its circum-
ference ; but when a longitudinal crack is produced its
tensile strength is destroyed at that point, and cannot again
be fully restored except by rebuilding.
When the side walls are of rubble masonry they are
usually lined with a course of brick-work laid in mortar, or
with a smooth coat of hydraulic cement mortar. The bot-
toms are frequently lined with a nearly flat invert arch of
brick.
All the materials and workmanship entering into this
class of structures should be of superior quality.
436. Ventilation of Conduits. Conduits of form and
construction similar to those above illustrated are usually
proportioned so that they are capable of delivering the max-
imum volume of water required when flowing about two-
thirds lull. Provision is then made for the free circulation
of a stratum of air over the water surface and beneath the
covering arch.
FIG 90.
FIG. 91.
Figs. 90 and 91 illustrate the form of ventilating shaft
and cover used upon the New Bedford, Mass., conduit.
CONDUITS UNDER PRESSURE
435
These shafts may be used also for man-hole shafts, which
are required at frequent intervals for inspection and care of
the conduit.
FIG. 92.
437. Conduits under Pressure. Fig. 92 illustrates a
<5onduit of locked bricks, designed by the writer to convey
water under pressure. The specially moulded bricks are
eight inches long and eight inches wide and two and one-
half inches thick. They have upon one side a mortise six
inches long, four and one-quarter inches wide, and one-half
inch deep, and upon the opposite side two tenons, each
matching in form a half mortise. When the bricks are laid
436 MASONRY CONDUITS.
in the shell the tenons at the adjoining ends of two bricks
fill the mortise in the brick over which the joint breaks.
In brick conduits as usually constructed the bricks have
their greatest length in a longitudinal direction, but here the
length is in circumferential direction. The object here is to
utilize to the fullest extent the tensile bonding strength of
the masonry, and then to reinforce this strength by inter-
locking the bricks themselves. The conduit cannot be rup-
tured by pressure of water without shearing off numerous
tenons in addition to overcoming the cohesive strength of
the masonry.
This system permits of vertical undulations in the grade
of the conduit within moderate limits, and reduces mate-
rially the amount of lift of the conduit required upon em-
bankments.
Upon long conduits it permits the insertion of stop-gates
and the examination and repair of any one section while
the other sections remain full of water. Also when of
a given sectional area and flowing full, and delivering
to a pump- well or directly into distribution-pipes a given
volume of water, it transfers more of the pressure due
to the head than the usual form of construction of like
sectional area, and thus reduces the lift of the pump or
increases the head upon the distribution. This is more
especially the case when the consumption is less than the
maximum.
438. Protection from Frost. The masonry of con-
duits must be fully protected from frost, or its cement
mortar will be seriously disintegrated by the freezing and
expansion of the water filling its pores. The frost coverings
are usually earthen embankments, of height above the top
of the masonry equal to the greatest depth to which frost
penetrates in the given locality. The level breadth of the
MASOXRY TO BE SELF-SUSTAINING. 437
top of the embankment should equal the breadth of the
conduit, and the side slopes be not less than i J to 1.
439. Masonry to be Self- sustaining. When the
conduit is in part or wholly above ground surface, its ma-
sonry should be self-sustaining under the maximum pres-
sure, independent of any support that may be expected /
from the embanked earth. The winds of winter generally {
clear the embankments very effectually of their snow cover-
ings, and leave them exposed to the most intense action
of frost.
In periods of most excessive cold weather the entire em-
bankment may be frozen into a solid arch, and by expan-
sion rise appreciably clear of the masonry, and possibly
exert some adhesive pull upon the hances of the arch. If
the conduit is then under full pressure, and not wholly
independent of earth support, a rupture at the crown of the
arch may result.
Each quadrant of the covering arch, above its springing
line, exerts a horizontal thrust at the springing line as indi-
cated in Fig. 92 by the shorter arrow, and the water pres-
sure exerts an additional horizontal thrust, as indicated by
the lower arrow in Fig. 92. When the conduit is just even
full, the point of mean intensity of this latter pressure is at
one-third the height from the bottom of the conduit.
The amount of horizontal pressure upon each side in
ach unit of length is equal to the vertical projection of the
submerged portion of that side, per unit of length into
the vertical depth from free water surface, of the centre of
gravity of the submerged surface, into the weight of one
cubic foot of water ; the depths being in feet, and weight
and pressure in pounds.
The product of weight of backing masonry at any given
depth below the crown of the arch into its coefficient of
438
MASONRY CONDUITS.
FIG. 93.
friction, should be greater than the sum of thrusts at that
depth, and for a safe margin to insure frictional stability
should be equal to double the sum of thrusts.
The backing masonry is liable to receive some pull from
the embankment, if one
side of the embankment
settles or slides, but if the
foundations of the sides of
the embankments are rea-
sonably firm, the earth at
the sides of the backings
may be assumed capable
of neutralizing the thrusts
due to the weight of cover-
ing earth upon the hances
of the arch.
44O. A Concrete Conduit. The use of hydraulic
concrete, or beton, is at present being more generally intro-
duced" into American hydraulic constructions, in those
localities where good quarried stones are not readily and
cheaply accessible, than has been practiced in years past.
Fig. 93 is introduced here as a matter of especial interest,
since it illustrates the form of a conduit constructed entirely
of beton, in the new Vanne water supply for the city of
Paris. This conduit is two meters (6.56 feet) in diameter.
The beton agglomere of this conduit is a very superior
quality of hydraulic concrete, which has resulted from the
experiments and researches of M. Francois Coignet, of Paris.
Gen. Q. A. Gillmore has described* in Professional
Papers, Corps of Engineers, U. S. Army, No. 19, the mate-
rials, compositions, manipulations, and properties of this
* Report on Beton Agglomere, or Coignet Beton. Washington, 1871.
EXAMPLE OF CONDUIT UNDER HEAVY PRESSURE. 439
"beton in a masterly manner, and has given several plates
illustrating some of the magnificent monolithic aqueducts
of concrete, spanning valleys and quicksands, in the great
forest of Fontainebleau, on the line of the Vanne conduit,
between La Vanne River and the city of Paris.
441. Example of Conduit under Heavy Pressure.
The details of the Penstock, leading water from the canal
above referred to ( 382), to the Manchester, N. H., -turbines
and pumps, are shown in Fig. 94.
This penstock is six hundred feet long, and six feet clear
internal diameter. Its axis at the upper end is under
twelve feet head of water, and at the lower end under thirty-
eight feet head of water. It was constructed, in place, in a
trench averaging thirteen feet deep. The staves, which are
of southern pitch-pine, 4 inches thick, were machine-dressed
to radial lines, and laid so that each stave breaks joint at its
end at a distance from the ends of the adjoining staves, after
the usual manner of laying long floors. The end-joints
where each two staves abut are closed by a plate of flat
iron, one inch wide, let into saw-kerfs cut in the ends of the
staves at right angles to radius. Thus a continuous cylin-
der is formed, except at the two points where changes of
grade occur. The hoops are of 2| x ^-inch rolled iron, each
made in two sections with clamping bolts, and they are
placed at average distances of eighteen inches between
centres.
Its capacity of delivery is sixty-five million gallons in
twenty-four hours, with velocity of flow not exceeding four
feet per second.* It was completed in the spring of 1874,
and has since been in successful use, requiring no repairs.
It lies in a ground naturally moist, and sufficiently satu-
* This penstock is more fully described in a paper read before the Ameri-
can Society of Civil Engineers in January, 1877. Vide Trans., March, 1877.
MEAN RADII OF CONDUITS. 441
rated to fully protect the wood-work from the atmospheric
gases.
The city of Toronto, Canada, has just completed a con-
duit of wood, which conveys water under pressure from the
filtering gallery on an island in Lake Ontario, opposite to
the city, about 7,000 feet, to the pumping-station on the
main land. The internal diameter of this conduit is 4 feet.
442. Mean Radii of Conduits. In the formula of
flow for open canals (323), the influence of the air pe-
rimeter is taken into consideration in establishing the value
, , -, -, sectional area, S
of the hydraulic mean depth, r = - ^ , and a
contour, o
fractional portion of the air perimeter, equal to its propor-
tional resistance, is added to the solid wet perimeter.
It is more especially necessary that the resistance of the
air perimeter be recognized in conduits partially full. As
the depth of water increases above half-depth, the influence
of the confined air section is, apparently, inversely as the
mean hydraulic radius of the stream.
If we compute, for circular conduits, values of r, as equal
to -r TT-j : T , we have at o depth, r = Od ; at one-
wet solid perimeter
fourth depth, r = .14734^ ; at one-half depth, r = .25d ; at
three-fourths depth, r = .30133d ; and at full depth, r = 25d.
This series gives a maximum value of r at about eight-tenths
depth and a decrease in its value from thence to full.
The relative discharging powers, in volume, of a circular
conduit, with different depths of water, are as the product
\/ > when S is the sectional area of the stream ; r, the
V 772'
mean hydraulic radius ; and m, a coefficient.
If for a given series of depths, in the same conduit, we
compute its series of volumes of discharge, neglecting the
442 MASONRY CONDUITS.
influence of the air perimeter, we arrive at the paradoxical
result that when the depth is eighty-eight hundredths of
full the volume flowing is ten per cent, greater than when
the conduit is full. This theoretical result has misled sev-
eral hydraulicians who have written upon the subject.
With a true value of r, the discharge has some ratio of
increase so long as sectional area of column of water in a
circular conduit increases ; but the maximum capacity of
discharge of a conduit is very nearly reached when it is
seven-eighths full.
TAB LE No. 9O.
HYDRAULIC MEAN RADII FOR CIRCULAR CONDUITS, PART FULL.
(Expressed in decimal parts of the diameter?)
RATIO OF FULL DEPTH.
o | .1 | .2 I .25 | .3 I -4 I -5 I -55 I -6 | .65 | .7 | .75 | .8 | .85 | .875 | .9 I -95 1 Full.
HYDRAULIC MEAN RADII, IN RATIO OF DIAMETER.
o | .058] .no| .136! .157! .200! .235 | .250! .263) .272] .275.1.278! .277] .273! .270! .265! .260] .250
443. Formulas of Flow, for Conduits. Rankine's
formula* for loss of head in an open conduit is,
A"- . v * m
r *f
from which, by transposition, we have the equation of
velocity,
,= ]?*= ]??(*. (2)
( ml \ ( m }
For value of the coefficient m he adopts Weisbach's for-
mula, viz. :
.00023
m = .0074 +
* Civi] Engineering, p. 678. London, 1872.
FORMULAS OF FLOW, FOR CONDUITS. 443
This formula for m gives a constant value to m, while v
remains constant, even though r varies. Experiment shows
that the variable r exerts a very appreciable influence upon
the value of the coefficient m, when
It is unfortunate that data for the construction of a table
of m for conduits, not under pressure, is so scanty. Their
values for brick conduits, or brick linings for a given series
of r, evidemy lie somewhere between the values of m for
smooth pipes under pressure, and the values of m for
straight open channels in earth.
The following column of values for the given series of r
are suggested merely as approximate mean values for
smooth conduits three-quarters full, and are placed between
columns of values of m for smooth pipes under pressure,
and for straight open channels in earth for convenience of
ready comparison.
They are applicable to the formulas, for conduits :
in
ml
mtf ,,
,
*=
in which
v velocity of flow, in feet per second.
T = hydraulic mean radius.
i = sine of inclination of water surface.
Ji vertical head lost in given length, in feet
I = given length, in feet.
444
MASONRY CONDUITS.
TABLE No. 9O.
COEFFICIENTS FOR SMOOTH CONDUITS, THREE-QUARTERS FULL.
(For a mean velocity of about 2.5 feet per second?)
Hydraulic mean radii
r in feet.
Coefficient w for
smooth pipes, under
pressure.
Coefficient m for
smooth conduits,
9gri
~ v* '
Coefficient m for open
channels in earth.
I
.00380
.OIOO
.0298
1-25
.00342
.0084
.0260
1.50
.00325
.0071
.0234
i-75
.00300
.0063
.O2I2
2
.OO28l
.0057
.0197
2.25
.0027
53
.0183
2.50
.OO26
.0050
.0172
2.75
.0048
.Ol6l
3
.0046
I53
3-25
.0045
.0143
3-5
.0044
.0131
3-75
.0042
.0137
4
.0040
.0127
A mean velocity of flow of about two and one-half_iket
per second is usually preferred in smooth conduits and
supply mains, when local circumstances permit the inclina-
tion and sectional area to be adapted to this end. Less
velocities, in conduits of three feet or more diameter, per-
mits the waters to deposit the sediments they have in sus-
pension.
444. Table of Conduit Data. The following table
gives such data as is at present obtainable respecting some
of the well-known conduits of masonry :
CONDUIT DATA.
445
TABLE No. 91.
CONDUIT DATA.
LOCALITY.
|
j
1
"3 5;
I 5
. ^
Q
r.
i.
v
per
sec.
in.
Daily de-
livery at
given
depth.
Total
daily
capacity.
Cochituate, Boston
Croton, New York
Washington Aq., D.C
Feet.
5
7-4I7
9
10
9
7.0522
c 66?
Feet.
6-333
8.458
8.667
7.667
I
^
Feet.
6.333
6.083
3-465
5-00
5-3
1.417
2.3415
I.8735
2.5241
.0000496
.00021
.00015
.0001
Feet.
i .0
2.218
1.893
.00452
.006435
00505
U.S.gal.
16,398,980
59,340,243
27i559i364
U.S. gal.
16,500,000
100,000,000
100,000,000
70,000,000
70.000,000
170,000,000
60,000,000
52,000,000
23,500,000
5,500,000
Sudbury, Boston. . . .
Baltimore
Loch Katrine, Glasgow..
Canal of Isabel II, Madrid
Vienna
6.85
2-5253
.0001578
1.7126
.00876
60,000,000
.000435
.0001
....
6.6'
6.6
5.00
....
Dhuis " ....
Pont du Gard, Nimes....
Pont Pyla, Lyons
Metz
4.OO
1.833
3-167
3-333
1-833
2.167
.0004
.00166
.001
.0004
.0003
.0002
.0003
2
2-95
2.783
...
Arcueil
Roquencourt, Versailles. .
3-925
2-583
1.333
.716
Montpellier.
X
o.S
....
CHAPTEE XXI.
MAINS AND DISTRIBUTION PIPES.
445. Static Pressures in Pipes. Passing from the
consideration of masonry conduits to that of pipes with
tough metal shells, the pressure strains and the capabilities
of resistance of the pipe metals to these strains, first de-
mand^ our attention.
The theoretical relations of thickness to pressure are so
simple that we may easily adapt any tough metal pipe to
withstand any practical static head pressure, however great.
By the term static pressure, we indicate the full pressure
due to the head of water, while standing at rest.
The unit of pressure area is commonly taken as one
square inch, and this is the area used
herein for the unit.
The pressure p upon the unit of
area a of a conduit or water-pipe, is
equal to the product of the given area
into the vertical height h of the surface
of water above the centre of gravity of
the given area, into the weight w of
one cubic foot of water (= 62.5 Ibs.)
divided by 144.
FIG. 95.
*1
a, x 7i x w
144
= .434^.
(1)
Let dbcef, Fig. 95, be the internal circumference of a
NEW-YORK
SCALE,
FORMS OF PIPE SOCKETS.
THICKNESS OF SHELL. 447
water-pipe, of diameter d, in inches ; then the total pressure
P of water upon the circumference is
P = S.UlQd x .434^. (2)
The maximum pressure acts upon each point of the cir-
cumference radially outward, tending to tear the shell
asunder.
The resultant of the maximum pressure upon any given
portion of the circumference a&, acts in a radial direction
ox, through the centre of gravity 6f the surface a&, and is
equal to the product of pressure into the projection or trace
of the surface ij, at right-angles to radius,
) x p\.
Also the resultant of the maximum pressure upon the
semi-circumference cbaf is equal to the product of pressure
into its trace gk^ at right-angles to the radial line cutting its
centre of gravity,
= f(area #&) x p\.
The trace of the semi-circumference is also equal to the
diameter d, and its resultant equals the product dp.
Opposed to the resultant ox is an equal resultant of the
pressure upon the semi-circumference fee.
These two resultants exert their maximum tensile strain
upon the pipe-shell at the points c and/.
446. Thickness of Shell resisting Static Pressure.
Let 8 be the cohesive strength or ultimate tenacity per
sq. in. of the metal of the shell, and t be the thickness cc^ and
ffi in inches of the shell, then we have for equation of resist-
ance of shell that will just balance the steady static pressure,
2tS=dp. (3)
from which we deduce the required thickness of shell :
448 MAINS AND DISTRIBUTION PIPES.
t _dp_ rp
'2S"~S 9
in which r equals radius in inches, =
It is not enough that the shell be able to just sustain the
steady static pressure, since this pressure may be increased
by " water -rams " incident to ordinary or extraordinary
use of the pipe, or the metal may have unseen weaknesses,
or deteriorate by use.
The thickness t should therefore be multiplied by a
coefficient, for safety, equal to 4, 6, 8, or 10 ; or the pressure
be assumed to be increased 4, 6, 8, or 10 times, or the
tenacity of the metal be taken at .1, .2, .3, or .4 of its test
value ; in which case the equation of t may take the form,
pr
= --., or t=2g. (5)
The pressure due to a given head H of water is greater
within a pipe when the water is at rest, than when the cur-
rent is flowing through the pipe at a steady rate, for when
the current is moving, a portion of the force of gravity is
consumed in producing that motion, and in balancing fric-
tions ; hence the effective head H v remaining at a given
point is less than the static head by an amount equal to the
(V 2 \
= Jl = ] T
and the head overcoming the Mctional resistances between
the reservoir and the given point in the length of the pipe
, ml
Ti - - x
r
, = H-(7i + h"). ( Vide 265.)
When a pipe has a stop-valve at its outflow, or in its
line, the pressure p, used in its formula of thickness , for
WATER-RAM. 449
any point above the valve, should be the static presssure of
the water at rest.
447. Water-ram. If any valve in a line or system of
water-pipes can be suddenly closed while the water is flow-
ing freely under pressure, such sudden closing of the valve
will produce a strain upon the pipes far greater than that
due to the static head of water.
For illustration, let any delivery-pipe, having a stop-
valve at its outflow end, be 1 ft. diameter = d\ , and 5280 ft.
long = Z, and the current of water filling it be flowing at a
uniform rate v of 5 feet per second. Then the momentum
M of this column of water, due to its weight and velocity, is
M = .785M 2 x w x I x jf (6)
= .7854 x 62.5 x 5280 x .3882
= 100,614.45 Ibs.
If the valve is closed and the flow checked instantaneous-
ly, this great force will act upon the valve and upon the
shell of the pipe. If the given length of column of water in
motion is doubled or quadrupled, the force of the ram will
be doubled or quadrupled. If the valve is one second or
one minute in closing, then the force will be distributed
through one second or one minute in time, and its intensity
will be correspondingly reduced. Also, if there are any
accumulations of air in the pipe at summits, they will help
to prolong the time of action and to modify the force be-
hind them.
No system of distribution-pipes should be fitted with
stop-valves of instantaneous action, lest the pipes be con-
itly in danger of destruction by "water rams."
Genieys made allowance, in the old water-pipes of Paris,
>r water-rams, of force equal to static heads of 500 feet,
29
450 MAINS AND DISTRIBUTION-PIPES.
but he used on his smaller mains plug- valves that might be
very rapidly closed.
With proper stop and hydrant valves, it is not probable
that the momentum strain will exceed that due to a steady
static head of 200 or 225 feet, but it is liable to be great in
pipes under low static heads as well as in pipes under great
heads, and it is in either case in addition to the static head.
The momentum strain must be fully allowed for, whether
the head be ten feet or three hundred feet.
448. Formulas of Thickness for Ductile Pipes.
Ordinarily, for ductile pipes, such as lead, brass, welded
iron, etc., an allowance of from 200 to 300 feet head is made
for the momentum strain, and the tenacity of the material
is taken at .25 or .3 of its ultimate resistance 8, in which
case the formula for thickness o ductile pipes, subject to,
water-ram,, may take the forai, ft ~^-z
, _ (7i + 230 ft.) rw _ (7i + 230)dw _ (7i + 230)^
(.258) x 144 " (.68) x 144 " 728)
in which 7i is the head of water, in feet.
w " " weight of one cubic foot of water, in Ibs.
r " " radius of the pipe, in inches.
d" " diameter of the pipe, in inches.
t " " thickness of the pipe-shell, in inches.
8 " " tenacity of the metal, per square inch.
If we substitute a term of pressure per square inch, p
(= .434^), for -T-7J- in the equation for thickness of ductile
pipes, it becomes
, _ (p + 100 pounds) r _ (p + 100) d fff .
.258 .68
If the pipes have merely a steady static pressure to sus-
MOULDING OF PIPES.
451
tain, then the term + 100 may be omitted, and the equation,
with factor of safety equal to 4, takes the simple form,
pr
'.258
pd
or with factor of safety equal to 6,
pd
.16667#~ .33333#'
(9)
(10)
449. Strengths of Wrought Pipe Metals. The fol-
lowing values of S give the tenacities of the respective ma-
terials named, in pounds per square inch of section of
metal, when the metal is of good quality for pipes :
TAB LE No. 92.
TENACITIES OF WROUGHT PIPE METALS.
WEIGHT
PER CU-
BIC INCH.
COEF.
6(/r).
COEF.
4 Or)-
COEF.
6 (pd).
COEF.
4 (Pd\
Pounds.
S. in Ibs.
.16667^.
.255".
33333S.
. 5 s.
Lead
2 -*86
.jo- 66
Block tin
H93
Glass
4i
766 66
1566 66
1150
J 533-33
Brass
4666 66
Copper ....
.3000
2 ,000
Wrought-iron, single riveted
" u double "
' 6 *
.2607
35ioo
liirii
8750
11666.66
17500
CAST-IRON PIPES.
45O. Moulding of Pipes. The successful founding
of good cast-iron pipes requires no inconsiderable amount
of skill, such as is acquired only by long practical experi-
ence, and keen, watchful observation.
The loam and sand of the moulds and cores must be
carefully selected for the best characteristics of grain, and
452 MAINS AND DISTRIBUTION-PIPES.
proportioned, combined, and moistened, so that the mix-
ture shall be of the right consistency to form smooth and
substantial moulds and cores, and be at the same time suf-
ficiently porous to permit the free exit of moisture and
steam during the process of drying. The moulds must be
filled and rammed with a care that insures ttteir stability
during the inflow of the molten metal, and must be dried
so there will be no further generation of steam during the
inflow ; and yet not be overdried so as to destroy the ad-
hesion among their particles, lest the grains of sand be
detached and scattered through the casting. The core rop-
ing of straw must be judiciously proportioned in thickness
for the respective diameters of their finished cores, and must
be twisted to a firmness that will resist the pressure of the
molten metal, so that the pipe will be free from swells and
the proper and uniform thickness of metal will be secured.
The mixture of the metals and fuel in the cupola must
be guided by that experience by which is acquired a fore-
knowledge of the degree of tenacity, elasticity, and general
characteristics of the finished castings. A superior class of
pipe is produced only when excellent materials are used,
and when superior workmanship and mechanical appli-
ances give to them accuracy of form and excellence of
texture.
451. Casting of Pipes. A certain thickness of shell,
of twelve-foot pipes, cast vertically, is required for each
diameter of pipe, to insure a perfect filling of the mould
before the metal chills, or cools, and also to enable the
pipes to be safely handled, transported, laid, and tapped.
In the smaller pipes this thickness is greater than that
ordinarily required to sustain the static pressure of the
water.
The necessary additional thickness, beyond that re-
THICKNESS OF CAST-IRON PIPES. 453
quired to resist the water pressure, decreases as the diam-
eter of the pipe increases.
There must, therefore, be affixed to the formula of thick-
ness of cast-iron pipes, a term expressing the additional
thickness required to be given to the pipes beyond that re-
quired to resist the pressure of the water, and this term
must decrease in value as the diameter increases in value.
452. Formulas of Thickness of Cast-iron Pipes.
The ultimate tenacity of good iron-pipe castings ranges
from 16,000 to 29,000 pounds per square inch of section of
metal. Their value of 8, the symbol of tensile strength
per square inch, is usually taken at 18,000 pounds, and the
coefficient of safety equal to 10, or the term of tensile resist-
ance is taken equal to .1$, or if an independent term is
introduced in the formula for the effect of water-ram, the
coefficient of S may be increased to, say .2.
Assuming that the probable or possible water-ram will
not produce an additional effect greater than that due to a
static pressure of 100 pounds per square inch, or head of
230 feet, then the formula for thickness of cast-iron pipes
may take the form,
,_
"
Oqq/1 & \ _ (& + 230>&0 ,
100/ " .48 x 144 "
(.28) x 144 100/ " (.48 )x 144
in which Ji is the head of water, in feet.
w " weight of one cubic foot of water, in Ibs.
r " internal radius of the pipe, in inches.
d " internal diameter of the pipe, in inches.
t " thickness of the pipe shell, in inches.
8 " tenacity of the metal, in pounds per sq. in.
If we substitute a term of pressure per square inch,
454 MAINS AND DISTRIBUTION PIPES
p ( .434A) for - -j, in the above equations for thickness
of cast-iron pipes, they become,
_ (p + 100)7- / eZ \ _ (p + IQOyZ
Tag" H 1 'loo/ -^r~
. . .333(1 -A). (12)
453. Thicknesses found Graphically. Since with a
constant head, pressure, or assumed static strain, the in-
crease of tensile strain upon the shell is proportional with
the increase of diameter, and also since the decrease of
additional thickness is proportional with the increase of
diameter, it is evident that if we compute the thickness of a
series of pipes, say from 4-inch to 48-inch diameters, for a
given pressure, by a theoretically correct formula, and then
plot to scale the results, with diameters as abscissas and
thicknesses as ordinates, the extremes of all the ordinates
will lie in one straight line ; and also, that if the thicknesses
for the minimum and maximum diameters of the series be
computed and plotted as ordinates, in the same manner,
and their extremities be connected by a straight line, the
intermediate ordinates, or thicknesses for given diameters
as abscissas, will be given to scale. This method greatly
facilitates the calculation of thicknesses of a series of
" classes" of pipes, and if the ordinates are plotted to large
scale, gives a close approximation to accuracy.
454. Table of Thicknesses of Cast-iron Pipes.
The following table gives thicknesses of good, tough, and
elastic cast-iron, with 8= 18,000 Ibs., for three classes of
cast-iron pipes, covering the ordinary range of static pres-
sures of public water supplies.
The thicknesses in the table are based upon the formula,
d
d\
-ioo/
THICKNESSES OF CAST-IRON PIPES.
455
TABLE No. 93,
THICKNESSES OF CAST-I'RON PIPES.
(When S = 18000 Ibs.)
CLASS A.
CLASS B.
CLASS C.
DIAMETER.
Pressure, 50 Ibs. per
square inch, or less.
Head, 116 feet.
Pressure, 100 Ibs. per
square inch.
Head, 230 feet.
Pressure, 130 Ibs. per
square inch.
Head, 300 feet.
THICKNESSES.
THICKNESSES.
THICKNESSES.
Inches,
3
Inches.
.3858
AP-
prox.
in.
H
Inches.
.4066
AP-
prox.
in.
H
Inches.
.4191
Ap-
prox.
in.
TV
4
4033
tt
43 ii
A
4477
TV
6
.4383
A
.4800
*
5050
\
8
4734
i
.5289
tt
.5622
TV
10
5083
*
5777
H
.6194
1
12
5433
A
.6266
1
.6766
14
.5783
if
6 755
7338
i
16
.6166
1
.7277
i
7944
18
.6483
7733
H
.8483
H
20
6833
tt
.8222
11
9055
B
22
7183
H
.8711
1
.9628
H
24
7533
|
.9200
I.02OO
I
27
.8058
9933
I
1.1058
'A
30
8583
1
i. 0666
'A
I.I9l6
i*
33
.9108
1.1400
i/ 2
1-2775
iA
36
9 6 33
H
1.2133
'A
L3633
4
40
1-0333
A
1.3111
'*
1.4778
'H
44
1.1033
i
1.4088
i
I.592I
i
48
i.i733
i*
1.5066
4
1.7066
i
In the following table are given the thicknesses of cast-
iron pipes, as used by various water departments.
456
MAINS AND DISTRIBUTION PIPES.
TABLE No, 93a.
THICKNESSES OF CAST-IRON PIPES, AS USED IN SEVERAL CITIES.
\
Q
PHILADELPHIA.
1
BALTIMORE.
BROOKLYN.
{
CHICAGO.
p
u
PROVIDENCE.
i
ROCHESTER.
I
ALLEGHENY.
DETROIT.
ALBANY.
MILWAUKEE.
DIAMETER, INCHES.
250
He
IOO
ad P
218
ress
1 2O
170
198
ures
130
170
for
125
whic
150
;h P
TOO
140
1 80
ipes
130
170
200
are
150
2OO
Clas
80
140
260
sed,
162
in fe
IOO
et.
144
2OO
JI50
200
4
6
6
8
8
10
12
12
16
16
20
20
2 4
24
30
30
30
36
4 8
f
TV
'V
TV
TV
Thic
A
H
A
1
if
kne
A
A
f-
tt
ft
sses
of P
ipe Shells, in
... .1 . i
incl
f
T
H
les.
TV
TV
I
I
f
f
1
1
7
if
A
'f
H
4
6
6
8
8
12
12
16
16
20
20
24
24
30
30
30
36
36
48
i
i
\
A
H
H
f
If
II
\l
if
ft
TV
A
11
f+
tt-
I
f
1
1
A+
*
^
*
f
i
f
tt
1
1
f
f
1
f
I
f
I
f
I
f
if
t
1
TnV
f
A
t
1
if
1
1 +
1
f
tt
f
if
1
I
if
....
7
f
I
1
f
1
if
i
i
1
1 +
it*
t
I
1
f
I
I
H
I
4
If
J
4
4
....
....
'A
4
4
I
4
4+
....
"A
jj
i
Ti
T-i 5 ,-
4
8
455. Table of Equivalent Fractional Expressions.
The following tables of equivalent expressions for fractions
of an inch and of a foot, may facilitate pipe calculations :
CAST-IRON PIPE JOINTS.
457
TABLE No. 94.
PARTS OF AN INCH AND A FOOT, EXPRESSED DECIMALLY.
Equivalent
INCHES. Dec. part of
Equivalent
Dec. part of
an inch.
a foot.
1-32 .03125
. 002604
1-16
.06250
.005208
3-32
09375
.007812
1-8
.12500
.010416
5-32
.15625
.010420
3-i6
7-32
1-4
.18750
.21875
.25000
.015625
.018229
.020833
INCHES.
Equivalent
Dec. parts of
a loot.
Dec. parts
of a foot.
Equiv. inches
and 32cl pts.,
nearly.
9-32
.28125
023437
5-16
n-32
3-8
13-32
, 7-16
15-32
1-2
17-32
9~l6
IQ-32
5-8
21-32
11-16
.31250
34375
37500
.40625
43750
.46875
.50000
.53125
56250
59375
.62500
.65625
.68750
.026041
.028645
.031250
.033854
036458
.039062
.041666
.044270
.046875
.049479
.052083
.054607
057291
I
2
3
4
6
8
9
10
ii
12
0833
.1667
.2500
3333
4167
.5000
.5833
.6667
7500
.8333
.9167
I.OOOO
.1
.2
3
4
'.6
7
.8
9
I.O
'f*
2*
3il
F
If
12
27 -72
.71875
.0^080^
**j j**
3-4
/ x u / O
.75000
v oy > -'yj
.062500
25-32
.78125
.065104
13-16
.81250
.067708
27-32
.84375
.070312
7-8
.87500
.072916
29-32
.90625
.075520
15-16
.93750
.078125
31-32
.96875
.080729
i
I.
083333
456. Cast-iron Pipe Joints. According to Crecy,*
cast-iron pipes were first generally adopted in London very
near the close of the last century. The great fire destroyed
many of the lead mains in that city. These were in part
replaced by wood pipes, but when water-closets were intro-
duced and more pressure was demanded, the renewals were
afterward wholly of iron.
* Encyclopedia of Civil Engineering, p. 549. London, 1865.
458 MAINS AND DISTRIBUTION-PIPES.
The earliest pipes had flanged joints with a packing ring
of leather, and were bolted together. These were two and
one-half feet in length. Those first generally used by the
New River Company were somewhat longer, and were
screwed rigidly together at the joints. This prevented
their free expansion * and contraction, with varying temper-
atures of water and earth, rendering them troublesome in
winter, when they were frequently ruptured. Cylindrical
socket-joints were then substituted. These were accurately
turned in a lathe, to a slightly conical form, and, being
luted with a little whiting and tallow, were driven together.
The length of the pipes was subsequently increased to
nine feet, and a hub and spigot-joint formed, adapted first
to a joint packing of deal wedges, and afterward to a pack-
ing of lead.
The hub and spigot-joint, with various slight modifica-
tions, has been generally adopted in the British and con-
tinental pipe systems, for both water and gas pipes ; but
the turned joint has by no means been entirely superseded
in European practice.
A variety of the forms given to the turned joint are illus-
trated and commented upon in a paper f recently read by
Mr. Downie in Edinburgh. The illustrations include turned
joints used in Glasgow, Launceston, Dundee, Flyde, Liver-
pool, Trieste, Sydney, Hobart Town, and Hamilton (Canada)
water- works, and in the Buenos Ayres gas-works. These
joints were also used by Mr. George H. Norman, the well-
known American contractor for water and gas works, in
gas works constructed by him in Cuba.
* M. Girard found that the lineal expansion of cast-iron pipes, when free
and in the open air was .C00036 of an inch for each additional degree of Fah-
renheit.
f Proceedings Inst. E. S., vol. vii, p. 16.
DIMENSIONS OF PIPE-JOINTS.
459
The turned joint has not as yet been adopted in the
pipe systems in the United States ; but in the new water-
work of Ottawa, Canada, completed in 1875 under the direc-
tion of Thos. C. Keefer, C.E., they were very generally used.
The depths of hub and of lead packing in the early Eng-
lish and Scotch pipes, and in fact in the first pipes used in
connection with the Fainnount, Croton, and Washington
aqueducts, exceeded greatly the depths at present used.
The pine-log water-pipes of Philadelphia had been gen-
erally replaced by cast-iron pipes as early as about 1819.
The forms of hubs and spigots then used, as designed by
Mr. Graffe, Sr., were very similar to those now used, ex-
cept that the hubs had somewhat greater depth. The
lengths of the pipes were nine feet, and other dimensions as
in the following table, from data in the "Journal of the
Franklin Institute" :
Diameter of pipe, in inches.
Thickness of shell
Depth of hub
3
f
31
10
I
5
12
[6
6
20
!
It is observed that the set, by which the lead is com-
pacted in the joint, acts upon the lead, ordinarily only to a
depth of from one to one and one-quarter inches. The lead
beyond the action of the set is of but little practical value,
and there is no advantage in giving the hemp packing an
excessive depth.
Deep joints run solid with lead often give to the line of
pipes such rigidity that it cannot accommodate itself to the
levenness of its bearings and weight of backfilling, espe-
Lly in ledge cuttings, and rupture results.
When trenches are too wet to admit of pouring the lead
Lccessfully, small, soft lead pipe may be pressed into the
>int and faithfully set up with good effect.
457. Dimensions of Pipe -joints. Fig. 96 is a re-
460
MAINS AND DISTRIBUTION-PIPES.
FIG. 96.
duced section of a bell and spigot of a 12-inch diameter
pipe. Dimensions of cast-iron pipe socket-joints for diam-
eters from 4-inch to 48-inch, corresponding to the letters in
the sketch, are given in the following table (No. 95), and
like data are given for flange-joints in the next succeeding
table, No. 96.
The weight of flanged pipes, per lineal foot, exclusive of
weight of flanges, which is given in Table No. 96, may be
computed by the following formula (vide 461) :
w = 9.817 (d + t) 1.
(13)
458. Templets for Bolt Holes. A sheet-metal tem-
plet for marking centres of bolt holes on flanges should be
laid out and pricked with the nicest accuracy, and have its
face side and one hole conspicuously marked.
On special castings intended for fixed positions the tem-
plet should be placed upon the flange so that the centre of
the marked hole shall fix the position of one bolt hole ex-
actly over the centre of the bore of the pipe when the pipe
shall be placed in position, then the bolt holes of abutting
flanges will match with uniformity.
DIMENSIONS OF PIPES.
461
TABLE No. 95.
DIMENSIONS OF CAST-IRON WATER-PIPES. (Fig. 96.)
(Thickness of shell is herein proportioned for 100 Ibs. static pressure.)
Diameter. I
'a
)-4
O
>
o
JS
!
a Thickness
S- of shell.
<0
^'
as
-_
*
lq
^ Joint room.
*
^
ce
W
ef
fP
kl
&m
7W71
to
<?j
in.
4
12-3
TV
3
TV
I*
i]
il
i
TV
f
i
A
t
1
2
. 6
12-3
i
3
I 5 *
If
il
it
i
TV
f
i
A
1
i
2
8
12-3
H
3
A
If
ii
4
-1
TV
f
i
TV
I
4
2i
10
12-3
it
3
A
If
i|
4
i
T 8 *
f
i
A
1
it
21
12
12-3^
I
3i
A
2
i|
ii
i
TV
1
i
A
1
ii
2i
14
12-31
H
3i
TV
2j
if
4
i
TV
1
i
T^
1
4
2*
16
I2-3|
I
3i
t
*i
if
if\
f
i
1
A
I
i
4
2f
18
12-3?
If
3i
f
2*
if
iA
f
i
1
TV
t
i
4
2f
20
i2-3i
II
3i
I
2l
if
iA
f
i
1
TV
I
1
4
2f
22
I2-3|
1
3f
t
2i
if
iA
f
i
I
A
t
I
if
3
24
I2-3|
ft
3f
t
2i
if
iA
f
i
I
A
1
I
if
3
27
12-4
I
4
TV
2f
il
ii
f
i
li
t
TV
I*
if
3i
30
12-4
'A
4
TV
2f
i|
ii
f
i
I*
t
TV
I*
if
3i
33
12-41
iA
4i
TV
2f
2
4
f
i
M
f
TV
I*
if
3i
30
i2-4i
iA
4j
t
2f
2
ii
f
i
4
TV
*
4
if
3i
40
12-41
IA
4i
i
2f
H
il
f
i
Ii
iV
*
H
2
3!
I2-4|
iM
4|
i
2|
2i
ii
f
i
M
TV
i
x*
2
3f
,
T2-4f
Ii
4f
i
3
2i
ii
f
i
If
TV
i
if
2
4
462
MAINS AND DISTRIBUTION-PIPES.
TAB LE No. 96.
FLANGE DATA OF FLANGED CAST-IRON PIPES.
Diam.
of
bore
of
pipe.
Diameter
of
flange.
Thick-
ness of
flange.
Approx.
weight
of one
flange.
No. of
bolts.*
Diam.
of
bolts.
Diameter
of circle of
bolts.
Distance
between
centres of
bolts.
Com-
mon
diam.
of valve
flanges.
Inches.
Inches.
Inches.
Pounds.
Inches.
Decimal
inches.
Decimal
inches.
Inches.
3
6i
3-45
8
&
5-6
2.19 9
8
4
7i
1
6.64
IO
i
6.7
2.105
9
6
10
8.56
10
A
8.9
2.796
1 1
8
I*i
tt
11.98
12
1
II. I
2.906
i3
10
Hi
7
^
16.5
14
I
13-3
2.985
16
12
17
tf
22.3
14
i
IS-S
3.478
18
14
19*
I
28.6
16
i
J 7-75
3.485
20
16
2lf
'A
36.8
18
f
20.0
3-49 1
22
18
*3j
4
45-5
20
i
22.2
3-487
24
20
26J
i*
56-9
20
i
24.4
3.833
26J
22
28J
4
62.8
22
1
26.5
3-784
28i
2 4
3J
4
65-4
24
1
28.6
3-744
3|
27
33l
'*
80.8
26
7
?
31.8
3.842
33l
30
36*
it
95-9
28
1
35-
3-927
36J
33
40
4
117
30
i
38-1
3-99
40
36
43i
-A
J 43
3 2
7
?
41.6
4.084 43$
40
471
'I
160
34
1
45-75
4.227
47l
44
54
4
197
36
1
50.0
4-363
54
48
56
4
224
40
1
54-1
4.249
56
* The number of bolts given in the table may be decreased when the
water pressures aiid transverse strains upon the bolts are light.
FLEXIBLE PIPE-JOINT.
463
If an even number of bolts are used, then there will be
a bolt vertically over and under the centre of the bore of
the pipe.
If the templet is not very exactly spaced the face side
should be placed against one flange with the marked hole
at top, and the back against the other abutting flange with
same hole at top ; otherwise the bolt holes may not exactly
match.
459. Flexible Pipe- Joint. It is sometimes necessary
to take a main or sub-main across a broad, deep stream or
FIG. 97.
estuary, or arm of a lake, where it is both difficult and
expensive to coffer a pipe course so as to make the usual
form of rigid joint. Different forms of ball and socket
464
MAINS AND DISTRIBUTION-PIPES.
flexible joints have been adopted for such cases, which
allow the pipes to be joined and the joints completed above
the water surface, and the pipe then to be lowered into
its bed.
Fig. 97 illustrates the form of joint designed by the
writer for a twenty-four inch pipe, which is especially
adapted to large-size pipe-joints. It is a modification of the
Glasgow " universal joint."
The difficulty of making the back part of the lead-pack-
ing of the joint firm and solid, which difficulty has here-
tofore interfered with the complete success of the larger
flexible pipes, is here overcome by separating the bell into
two parts, so as to permit both the front and rear parts of
the packing to be driven.
In putting together this joint, the loose ring is passed
over the ball-spigot and slipped some distance toward the
FIG. 98.
centre of the pipe ; the ball-socket is then entered into the
solid part of the bell and its lead joint packing poured and
snugly driven ; the loose ring is then bolted in position, and
its lead joint packing is poured and firmly driven, also.
This secures a solid packing at both front and rear of the
WEIGHTS OF CAST-IRON PIPES. 465
joint, capable of withstanding the strain that comes upon it
as the pipe is lowered into position, and ensures a tight
joint. The ball-spigot is turned smooth in a lathe to true
spherical form.
Fig. 98 illustrates J. B. Ward's patent flexible joint.
460. Thickness Formulas Compared. The results
given by some of the well-known formulas for thicknesses
of cast-iron pipes, may be compared in Table No. 97.
461. Formulas for Weights of Cast-iron Pipes.
The mean weight of cast-iron is about 450 pounds per cubic
foot, or .2604 pounds per cubic inch.
Let d be the diameter of a cast-iron pipe, in inches ;
, the thickness of the pipe-shell, in inches ; and n the ratio
of circumference to diameter (= 3.1416) ; then the cubical
volume V l , in inches, of a pipe-shell (neglecting the weight
of hub), is, for each foot in length,
V l = (d + ) x t x TT x 12. (14)
When the length of a pipe is mentioned, it is commonly
the length between the bottom of the hub and the end of
the spigot that is referred to ; that is, the net length of the
pipe laid, or which it will lay.
The average weight of a pipe per foot includes the
weight of the hub, which, as thus spoken of, is assumed to
be distributed along the pipe.
The weights of the hubs, of general form shown in
Fig. 96, and whose dimensions are given in Table No. 95
(p. 461), increase the average weight per foot of the twelve-
foot light pipes, approximately, eight per cent. ; of the
medium pipes, seven and one-half per cent. ; and of heavier
pipes, seven per cent.
The equation for cubical volume of pipe-metal, includ-
ing hub, is
30
466
M\INS AND DISTRIBUTION-PIPES.
T A B I E No. 9*7.
FORMULAS FOR THICKNESS OF CAST-IRON PIPES COMPARED.
Assumed static pressure, 75 Ibs. per square inch. Assumed tenacity of metal, 18,000 Ibs. per
square inch.
AUTHORITY.
EQUATIONS.
DIAMETERS.
48 in.
4 in.
12 in.
24 in.
Equation (12), 452. .
M Dupuit . .
(/ + ioo)</ / d\
Thick-
ness.
Inches.
.4172
455
4550
.3899
4534
3776
.4074
.2887
4175
.3600
3334
.4129
.4900
3542
4554
4384
.4496
Thick-
ness.
Inches.
.5850
.5766
5750
.4897
.6002
5794
.6121
.5000
.6126
6235
.5002
.6148
.6699
5625
.6461
7152
.6488
Thick-
ness.
Inches.
.8367
.8333
7550
6394
.8204
.8069
.7242
.7071
953
.8818
7504
.9176
9397
.8750
9322
1.1304
.9476
Thick-
ness.
Inches.
1.3400
1.3466
1.1150
9389
1.2608
1.1750
1.0684
I.OOOO
1.4902
1.2470
1.2508
1.5232
1-4795
1.5000
1.5000
1.9608
1-5452
.*S h ' 333 l 1 IO oJ
t = (.coi6nd) + .013^ + .32
t= (.015^) +.395..
/ ( aoz'&nd) +34
J. F. D'Aubuisson...
Julius Weisbach
Dionysius Lardner. .
Thomas Box
t ( ooTfir) + 78
t - ji^ + . I5 l + _M_
G. L. Molesworth...
Wm. J. M. Rankine.
John Neville
( 10 ) 25000
{.37 for 4" to 12" )
.50 U 12 " 30 >
.62 " 3 " 50 )
,-./Z
V 48
Thos. Hawksley
Baldwin Latham
t = .rtVd
whd
t + .2";
James B. Francis. . .
Thos. J. Whitman...
M. C. Meigs
J H Shedd
28.85 1 5 "
t = (.000058^^9 + .0152^ + .312
t = (.oo45</) + .4 .oo-Lid
t ( 0260416^) +25
J? ~~ ( oooo8A</) + old + .36
J F Ward
Jos. P. Davis
t = (.oo475rf) + .35
In which / = thickness of pipe wall, in inches.
d = interior diameter of pipe, in inches.
h head of water, in feet
w = weight of a cubic foot of water, = 62.5 Ibs.
= number of atmospheres of pressure, at 33 feet each.
/ = pressure of water, in pounds per square inch.
.S 1 = ultimate tenacity of cast-iron, in pounds per square inch.
WEIGHTS OF CAST-IRON PIPES. 467
V=(d + 1.08Q x t x TT x 12. (15)
Let Wi be the weight per cubic inch of the metal
(= .2604 Ibs.), and w the average weight per foot of the pipe,
then we have for equation of average weight per foot, of
twelve-foot pipes,
w = 12 (d + 1.08Q t n w,. (16)
t
To compute the average weight per lineal foot of an
18-inch diameter pipe, twelve feet long, and f J inch thick in
the shell, assign the numerical value to the symbols, and
the equation is :
w = 12 [18 + (1.08 x .65625)] x .65625 x 3.1416 x .2604
= 120.58 pounds.
In the equation, 12, TT, and Wi are constants, and may be
united, and their product (= 9.81687) supply their place in
the equation, when the equation for average weight per
foot is,
w = 9.82 (d + 1.08Q ' * ; (17)
and for the total weight of a 12-foot pipe :
W = 117.8 (d + 1.08Q t. (18)
462. Table of Weights of Cast-iron Pipes, The
following table gives minimum weights of three classes of
cast-iron pipes, of good, tough, and elastic cast-iron (with
8 = 18,000 Ibs.), for heads up to 300 ft. ; also, approximate
weights of lead required per joint for the respective diam-
eters, from 4 to 48 inches, inclusive.
468
MAINS AND DISTRIBUTION-PIPES.
TABLE No. 98.
MINIMUM WEIGHTS OF CAST-IRON PIPES.
CLASS A.
CLASS B.
CLASS C.
Head, n6feet.
Head, 230 feet.
Head, 300 feet.
Pressure, 50 Ibs.
Pressure, 100 Ibs.
Pressure, 130 Ibs.
.
c
1
>
1
% ^
ej
, L
& >
Bl
I
B
*j < o
- 1 - 1 ^ PS
JL-f
.s
a
P
o
til
<u S x
II
'-> +J
1
f||
ft
|
jj 5
If
o
en
c
*
hoc N
r*
||
I
|l|
3|
c
o
3
\*\
I"!
1
1
> n
H
H
> if
^ g
^
H
> n
H"
Q
in.
r*.
IBs.
/^.
in.
/&.
Ibs.
in.
Ibs.
Ibs.
in.
Ibs.
4
.4033
17.57
211
43"
18.94
227
4477
19.69
236
i|
4-25
6
8
4383
4734
27.87
39.67
Si
.4800
.5289
30.71
44.5
369
534
5050
.5622
32.43
47-49
570
if
6.25
8.25
10
5083
52.66
632
5777
60.25
7 2 3
.6194
64.85
778
T H
10.25
12
5433
67.12
805
.6266
76.20
914
.6766
84-53
1014
2
13.00
3
x!
83.04
100.90
996
I2II
6755
.7277
97.68
"9-93
1172
1439
7338
106.54
I3L45
1278
2
15.00
24.25
18
20
.6483
.6833
"9-35
1432
l6 7
7733
.8222
143.00
168.61
1716
2023
9055
1 57-5 I
186.45
^890
2237
3
27.25
30-75
22
.7183
160.64
1928
.8711
196.00
2352
.9628
217.74
2613
2 i
35-25
24
2 7
183.55
220.53
2203
2646
.9200
9933
225.75
273.76
2709
3285
.0200
.1058
25L33
306.15
3016
3674
S
38.25
51-25
30
.9108
.9633
260.66
304.00
350.31
3128
3648!
4204
1.0666
1.1400
1.2183
326.01
383-13
444.48
3912
4598
5334
.1916
2775
3633
366.00
43 I - I 5
501.48
4392
5i74
6018
2
28
56.75
62.25
79-50
40
3
1.0333
1.1033
1.1733
417.20
489.50
567-63
5006
6812
1.3111
1.4088
1.5066
533-iS
629.70
734-iQ
6398
7556
8809
4778
5921
.7066
603.45
7I4-55
835.00
7241
8575
10020
5
88.75
107.75
III.OO
The following table gives the weights of pipes that have
"been used by various water departments for their maximum
pressures :
* Vide thicknesses of pipes in Table No. 93, p. 455.
INTERCHANGEABLE JOINTS.
469
TABLE No.
WEIGHTS OF CAST-IRON PIPES, AS USED IN SEVERAL CITIES FOR
THEIR MAXIMUM PRESSURES.
DELPHIA.
o
S5
w
K
O
3
t
S3
s
6
o
3ENCE.
J
p
H
(5
Id
S
<
Q
Z
O
\UKEE.
a
X
u
PH
&
I
1
CQ
S
u
X
O
i
OH
U
1
I
3
X
u
X
u
"
1
2
a
H
s
$
Maximum Head, in feet
|
fi
Q
R.
R.
R.
R.
R.
R.
S.-P.I R. R.
S.-P.
S.-P.
R. &
D.-P.
D.-P.
R.
R. &
S.-P.
250
100
180
218
198
170
125 1 l8ol 200l 260
175
200
250
237
200
Average "Weights, per lineal foot, in pounds.
T? 1
14
000\*.<j
19
3 1
42
.?.
20
5
28 1
40
18
55
35
sef
50
'33J
49
34
49
24
ii
it
20
32
45
20
3
45
35
5
4 6
t-6
87
col
60
12
71
86
81
85
90
85
83!
85"
8.S
123
85
75
86
100
87
12
3
*I25
S
124
130
128
i
17O
I2Q 1
20
24
3
37
330
170
235
340
231
337
200
208
183
250
178!
2 39
2413
239
257
i
265
334
202
257
170
230
330
%
20
24
30
350
407 '-
325
06
-icH
400
13
45
472
412
^6
585 696
606
(U
48
The initials in the horizontal column of heads indicate the systems of pressure, viz., R M res-
ervoir ; S.-P., stand-pipe ; and D.-P., direct pressure.
463. Interchangeable Joints. When several classes
of pipes, varying in weight for similar diameters, enter into
the same system of distribution, as, for instance, in an un-
dulating town, with considerable differences in levels, there
is an advantage in making the exterior diameters the con-
stants, instead of the interiors, for then the spigots and bells
of both plain and special castings, and of valves and
hydrants, have uniformity, and are interchangeable, as occa-
sion requires, and the different classes join each other with-
>ut special fittings.
' The Ottawa pipe weights classed as of 4 and 14 inch diameters are in
5 and 15 inch diameters respectively.
470 MAINS AND DISTRIBUTION-PIPES.
If it is objectionable to increase and decrease the interior
diameters of the light and heavy classes, then the object
may be attained by increasing the thickness of the ends of
the light and medium classes, so far as they enter the hubs.
464. Characteristics of Pipe-Metals. The metal
of pipes should be tough and elastic, and have great
tenacity. In proportion as these qualities are lacking, bulk
of metal, increased in a geometrical ratio, must be sub-
stituted to produce their equivalents. In our formula given
above ( 452) for thickness of cast-iron, it will be re-
membered that we were obliged to add a term of thickness
j .333(1 ;j--A I to enable the pipes to be safely handled.
If the metal is given great degrees of toughness and elas-
ticity, we may omit, for the larger pipes, this last member
of the formula ; but now we add to each twelve-foot piece
of pipe, of 20-inch diameter, five or six hundred pounds ;
36-inch diameter, six or eight hundred pounds, etc., that
would not be required with a superior metal.
It is expensive to freight this extra metal a hundred or
more miles, and then to haul it to the trenches and swing it
into place, and at the same time to submit to the breakage
of from three to five per cent, of the castings because of the
brittleness of the inferior metal.
It is well known that the same qualities of iron stone, and
of fuel, may produce from the same furnace very different
qualities of pigs, and it is the smelter's business to know,
and he generally does know, whether he has so proportioned
his materials and controlled his blast, as to produce pigs
that when remelted will flow freely into the mould, take
sharply its form, and become tough and elastic castings.
The founders will supply a refined and homogeneous iron,
if such quality is clearly specified, and it is well worthy of
CHARACTERISTICS OF PIPE METALS. 471
consideration in the majority of cases whether such iron
will not be in fact the most economical, at its fair additional
cost, if extra weight, extra freight and haulage, and extra
breakage, are duly considered.
Expert inspectors cannot with confidence pronounce
upon the quality of the cast metal from an examination
of its exterior appearance, nor infallibly from the appear-
ance of its fracture. Wilkie says * of the fracture of good
No. 1 cast-iron, that it shows a dark gray color - nth high
metallic lustre ; the crystals are large, many of them shining
like particles of freshly-cut lead ; and that however thin
the metal may be cast, it retains its dark gray color. It
contains from three to five per cent, of carbon. This is
the most fusible pig iron and most fluid when melted, and
superior castings may be produced from it.
No. 3 has smaller and closer crystals, which diminish in
size and brightness from the centre of the casting toward
the edge. Its color is a lighter gray than No. 1, with less
lustre. No. 2 is intermediate in appearance and quality
between Nos. 1 and 3.
The "bright," "mottled," and "white" irons have still
lighter colored fractures, with a white "list" at the edges,
are less fusible, and are more crude, hard, and brittle.
The mottled and white irons are sometimes produced by
the furnace working badly, or result from using a minimum
of fuel with the ore and flux.
The crystals of the coarser kinds of cast-irons were found
by Dr. Schott, in his microscopical examinations of frac-
tures, to be nearly cubical, and to become flatter as the
proportion of carbon decreased and the grain became more
uniform.
* " The manufacture of Iron in Great Britain." London, 1857.
472 MAINS AND DISTRIBUTION PIPES.
In wrought iron, the double pyramidal form of the cast
crystal is almost lost, and has become flattened down to
parallel leaves, forming what is termed the fibre of the iron.
In steel the crystals have become quite parallel and
fibrous.
465. Tests of Pipe Metals. The toughness and elas-
ticity of pipe metal may be tested by taking sample rings
of, say, 24-inch diameter, 1-inch width, and f -inch thickness,
hanging them upon a blunt knife-edge, and then suspending
weights from them, at -a point opposite to their support,
noting their deflections down to the breaking point ; also, by
letting similar rings fall from known heights upon solid an-
vils. The iron may also be submitted to what is termed the
"beam test," generally adopted to measure the transverse
strength and elasticity of castings for building purposes.
In such case the standard bar, Fig. 99, is 3 ft. 6 in. long,
2 in. deep, and 1 in. broad, and
FlG - " is placed on bearings 3 ft. apart,
and is loaded in the middle till
broken.
Iron that has been first skill-
fully made into pigs, from good
ore and with good fuel, and has
then been remelted, should sustain in the above described
beam test, from 4,000 to 4,500 pounds, and submit to a de-
flection of from ^ to J-inch.
The tenacity of the iron is usually measured by submit-
ting it to direct tensile strain in a testing machine, fitted for
the purpose. Its tenacity should reach an ultimate limit
of 25,000 pounds per square inch of breaking section, while
still remaining tough and elastic. Hard and brittle irons
may show a much greater tenacity, though making less
valuable pipes.
THE PRESERVATION OF PIPE SURFACES. 473
466. The Preservation of Pipe Surfaces. The
uncoated iron mains first laid down in London, by the New
River Company, were supposed to impart a chalybeate
quality to the water, and a wash of lime-water was applied
to the interiors of the pipes before laying to remedy this evil.
Before iron pipes had been long in use, in the early part
of the present century, in those European towns and cities
supplied with soft water, it was discovered that tuberculous
accretions had formed so freely upon their interiors as to
seriously diminish the volume of flow through the pipes of
three, four, and six-inch diameters.
This difficulty, which was so serious as to necessitate the
laying of larger distribution pipes than would otherwise
have been necessary, engaged the attention of British and
continental engineers and chemists from time to time. Many
experimental coatings were applied, of silicates and oxides,
and the pipes were subjected to baths of hot oil under
pressure, with the hope of fully remedying the difficulty.
A committee of the British Association also inquired into
the matter in connection with the subject of the preservation
of iron ships, and instituted valuable experiments, which
are described in two reports of Robert Mallet to the Asso-
ciation.
A similar difficulty was experienced with the uncoated
iron pipes first laid in Philadelphia and New York.
In the report of the city engineer of Boston, January,
L852, mention is made of some pipes taken up at the South
Boston drawbridge, which had been exposed to the flow
of Cochituate water nine years.
He remarks that " some of the pipes were covered inter-
nally with tubercles which measured about two inches in
area on their surfaces, by about three-quarters of an inch
in height, while others had scarcely a lump raised in them.
474 MAINS AND DISTHIBUTION-PIPES.
Those which were covered with the tubercles were corroded
to a depth of about one- sixteenth of an inch ; the iron to
that depth cutting with the knife very much like plumbago."
Mr. Slade, the engineer, expressed the opinion, after com-
paring the condition of these pipes with that of pipes exam-
ined in 1852, that the corrosion is very energetic at first,
but that it gradually decreases in energy year by year.
The process used by Mons. Le Beuffe, civil engineer of
Vesoul, France, for the defence of pipes, as communicated*
by him to Mr. Kirk wood, chief engineer of the Brooklyn
Water- works, " consists of a mixture of linseed oil and
beeswax, applied at a high temperature, the pipe being
heated and dipped into the hot mixture.
The varnish of M. Crouziere, tested on iron immersed in
sea-water at Toulon, by the French navy, consisted of a
mixture of sulphur, rosin, tar, gutta-percha, minum, blanch
de ceruse, and turpentine. This protected a plate of
wrought iron perfectly during the year it was immersed.
A process that has proved very successful for the preser-
vation of iron pipes used to convey acidulated waters from
German mines, is as follows :f "The pipes to be coated
are first exposed for three hours in a bath of diluted sul-
phuric or hydrochloric acid, and afterward brushed with
water ; they then receive an under-coating composed of
34 parts of silica, 15 of borax, and 2 of soda, and are ex-
posed for ten minutes in a retort to a dull red heat. After
that the upper coating, consisting of a mixture of 34 parts
of feldspar, 19 of silica, 24 of borax, 16 of oxide of tin, 4 of
fluorspar, 9 of soda, and 3 of saltpetre, is laid over the inte-
rior surface, and the pipes are exposed to a white heat for
twenty minutes in a retort, when the enamel perfectly unites
* Vide Descriptive Memoir of the Brooklyn Water- works, p. 43.' N. Y., 1867.
f Vide "Engineering." London, Jan., 1872, p. 45.
**'>**<'
'*/,, *" '
PRESERVATION OF PIPE SURFACES. w/ / y V ; 475
with the cast-iron. Before the pipes are quite cooled down,
their outside is painted with coal-tar. The above ingre-
dients of the upper coating are melted to a mass in a cru-
cible, and afterwards with little water ground to a fine
paste."
Prof. Barff, M.A., proposes to preserve iron (including
iron water-pipes) by converting its surfaces into the mag-
netic or black oxide of iron, which undergoes no change
whatever in the presence of moisture and atmospheric
oxygen.
He says, "The method which long experience has taught
us is the best for carrying out this process for the protection
of iron articles, of common use, is to raise the temperature
of those articles, in a suitable chamber, say to 500 F., and
then pass steam from a suitable generator into this cham-
ber, keeping these articles for five,- six, or seven hours, as
the case may be, at that temperature in an atmosphere of
superheated steam.
" At a temperature of 1200 F., and under an exposure
to superheated steam for six or seven hours, the iron surface
becomes so changed that it will stand the action of water
for any length of time, even if that water be impregnated
with the acid fumes of the laboratory."
The first coated pipes used in the United States, were
imported from a Glasgow foundry in 1858. These were
coated by Dr. Angus Smith's patent process, which had
been introduced in England about eight years earlier.
Dr. Smith's Coal Pitch Varnish is distilled from coal-tar
until the naphtha is entirely removed and the material
deodorized, and Dr. Smith recommends the addition of five
or six per cent, of linseed oil.
The pitch is carefully heated in a tank that is suitable
to receive the pipes to be coated, to a temperature of about
476 MAINS AND DISTRIBUTION-PIPES.
300 degrees, when the pipes are immersed in it and allowed
to remain until they attain a temperature of 300 Fah.
A more satisfactory treatment is to heat the pipes in a
retort or oven to a temperature of about 310 Fah., and
then immerse them in the bath of pitch, whicli is maintained
at a temperature of not less than 210.
When linseed oil is mixed with the pitch, it has a ten-
dency at high temperature to separate and float upon the
pitch. An oil derived by distillation from coal-tar is more
frequently substituted for the linseed oil, in practice.
The pipes should be free from rust and strictly clean
when they are immersed in the pitch-bath.
467. Varnishes for Pipes and Iron-work. A good
tar varnish, for covering the exteriors of pipes where they
are exposed, as in pump and gate houses, and for exposed
iron work generally, is mentioned* by Ewing Matheson,
and is composed as follows : 30 gallons of coal-tar fresh,
with all its naphtha retained ; 6 Ibs. tallow ; 1 J Ibs. resin ;
3 Ibs. lampblack ; 30 Ibs. fresh slacked lime, finely sifted.
These ingredients are to be intimately mixed and applied
hot. This varnish may be covered with the ordinary lin-
seed-oil paints as occasion requires.
A Hack varnish, that has been recommended for out-
door iron work, is composed as follows : 20 Ibs. tar-oil ;
5 Ibs. asphaltum ; 5 Ibs. powdered rosin. These are to be
mixed hot in an iron kettle, with care to prevent ignition.
The varnish may be applied cold.
468. Hydraulic Proof of Pipes. When the cast-
iron pipes have received their preservative coating, they
should be placed in an hydraulic proving-press, and tested
by water pressure, to 300 Ibs. per sq. in. ; and while under
" Works in Iron," p. 281. London, 1873.
HYDKAULIC PROOF OF PIPES.
477
the pressure be smartly rung with, a hammer, to test them
for minor defects in casting, and for undue internal strains.
Fig. 100 is one of the most simple forms of hydraulic
proving-presses. The cast-iron head upon the left is fixed
stationary, while toward the right is a strong head that is
movable, and that advances and retreats by the action of
FIG. 100.
the screw working in the nut of the fixed head at the right.
When the pipe is rolled into position for a test, suitable
gaskets are placed upon its ends, or against the two heads,
and then by a few turns of the hand- wheel of the screw, the
movable head is set up so as to press the pipe between the
two heads. Levers are then applied to the screw, and the
pressure increased till there will be no leakage of water at
the ends past the gaskets. The air-cock at the right is then
opened to permit escape of the air, and the water- valve at
the left opened to fill the pipe with water. The hydraulic
pump and the water-pressure gauge, which are attached at
the left, are not shown in the engraving. When the pipe is
filled with water, and the valves closed, the requisite pres-
sure is then applied by means of the pump. Care must be
taken that all the air is expelled, before pressure is applied,
lest in case of a split, the compressed air may scatter the
pieces of iron with disastrous results.
FIG. 101.
W////////////////K ' '////MW/W////
SINGLE BRANCH.
FIG. 102.
FIG. 103.
CEMENT-LINED AND COATED PIPES.
479
469. Special Pipes. Fig. 101 is a section through a
single Branch, with side views of lugs for securing a cap or
hydrant branch.
Fig. 102 is a section through a Reducer.
Fig. 103 is a section through a Bend.
FIG. 104.
FIG. 105.
Fig. 104 is a section through a Sleeve, the upper half
being the form for covering cut ends of pipes, and the lower
half the form for uncut spigot ends.
Fig. 105 is a part section and plan of a clamp Sleeve.
WROUGHT-IRON PIPES
47O. Cement-Lined and Coated Pipes. Sheet-iron
water-pipes, lined and coated with hydraulic cement mor-
tar, by a process invented by Jonathan Ball, were laid in
Saratoga, N. Y., to conduct a supply of water for domestic
purposes to some of the citizens, as early as 1845.
The inventor, who was aware of the ready corrosion of
wrought-iron when exposed to a flow of water and to the
dampness and acids of the earth, had observed the pre-
servative influence of lime and cement when applied to iron,
and saw that with its aid, the high tensile strength of
480 MAINS AND DISTRIBUTION-PIPES.
wrought or rolled iron, could be utilized in water-pipes to
sustain considerable pressures of water, and the weight of
the iron required, thus be materially reduced.
The reduction in the weight of the iron reduced also the
total cost of the complete pipe in the trench.
The favorable qualities of hydraulic cement as a conduc-
tor of potable waters had long been well-known, for the
Romans invariably lined their aqueducts and conduits
with it.
Twenty-five or thirty towns and villages, and a number
of corporate water companies had already adopted the
wrought-iron cement-lined water pipes in their systems, and
still others were experimenting with it at the breaking out
of the civil war in 1861.
As one result of the war, the price of iron* rose to more
than double its former value, and the difference in cost be-
tween cast and wrought iron pipes became conspicuous, and
the cost of all pipes rose to so great total sums that the pipe
of least first cost must of necessity be adopted in most
instances, almost regardless of comparative merits. So
long as the high prices of iron and of labor remained firm,
the contractors for the wrought-iron were enabled to lay it
at a reduction of forty per cent, from the cost of the cast-
iron pipe.
Increased attention to sanitary improvements led many
towns to complete their water supplies even at the high
rates, and many hundred miles of the cement-lined pipes
came into use.
471. Methods of Lining. Its manufacture is simple.
The sheet-iron is formed and closely riveted into cylinders
* New York and Philadelphia prices current record the nearly regular
average monthly increase in the price of Anthracite Pig Iron No. 1, from 18f
dollars per ton of 2240 pounds in August, 1861, to 73f dollars per ton in
August, 1864.
COVERING. 481
of seven or eight feet in length, and of diameter from one
to one and one-half inches greater than the clear bore of the
lining is to be finished. The pipe is then set upright and a
short cylinder, of diameter equal to the desired bore of the
pipe, is lowered to the bottom of the pipe. Some freshly
mixed hydraulic cement mortar is then thrown into the pipe
and the cylinder, which has a cone-shaped front ; and guid-
ing spurs to maintain its central position in the shell, is
drawn up through the mortar. A uniform lining of the
mortar is thus compressed within the wrought-iron shell.
The ends are then dressed up with mortar by the aid of a
small trowel or spatula, and the pipes carefully placed upon
skids to remain until the cement is set.
The interiors of the pipe-linings are treated to a wash of
liquid cement while they are still fresh, so as to fill their pores.
In another process of lining, a smoothly-turned cylin-
drical mandril of iron, equal in length to the full length of
the pipe, and in diameter to the diameter of the finished
bore, is used to form the bore, and to compress the lining
within the shell. A fortnight or three weeks is required for
the cement to set so as safely to bear transportation or haul-
age to the trenches. In the meantime the iron is or should
be protected from storms and moisture, and also from the
direct rays of the sun, which unduly expands the iron, and
separates it from a portion of the cement lining.
472. Covering. When these pipes are laid in the
trench, a bed of cement mortar is prepared to receive them,
and they are entirely coated with about one inch thickness
of cement mortar, as is shown in the vertical section of a
six-inch pipe, Fig. 106.
The writer has used upwards of one hundred miles of
this kind of pipes, and the smaller sizes have proved uni-
formly successful.
31
482
MAINS AND DISTRIBUTION-PIPES.
FIG. 106.
The iron is relied upon wholly to sustain the pressure
of the water and resist the effects of water-rams. The
cement is depended upon to preserve the iron, which object
it has accomplished during the term these pipes have been
in use, when the cement was good and workmanship faith-
ful, which, unfortunately for this class of pipe, has not
always been the case, and the reputation of the pipe has
suffered in consequence.
FIG. 107.
473. Cement- Joint. A sheet -iron sleeve, about eight
inches long, as shown in Fig. 107, is used in the common
form of joint to cover the abutting ends of the pipe as they
are laid in the trench.
The diameter of the sleeve is about one inch greater than
the diameter of the wrought-iron pipe shell, and the annular
space between the pipe and sleeve is filled with cement. The
sleeve and pipe are then covered with cement mortar.
In a more recently patented form of pipe, the shell has a
taper of about one inch in a seven-foot piece of pipe, and
CAST HUB-JOINTS.
483
the small end of one piece of pipe enters about four inches
into the large end of the adjoining pipe, thus forming a
lap without a special sleeve. The thickness of lining in
these pipes varies, but the bore is made uniform.
474. Cast Hub- Joints. The writer having experienced
some difficulty with both the above forms of cement-joints, of
the larger diameters, and desiring to substitute lead pack-
ings for the cement, in a 20-inch force main, to be subjected
to great strains, devised the form of joint shown in Fig. 108.
FIG. 108.
In this case the wrought-iron shells were riveted up as
for the common 20-inch pipe, and then the pipe was set
upon end in a foundry near at hand, a form of bell moulded
about one end, and molten iron poured in, completing the
"bell in the usual form of cast-iron bell. A spigot is cast
upon the opposite end in a similar manner. The lead pack-
ig is then poured and driven up with a set, as the pipes
laid, as is usual with cast-iron pipes. The joint is as
Lccessfui in every respect as are the lead-joints of casiriron
ipes.
The force-main in question has been in use upwards of
years, and water was, during several months of its
484
MAINS AND DISTRIBUTION-PIPES.
earliest use, pumped through it into the distribution pipes,
on the direct pumping system.
For lead joints on wrought-iron pipes from ten to sixteen
inches diameter inclusive, about four inches width of the
edge of the spigot end sheet may be rolled thicker, so as to
bear the strain of caulking the lead, as a substitute for the
cast spigot.
475. Composite Branches. The wrought - iron
branches were originally joined to their mains by the appli-
cation of solder, the iron being first tinned near and at the
junction. After the successful pouring of the bells, the
experiment was tried of uniting the parts by pouring molten
metal into a mould, formed about them, the metal being
FIG. 109.
cast partly outside and partly inside the pipes, as in the
case of the hub-joint. The parts were rigidly and very sub-
stantially united by the process, which is in practical effecl
equal to a weld.
Fig. 109 shows a section of a double six-inch branch o]
a twelve-inch sub-main.
THICKNESS OF SHELLS FOR CEMENT LININGS.
485
Fig. 110 is a section of a wrouglit-iron angle with its
parts united by a cast union.
Several holes, similar to the rivet holes of the pipe, are
punched near the ends to be united at different points in
the circumference, so that the metal flows through them,
as shown in the sketches.
FIG. 110.
The writer has used these branches and angles exclu-
sively in several cities, in wrought-iron portions of the
distribution-pipes, without a single failure.
476. Thickness of Shells for Cement Linings.
When computing the thickness of sheets for the shells of
wrought-iron cement-lined pipes, the internal diameter of
the shell itself, and not of finished bore, is to be taken.
The longitudinal joints of the shells for pipes of 12-inch and
iter diameters, should be closely double riveted.
The tensile strength of the shells, when made of the best
Lates, may be assumed, if single riveted, 36,000 pounds
per square inch, and double riveted 40,000 pounds per
square inch.
A formula of thickness, given above, with factor of
safety = 4, in addition to allowance for water-ram, may be
used to compute the thickness of plates, viz.:
(19)
486
MAINS AND DISTRIBUTION-PIPES.
in which t is the thickness of rolled plate, in inches.
d " diameter of the shell, in inches.
p " static pressure due to the head in Ibs. per
sq. in. = .434 7i.
S " tenacity of riveted shells, in Ibs. per. sq. in.
The following table gives the thickness of shells for
cement linings, and the nearest No. of Birmingham gauge
in excess, suitable for heads of from 100 to 300 feet, by
formula,
*-(p-
TABLE No. 99.
THICKNESS OF WROUGHT IRON PIPE SHELLS.
(Diameters 4" to 10" single riveted, S = s6,ooolbs. Diameters 12" and upward, double riveted,
S = 40,000 Ibs.)
HEAD 116 FEET.
HEAD 175 FEET.
HEAD 300 FEET.
DIAMETER
OF BORE.
DIAMETER
OF SHELL.
Thickness
by
Formula.
Nearest
No. Birm.
Gauge in
Excess.
Thickness
by
Formula.
Nearest
No. Birm.
Gauge in
Excess.
Thickness
by
Formula.
Nearest
No. Birm.
Gauge in
Excess.
Inches.
Inches.
Inches.
Inches.
Inches.
4
5
.0417
*9
.0486
18
.0639
16
6
7
.0528
17
.0681
15
.0894
13
8
9-25
.0771
15
.0899
13
.1182
ii
10
11.25
0937
13
.1094
12
1437
9
12
T 3-25
.0994
12
IT 59
II
.1524
8
14
15-25
.1144
12
1334
10
-1754
7
16
17-5
1313
10
1532
8
.2OI2
6
18
ip-5
.1463
9
.1706
7
.2242
5
20
21.5
.1613
8
.1881
6
.2472
3
22
23-5
.I76 3
7
.2056
5
.2702
2
24
2 5-5
.1913
6
.2236
4
.2932
I
Shells having less factors of safety than our formula
gives, have been used in many small works. A factor
equal to 6, to include effect of water-ram, should always
LINING COVERING, AND JOINT MORTAR. 487
taken, and this may be found directly by a formula in the
following form :
477. Gauge Thickness and Weights of Rolled
Iron. The following table (No. 100) gives the thicknesses
and weights of sheet-iron, corresponding to Birmingham
gauge numbers ; also thicknesses and weights increasing
by sixteenths of an inch.
478. Lining, Covering, and Joint Mortar. The
lining mortar and covering mortar should have the volume
of cement somewhat in excess of the volume of voids in the
sand, or, for linings, equal parts of the best hydraulic
cement and fine-grained, sharp, silicious sand; and, for
coverings, two-fifths like cement and three-fifths like sand.
The joint mortar should be of clear cement, or may be
of four parts of good Portland cement, and one part of
hydraulic lime, with just enough water to reduce it to a
stiff paste.
This kind of pipe demands very good materials for all
its parts, and the most thorough and faithful workmanship.
A concrete foundation should be laid for it in quicksand,
or on a soft bottom, and a bed of gravel, well rammed,
should be laid for it in rock trench, and exceeding care
must be taken in replacing the trench back-fillings. Poor
materials or slighted workmanship will surely lead to after
annoyance.
Some of the cement-lined pipes are given a bath in hot
asphaltum before their linings are applied. In such case, a
sprinkling of clean, sharp sand over their surfaces imme-
diately after the bath, while the coating is tacky, assists in
forming bond between the cement and asphaltum.
488
MAINS AND DISTRIBUTION-PIPES.
TABLE No. 1OO.
THICKNESSES AND WEIGHTS OF PLATE-IRON.
Birming-
ham
gauge
No.
Thickness.
Weight of a
square foot.
Thickness,
in
sixteenths
of an inch.
Thickness,
in decimals of
an inch.
Weight of
a square foot
Inches.
Pounds.
Inches.
Inches.
Pounds.
OOOO
-454
18.35
A
.03125
1.263
000
425
I7.I8
yV
.06250
2.526
00
.38
15.36
A
09375
3.789
34
x 3-74
k
.12500
5.052
I
3
12.13
A
.15625
6.315
2
.284
11.48
A
.18750
7.578
3
259
10.47
A
.21875
8.841
4
238
9.619
\
.25OOO
IO.IO
5
.22
8.892
A
.28125
H-37
6
.203
8.205
~TZ
^SO
12.63
7
.18
7.275
ii
34375
13.89
8
I6 5
6.669
i
.37500
15.16
9
.148
5.981
H
.40625
16.42
10
.134
5.416
lV
43750
17.68
ii
.12
4.850
T
46875
18.95
12
13
.109
-95
4-405
3.840
A
.50000
56250
20.21
22.73
14
.083
3-355
1
.62500
25.26
15
.072
2.910
tt
.68750
27-79
16
.065
2.627
i
.75000
30.31
17
.058
2.344
Jt
.81250
32.84
18
.049
.980
7
"g"
.87500
35-37
19
.042
.697
tt
.93750
37.89
20
35
415
I
i
40.42
21
.032
293
T rV
1.06250
42.94
22
.028
.132
4
1.12500
4547
23
025
I.OIO
1.18750
48.00
24
.022
.8892
if
1.25000
50-5 2
25
.02
.8083
1.31250
53.05
26
.018
7225
if
L37500
55-57
27
.016
.6467
1.43750
58.10
28
.OI4
5658
ij
1.50000
60.63
29
.013
5254
T T%
1.56250
63-15
30
.012
.4850
14
1.62500
65.68
31
.010
.4042
I T6'
1.68750
68.20
32
.009
.3638
I t
1.75000
70.73
33
.008
3233
I T
1.81250
73.26
34
.007
.2829
4
1.87500
75.78
35
.005
.2021
'If
1-9375
78.31
36
.004
.1617
2
2
80.83
ASPHALTUM-BATH FOR PIPES.
489
479. Asphaltum-coateil Wrought-iron Pipes.
Wrought-iron pipes, coated with asphaltum, have been
used almost exclusively in California, Nevada, and Oregon,
some of those of the San Francisco water supply being
thirty inches in diameter.
Some of these wrought-iron pipes, in siphons, are sub-
jected to great pressure, as, for instance, in the Virginia
City, Nevada, supply main, leading water from Marlette
Lake.
This main is 11| inches diameter, and 37,100 feet in
length, and crosses a deep valley between the lake, upon
one mountain and Virginia City upon another. The inlet,
where the pipe receives the water of the lake, is 2,098 feet
above the lowest depression of the pipe in the valley, where
it passes under the Virginia and Truckee Railroad, and the
delivery end is 1528 feet above the same depression. A
portion of the pipe is subjected to a steady static strain of
750 pounds per square inch.
The thickness of this pipe-shell varies, according to the
pressure upon it, as follows :
Head in feet <
200
or
200
to
33
to
430
to
570
to
7 00
to
95
to
1050
to
1250
to
1400
and
less.
33>
43
57
700
950
1050
1250
1400
over.
No. of iron, Birmingham gauge . . .
16
15
14
12
II
9
7
5
3
Thickness in inches
.06 5
087
.IOQ
.12
.148
.18
.22
250
The joints are covered with a sleeve, and the joint pack-
ing is of lead.
48O. Asphaltum -Bath for Pipes. A description of
the asphaltum coating, as prepared for these pipes by
Herman Schussler, C.E., under whose direction many pipes
have been laid, is given in the January, 1874, Report of
J. Nelson Tubbs, Esq., Chief Engineer of the Rochester
Water- works, as follows, in Mr. Schussler' s language :
490 MAINS AND DISTRIBUTION-PIPES.
"The purest quality of asphaltum (we use the Santa
Barbara) is selected and broken into pieces of from the size
of a hen' s egg to that of a fist. With this, three or four
round kettles are filled full, then the interstices are filled
with the best quality of coal tar (free from oily substances),
and boiled from three to four hours, until the entire kettle
charge is one semi-fluid mass, it being frequently stirred up.
The best and most practical test then, as to the suitability
of the mixture, is to take a piece of sheet-iron of the thick-
ness the pipe is made of, say six inches square, it being
cold and freed from impurities, and dip it into the boiling
mass, and keep it there from five to seven minutes. Imme-
diately after taking it out, plunge it into cold water, if
possible near the freezing-point, and if, after removal from
the water, the coating don't become brittle, so as to jump
off the iron in chips, by knocking it with a hammer, but
firmly adheres (like the tin coating to galvanized iron), the
coat is good and will last for ages. If, on the other hand,
it is brittle, it shows that there is either too much oil in the
tar or asphaltum, or the mixture was boiled too hot, or
there was too much coal-tar in the mixture ; as adding coal-
tar makes the mixture brittle, while by adding asphaltum
it becomes tough and pliable. The pipes are immersed in
the bath as thus prepared."
Wrought-iron pipes of this description are extensively
used in France, in diameters up to 48 inches.
They are first subjected to a bath of hot asphaltum, and
then the exteriors are coated with an asphaltum concrete,
into which some sand is introduced, as into the cement-
covering above described.
481. Wrought Pipe Plates. The shells of wrought-
iron conduits and pipes should be of the best rolled plates,
of tough and ductile quality, of ultimate strength not less
WYCKOFFS PATENT PIPE. 491
than 55,000 Ibs. per square inch, and that will elongate
fifteen per cent, and reduce in sectional area twenty -five per
cent, before fracture.
WOOD PIPES.
482. Bored Pipes. The wooden pipes used to replace
the leaden pipes, in London, that were destroyed by the
great fire, three-quarters of a century ago, reached a total
length exceeding four hundred miles. These pipes were
bored with a peculiar core-auger, that cut them out in
nests, so that small pipes were made from cores of larger
pipes.
The earliest water-mains laid in America were chiefly of
bored logs, and recent excavations in the older towns and
cities have often uncovered the old cedar, pitch-pine, or
chestnut pipe-logs that had many years before been laid by
a single, or a few associated citizens, for a neighborhood
supply of water.
Bored pine logs, with conical faucet and spigot ends,
and with faucet ends strengthened by wrought-iron bands,
were laid in Philadelphia as early as 1797.
Detroit had at one time one hundred and thirty miles of
small wood water-pipes in her streets.
483. Wyckoff's Patent Pipe. A patent wood pipe,
manufactured at Bay City, Michigan, has recently been
laid in several western towns and cities, and has developed
an unusual strength for wood pipes. Its chief peculiarities
are, a spiral banding of hoop-iron, to increase its resistance
to pressure and water-ram ; a coating of asphaltum, to
preserve the exterior of the shell ; and a special form of
thimble-joint.
Fig. Ill is a longitudinal section through a joint of this
wood pipe, showing the manner of inserting the thimble,
492 MAINS AND DISTRIBUTION-PIPES.
FIG. 111.
and Fig. 112 is .an exterior view of the pipe, showing the
spiral banding of hoop-iron, and the asphaltum covering.
The manufacturer's circular, from which the illustra-
tions are copied, states that the pipes made under this
FIG. 112.
patent are from white pine logs, in sections eight feet long.
The size of the pipes is limited only by the size of the suit-
able logs procurable for their manufacture.
Judged by schedules of factory prices, these pipes do
not appear to be cheaper in first cost than wrought-iron
pipes.
FIGS. 114, 115.
FLOWERS STOP-VALVE. (.blowers Brothers, Detroit.)
FIGS. 116, 117.
COFFIN'S STOP- VALVE. (Boston Machine Co., Boston.)
CHAPTEE XXII.
DISTRIBUTION SYSTEMS, AND APPENDAGES.
484. Loss of Head by Friction. In the chapter
upon flow of water in pipes (XIII, ante), we have discussed
at length the question of the maximum discharging ca-
pacities of pipes. When planning a system of distribution
pipes for a domestic and fire service, it is quite as import-
ant to know how much of the available head will be con-
sumed by, or will remain after, the passage of a given
quantity of water through a given pipe.
For a really valuable fire service, the effective head
pressure remaining upon the pipes, with full draught,
should be, in commercial and manufacturing sections of a
town, not less than one hundred and fifty feet, and in
suburban sections, not less than one hundred feet.
Water at such elevations, near a town, has a large com-
mercial value, whether it has been lifted by the operations
of nature and retained by ingenuity of man, or has been
pumped up through costly engines and with great expend-
iture of fuel.
When such head pressures are secured at the expense
of pumps and fuel, they are too costly to be squandered in
friction in the pipes. Such frictional loss entails a corre-
sponding daily expense of fuel so long as the works exist.
In such case, the pipes may be economically increased in
size until the daily frictional expense capitalized, approxi-
mates to the additional capital required to increase the
given pipes to the next larger diameters.
494 DISTRIBUTION SYSTEMS, AND APPENDAGES.
The frictional head h" in pipes under pressure, is found
by the formula,
. (1)
The frictional head for a given diameter is as the square
of the velocity, nearly (v 2 m) and, for different diameters,
inversely as the diameters.
The coefficient* m decreases in value as the velocity
increases, and for a given velocity decreases as the diameter
increases.
485. Table of Frictional Heads in Pipes. The
following table (No. 101, p. 493) we have prepared to facili-
tate frictional head calculations, and to show at a glance the
frictional effect of increase of velocity, in given pipes from
4 to 36 inch diameters. The second and last columns show
also the theoretical volume of delivery through clean, smooth
pipes at different given velocities.
The fourth column gives approximate values of the
coefficient m for given diameters and velocities, and for
clean smooth pipes under pressure.
* Vide Table No. 62, page 248, of coefficients (m) for clean, slightly tuber-
culated, and foul pipes ; also 274, page 250, for formula of frictional resist-
ance to flow.
. ^RICTIONAL HEADS IN PIPES.
495
TABL E No. 1 Ol.
FRICTIONAL HEAD IN MAIN AND DISTRIBUTION PIPES (in each
1000 feet length). ti' = V 1 * (qm) -,
Diam.
of
pipe.
Volume of
water
delivered
Velocity
of
flow.
Coefficient
of
friction.
Frictional head
per 1000 feet.
U. S. gallons
in 24 hours.
Inches.
Cu.ft.per
inin.
Feet per
second.
Feet.
Gallons.
4
5
958
.00714
1.221
53,856
7-5
1-437
.00695
2.675
80,784
10
1.916
.00680
4.653
I07JI2
12.5
2.394
.00666
7.114
134,640
15
2.873
.00654
10.06
161,568
17-5
3-295
.00644
13.03
188,496
20
3-831
.00633
17.32
215,424
6
17-5
1.409
.00666
1.643
188,496
20
1.701
.00655
2.355
215,424
22.5
I.9I3
.00648
2.946
242,352
25
2.126
.00646
3.628
269,280
27-5
2-339
.00638
4.337
296,208
30
2-551
.00634
5.126
323.136
35
2.976
.00623
6.855
376,992
40
3.401
.00615
8.838
430,848
45
3.827
.00610
11.100
484,704
,.
8 30
1.429
.00644
1.225
323,136
35
1.685
.00635
1.680
376,992
40
1.905
.00628
2.124
430,848
45
2.143
.00620
2.654
484,704
50
2.381
.00615
3.249
538,560
55
2.619
.00609
3.893
592,416
60
2.857
.00603
4.587
646,272
65
3-095
.00600
5.356
700,128
70
3-331
.00596
6.159
753,984
75
3-571
.00592
7.035
807,840
80
3-809
.00589
7.963
861,696
85
4.048
.00586
8.948
915,552
90
4.298
.00584
10.056
969,408
10
60
1.835
.00614
1.541
646,272
70
2.141
.00606
2.071
753,984
80
2-447
.00597
2.665
861,696
90
2.752
.00590 i 8.331
969,408
100
3-058
.00584
4.071
1,077,120
no
3.364
.00578
4.876
1,184,832
120
3.670
-00572
5.743
1,292,544
130
3-976
.00569
6.706
1,400,256
140
4.281
.00566
7.733
1,507,968
150
4-587
.00562
8.815'
1,615,680
496
DISTRIBUTION SYSTEMS, AND APPENDAGES.
TABLE No. 1O1 (Continued).
FRICTIONAL HEAD IN MAIN AND DISTRIBUTION PIPES (in each
1000 feet length).
Diam.
of
pipe.
Volume of
water
delivered.
Velocity
of
flow.
Coefficient
of
friction.
Frictional head
per 1000 feet.
U. S. gallons
in 24 hours.
Inches.
Cu.ft.per
min.
Feet per
Second.
Feet.
Gallons.
12
1 2O
2.548
.00581
2.343
1,292,544
I 4
2.972
.00571
3.133
1,507,968
1 60
3-397
.00563
4.036
1,723,392
1 80
3.821
00555
5.033
1,938,816
200
4.246
.00551
6.171
2,154,240
22O
4.637
.00546
7.407
2,369,664
240
5-098
.00542
8.755
2,585,088
14
175
2.721
.00560
2. 207
1,884,960
200
3.109
00553
2.845
2,154,240
225
3-498
.00546
3.550
2,423,520
250
3.887
.00542
4.359
2,692,800
275
4-275
.00537
4.989
2,962,080
300
4-665
.00538
6.232
3,231,360
325
5-053
.00530
7.203
3,500,640
350
5-597
.00524
8.738
3,769,920
16
225
2.682
00554
1.857
2,423,520
250
3.099
.00538
2.408
2,692,800
275
3.226
.00536
2.599
2,962,080
300
3.576
.00530
3.158
3,231,360
325
3.874
.00526
3.679
3,500,640
350
4.172
.00523
4-242
3,769,920
375
4.471
.00520
4.844
4,039,200
400
4.768
.00518
5.488
4,308,480
425
5.066
.00515
6.159
4,577,760
450
5.368
.00508
6.848
4,847,040
475
5.676
.00510
7.657
5,116,320
500
5.961
.00507
8.395
5,385,600
IS
300
2.830
.00530
1.758
3,231,260
350
3-301
.00519
2.342
3,769,920
400
3-773
.00513
3.024
4,308,480
450
4-245
.00508
3.791
4,847,040
500
4.717
. 00504
4.644
5,385,600
550
5.188
.00499
5.562
5,924,160
600
5.660
.00497
6.594
6,462,720
650
6.132
.00495
7.708
7,OOI.28o
675
6.367
.00494
8.293
7,270,560
FBICTIONAL HEADS IN PIPES.
497
TABLE 1 O 1 (Continued).
FRICTIONAL HEAD IN MAIN AND DISTRIBUTION PIPES (in each
1000 feet length).
Diam.
of
pipe.
Volume of
water
delivered.
Velocity
of
flow.
Coefficient
of
friction.
Frictional head
per looo feet.
U. S. gallons
in 24 hours.
Inches.
Cu.ft.per
mtn.
Feet per
second.
Feet.
Gallons.
20
350
2.674
.00516
1.375
3,769,920
4OO
3-056
.00509
1.731
4,308,480
450
3.438
.00503
2.215
4,847,040
500
3-821
.00500
2.720
5,385,600
550
4.2O2
.00496
3.264-
5,924,160
600
4.585
.00493
3.862
6,462,720
650
4.967
.00490
4.505
7,OOI,28o
700
5.341
.00487
5.177
7,539,840
750
5-731
.00484
5.924
8,078,400
800
6.II3
.00481
6.698
8,616,960
850
6.572
.00479
7.710
9,155,520
900
6.878
.00477
8.409
9,694,080
24
550-
2.918
.00484
1.280
5,924,160
600
3.183
.00482
1.517
6,462,720
650
3-449
.00477
1.762
7,OOI,28o
700
3.714
.00475
2.035
7,539,840
750
3-979
.00473
2.326
8,078,400
800
4.245
.00471
2.636
8,616,960
-
850
4.510
.00469
2.963
9^55,520
QOO
4-775
.00467
3.307
9,694,080
950
5.041
.00466
3.678
10,232,640
1000
5-306
.00464
4.057
10,771,200
1050
5-571
.00463
4.463
11,309,760
IIOO
5.826
.00462
4.871
11,848,320
1150
6.314
.00459
5.684
12,386,880
I2OO
9-367
.00457
5.754
12,925,440
1250
6.633
00455
6.218
13,464,000
27
800
3-353
.00465
1.410
8,616,960
900
3-772
.00461
1.811
9,694,080
1000
4.192
.00457
2.217
10,771,200
IIOO
4.611
.00453
2.659
11,848,320
I2OO
5-030
.00451
3.150
12,925,440
1300
5-454
.00449
3.687
14,002,560
I4OO
5.868
.00447
4.250
15,079,680
1500
6.287
.00445
4.856
16,156,800
1600
6.707
.00443
5.502
17,233,920
1700
7.126
.00439
6.155
18,311,040
498
DISTRIBUTION SYSTEMS, AND APPENDAGES.
TABLE No. 1 Ol (Continued).
FRICTIONAL HEAD IN MAIN AND DISTRIBUTION PIPES (in each
1000 feet length).
Diam.
of
pipe.
Volume of
water
delivered.
Velocity
of
flow.
Coefficient
of
friction.
Frictional head
per looo feet.
U. S. gallons
in 24 hours.
Inches.
Cu.ft.per
tnin.
Feet per
second.
Feet.
Gallons.
30
IOOO
3-396
.00448
1.28Jp
10,771,200
1200
4-075
.00441
1.820
12,925,440
I4OO
4-754
.00438
2.460
15,079,680
1600
5-433
.00434
3.257
I7,233,9 2
I800
6. 112
.00429
4.009
19,388,160
2OOO
6.791
.00428
4.904
21,542,400
2200
7.471
.00425
5.894
23,696,640
24OO
8.149
.00421
6.947
25,850,880
36
1500
3.536
.00419
1.085
16,156,800
2OOO
4-708
.00412
1.891
21,542,400
2500
5.894
.00406
2.920
26,928,000
3000
7-073
.00401
4.154
32,313,600
3500
8.252
.00397
5.598
37,699,200
4OOO
9-431
.00394
7.257
43,084,800
486. Relative Discharging Capacities of Pipes.
The volume of water delivered, <?, by a pipe, is, as we have
seen ( 296), equal to the product of its section 8 9 into its
mean velocity of flow v,
The equation of velocity is,
I m )
hence we have, for full pipes,
By uniting the two terms of d, within the vinculum, we
have the equation of volume,
RELATIVE CAPACITIES OF PIPES. 499
For a given inclination, all the terms in the right-hand
member are constant, except d and m. We have then the
relative discharging powers of pipes, as the quotients, , or
772-
nearly as the square roots of the fifth powers of the diam-
eters.
By transposition of the equation for volume, q, we have
the equation for diameter, d,
_ ,
~ X ' X '
.61685
By this we perceive that the relative diameters required
for equally effective deliveries are as the products (fm, or
nearly as the squares of the volumes.
487. Table of Relative Capacities of Pipes. The
following table (No. 102) of approximate relative discharg-
ing powers of pipes, will facilitate the proper proportioning
of systems of pipe distributions. It shows at a glance the
ratio of the square root of the fifth power of any diameter,
from 3 to 48 inches, to the square root of the fifth power of
any other diameter within the same limit.
In the second column of this table, the diameter 1 foot
is assumed as unit, and the ratios of the square roots of the
fifth powers of the other diameters, in feet, are given oppo-
site to the respective diameters in feet written in the first
column. Thus the approximate relative ratio of discharging
power of a 3-foot pipe to that of a 1-foot pipe is as 15.588 to
1 ; and of a .5 foot pipe to a 1-foot pipe as .1768 to 1 ; also
the relative discharging power of a 4-foot pipe (= 48-inch)
is to that of a 2-foot pipe (= 24-inch) as 32 to 5.657 ; and of
500
DISTRIBUTION SYSTEMS, AND APPENDAGES.
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DEPTHS OF PIPES. 501
a 2.5-foot pipe to the combined discharging powers of a
2-foot and 1.5-foot pipes as 9.859 to (5.657 + 2.756).
The last vertical column gives the diameters in inches,
as does also the horizontal column at the head of the right-
hand section of the table.
The numbers in the intersections of the horizontal and
vertical columns from the diameters in inches give also
approximate relative discharging capacities. For instance,
if we select in the vertical column of diameters that of the
48-inch pipe and desire to know how many smaller pipes it
is equal to in discharging capacity, we trace along the hori-
zontal column from it, and find that it is equal to 15.59,
sixteen -inch pipes, or 5.65 twenty-four-inch pipes, or 1.58
forty -inch pipes, etc. Also, for other diameters, we find
that a 24-inch pipe is equal to 32 six-inch pipes, or 2.05
eighteen-inch pipes, and a 12-inch pipe is equal to 5.65 six-
inch pipes.
488. Depths of Pipes. The depths at which pipes
are to be placed, so they shall not be injured by traffic or
frost, is a matter for special local study, general rules being
Ibut partially applicable. The depth is controlled in each
given latitude, or thermic belt, by first, the stability of the
earth, whether it be soft and quaky, or heavy clay, or close
sand, or rock ; second, whether the ground be saturated by
surface waters that remain and freeze and conduct down
frost, or by living springs flowing up and opposing deep
penetration of frost ; third, whether the ground be porous,
well underdrained to a level below the pipes, and the pores
filled with air, which is a good non-conductor ; and fourth,
whether the winds sweep the snows off from given localities
and leave them unprotected, or given localities are shaded
.and the severity of night is uncounteracted at noonday.
Along those thermic lines whose latitudes at the Atlan-
502
DISTRIBUTION SYSTEMS, AND APPENDAGES.
tic coast are as given, the depths of the axes of the pipes, in
close gravelly soils, may be approximately as follows :
TA B L E No. 1O3.
APPROXIMATE DEPTHS FOR AXES OF WATER-PIPES.
DlAM.
LATITUDE
40 North.
LATITUDE
42 North.
LATITUDE
44 North.
DlAM.
LATITUDE
40 North.
LATITUDE
42 North.
LATITUDE
44 North.
Depth of
Depth of
Depth of
Depth of
Depth of
Depth of
axis.
axis.
axis.
axis.
axis.
axis.
II
i n
/ it
t it
//
t n
i ff
i n
4
4-8
52
62
20
4 10
5 5
6-3
6
4-8
52
62
22
4 10
5 5
6-3
8
47
5i
62
24
4 ii
5 6 64
10
47
5i
62
27
4 ii
5 7 64
12
4-7
51
62
30
5 o
5-8
6-4
14
47
52
62
33
5 o
5-9
6-5
16
4-8
53
62
36
5 o
5io
66
18
49
54
6-3
40
5 i
5-i i
6-7
There is a general impression that the water passed into
pipes, will in a very short time take the temperature of the
ground in which the pipes are laid. Close observation does
not confirm this impression.
If water at a high temperature is admitted to a deep
pipe system, in the early summer, while the ground is yet
cool, the consumers will derive but little benefit from the
coolness of the earth, and this is especially the case when
the pipes are coated and lined with cement.
Frost also penetrates at various points as low as the
bottoms of sub-mains, without seriously interfering with
the flow, and water-pipes are often suspended beneath
bridges, where ice forms in the river near by, a foot or more
in thickness, without their flow being interfered with. An
eight or ten inch pipe will resist cold a long time before it
will freeze solid.
The hydrants, small dead ends, and service-pipes are
RATES OF CONSUMPTION OF WATER. 503
most sensitive to cold, and their depths and coverings should
receive especial attention.
Dead ends should be avoided as much as possible, and
circulation maintained for the protection of the pipes against
frost, as well as to maintain the purity, or to prevent the
fermentation of the motionless water.
489. Elementary Dimensions of Pipes. A table
of the elementary dimensions of pipes facilitates so much,
pipe calculations, that we insert it here (p. 504). The last
column gives also the quantity of water required to fill each
lineal foot of the pipes, when laid complete, or the quan-
tities they contain.
490. Distribution Systems. We have now reduced
to tabular form the data that will assist in establishing the
proportions of the several parts of a system of distribution
pipes, for the domestic and fire supply of a town or city.
For illustration, let us assume a case of a thriving young
city of 25,000 inhabitants, situated on the bank of a naviga-
ble river, and that the contour of the land had permitted
its streets to be straight, and to intersect at right-angles.
In such case its system of distribution pipes will form a
series of parallelograms, inclosing one, two or more of the
city blocks, as circumstances require, substantially as is
shown in the plan of a system of pipes, Fig. 113.
491. Rates of Consumption of Water. The healthy
>wth of the city gives reason to anticipate an increase to
>,000 inhabitants within a decade, and this number at
should be provided for in the first supply main, the
reservoir, and such parts as are expensive to duplicate,
id a larger number should be provided for in the con-
Luit, and such parts as are very expensive and difficult to
luplicate.
The continued popularization of the use of water, and
504
DISTRIBUTION SYSTEMS, AND APPENDAGES.
TABLE No. 1O4.
ELEMENTARY DIMENSIONS OF PIPES.
Diameter
Diameter.
Contour.
Sectional area.
Hydraulic
mean radius.
Cubical con-
tents per lineal
foot.
Inches.
Feet.
Feet.
Sq.feet.
Cubicfeet.
i
.0417
.1310
.001366
.0104
.001366
i
.0625
.1965
.003068
.0156
.003068
I
.083
.26l8
.005454
.0208
.005454
'I
.1250
39 2 7
.OI227
.0312
.OI227
ij
.1458
.4581
.01670
.0364
.01670
2
.1667
.5235
.02232
.0418
.02232
3
.250
.7854
.04909
.0625
.04909
4
3333
1.047
.08726
0833
.08726
6
.5000
I-57I
-19635
.1250
19635
8
.6667
2.094
3490
.1666
-3490
10
.8333
2.618
5454
.2083
5454
12
I.OOOO
3.142
.7854
.2500
7854
14
1.1667
3.66 5
1.069
.2916
1.069
16
t-3333
4.189
J -397
3333
r-397
18
1.5000
4-713
1.767
.3750
1.767
20
1.6667
5-235
2.181
.4166
2.181
24
2.00OO
6.283
3.142
.5000
3.142
27
2.250O
7.069
3.976
-56^5
3-976
30
2.5OOO
7.854
4.909
.6250
4.909
33
2.7500
8.639
5-940
.6875
5-940
36
3.OOOO
9.425
7.069
.7500
7.069
40
3-3333
10.47
8.726
.8333
8.726
44
3-6667
11.52
10.558
.9166
10.558
48
4.0000
12.56
12.567
.OOOO
12.567
54
4.5000
14.14
I5-905
. 1250
15-905
60
5.0000
15.71
J 9- 6 35
.2500
I9-635
72
6. oooo
19.29
29.607
.5000
29.607
84
7.0000
21.99
38.484
.7500
38.484
96
8. oooo
25.45
50.265
2. OOOO
50.265
7
s-t-
* .1
fcl -
IT
7 i * :
G F E
506 DISTRIBUTION SYSTEMS, AND APPENDAGES.
the increasing demand for it for domestic, irrigating, orna-
mental, and mechanical purposes, with the increasing waste
to which they all tend, requires that at least an annual
average of 75 gallons per capita daily must be provided for
the 35,000 persons.
In our discussion of the varying consumption of water
( 19), it is shown that in certain seasons, days of the week,
and hours of the day, the rate of consumption, independent
of the fire supply, is seventy-five per cent, greater than the
average daily rate for the year. In anticipation of this
varying rate, we should proportion our main for not less
than fifty per cent, increase (= 75 x 1.50 = 112.5), or for a
rate of 112.5 gallons per capita daily, which for 35,000 per-
sons equals a rate of 365 cubic feet per minute.
492. Rates of Fire Supplies. For fire supply we
anticipate the possibility of two fires happening at the same
time requiring ten hose streams each. The minimum fire
supply estimate is, then, twenty hose streams of say 20
cubic feet per minute, or a total of 400 cubic feet per minute.
The combined rate of flow of fire and domestic supply is
(365 + 400) 765 cubic feet per minute.
493. Diameter of Supply Main. Turning now to the
table of Frictional Head in Distribution Pipes, and looking
for volume in the second column, we find that a 24-inch
pipe will deliver 765 cubic feet per minute, with a velocity
of flow of about 4 feet per second, and with a loss of head
of about 2.5 feet in each thousand feet length of main. A
20-inch pipe will deliver the same volume with a velocity
of flow of about 5.75 feet per second, and with a loss of
head of about 6 feet in each thousand feet length. Unless
the main is short, this velocity, and this loss of head, in-
creased by the loss at angles and valves, is too great. We
adopt, therefore, the 24-inch diameter for supply main.
MAXIMUM VELOCITIES OF FLOVT3 / ''<S'
^
<> *" /*
494. Diameters of Sub-Mains. We now compute Oj^
the portions of the whole supply that will be required in /
each section of the city. If our plan of distribution i^J^/
divided into twelve sections, then the average section sup-
ply is one-twelfth of the whole. We find, for instance, that
Sec. 1 requires 85 per cent, of the average ; Sec. 3, 125 per
cent, of the average ; Sec. 12, 100 per cent, of the average ;
Sec. 22, 95 per cent, of the average, etc.
Now, with the aid of the table of relative discharging
powers of pipes, and the table of frictional heads in pipes,
we can readily assign the diameters to the sub-mains that
are to distribute the waters to the several sections, adding
to the domestic and fire supply volumes for the nearest
sections the estimated volumes that are to pass beyond them
to remoter sections.
This done, we may sum up the frictional losses of head
along the several lines from the supply to any given point,
and deduct the sum from the static head, and see if the
required effective head remains. The volume and effective
head are matters of the utmost importance, when the pipes
are depended upon exclusively to supply the waters re-
quired for fire extinguishment. The lack of these has cost
several of our large cities a million dollars and more in a
single night.
An inspection of the table of Frictional Head shows how
rapidly the friction increases when velocity increases. The
increase of frictions are, in the same pipe, as the increase of
squares of velocities (tfm\ nearly.
495. Maximum Velocities of Flow. As a general
rule, the velocities in given pipes should not exceed, in feet
per second, the rates stated in the following table for the
respective diameters.
508 DISTRIBUTION SYSTEMS, AND APPENDAGES.
TABLE No. 1 OB.
MAXIMUM VELOCITIES OF FLOW IN SUPPLY AND DISTRIBUTION PIPES.
Diameter, in inches
4
6
8
10
12
14
16
18
20
22
24
27
3
33
36
Velocity, in ft. per sec. .
2.5
2 .8
3
3-3
3-5
3.9
4.2
4-5
4-7
5
5-3
5.8
6.2
6.6! 7
496. Comparative Frictions. As regards friction
alone in any given pipe, it does not matter whether the
water is flowing up a hill or down a hill, or materially if
the pressure is great or little; or in long, conical, and
smooth pipes, whether the water is flowing toward the large
end or toward the small end. The total friction will be the
same in both directions in the first case, and will also be the
same in both directions in the last case. In the conical
pipe, however, the friction per unit of length, or per lineal
foot, will be less than the average at the large end, because
the velocity of flow will be less there, and more than the
average at the small end. The total frictional head will be
the same as though the whole pipe had a uniform diameter
just equal to the diameter in the conical pipe at the point
where the friction is equal to the average for the whole
length.
497. Relative Rates of Flow of Domestic and
Fire Supplies. The actual consumption of water by the
fire department for the extinguishment of fires, in any city,
per annum, is very insignificant when compared with either
the domestic, the irrigation and street sprinkling, or the
mechanical supply for the same limit of time, yet it has
appeared above that the pipe capacity required for the fire
service, in the general main of a small city, exceeds that
required for the whole remaining consumption. If we
examine this question still closer, taking a length of 1200
feet of distribution pipe in a closely built up section of the
REQUIRED DIAMETERS FOR FIRE SUPPLIES. 509
city, we find on the 1200 feet length, say 40 domestic service
pipes, and consumption of say 750 gallons each per day, or
total of 15000 gallons per day. Making due allowance for
fifty per cent, increase of flow at certain hours, we have a
required delivery capacity of 1.5 cubic feet per minute to
cover this whole consumption. On the same 1200 feet of
pipe there are, say four fire-hydrants. If in case of fire we
take from these hydrants only four streams, in all, of 20
cubic feet per minute each, we require a delivery capacity
of 80 cubic feet per minute. In this case, which is not an
uncommon one, the required capacity for the fire service is
to that for the remaining service as 80 to 1.5.
If the given pipe, 1200 feet long, is a six-inch pipe, sup-
plied at both ends, then the delivery for fire at each end is
forty cubic feet per minute. Referring to the table of fric-
tional head, we find that this quantity requires a velocity of
flow of 3.401 feet per second, and consumed head, in fric-
tion, at the rate of 8.8 feet per thousand feet.
If the 80 cubic feet per minute must all come from one
end of the pipe, then the pipe should be eight inches diam-
eter, in which case the velocity will be nearly four feet per
second and the head consumed at the rate of about eight
feet per thousand feet length.
498. Required Diameters for Fire Supplies.
As a general rule, the minimum diameters of pipes for sup-
plying given numbers of hydrant streams, when the given
pipes are one thousand feet long, and static head of water
one hundred and fifty feet, are as follows :
510
DISTRIBUTION SYSTEMS, AND APPENDAGES.
TABLE No. 1O6.
DIAMETERS OF PIPES FOR GIVEN NUMBERS OF HOSE STREAMS.
6
8
Approximate total quantity of water,
60
Rn
160
1 80
Required diameter of pipe, in inches. .
4
?
8
8
10
10
10
12
12
12
12
14
Number of hose streams
rfi
18
Approximate total quantity of water,
in cubic feet per minute.
"fin
"Ro
060
080
4.60
.g
Required diameter of pipe, in inches. .
14
14
14
16
16
jw
16
JOU
16
16
16
18
4 i8
18
If the pipes are short, the velocities of flow may be
increased somewhat, for a greater ratio of loss of head per
unit of length is then permissible.
If the pipe is supplied from both ends, then the nnmber
of hose streams may be doubled without increase of the
frictional head ; hence the advantage of so distributing the
sub-mains as to deliver a double supply to as many points
as possible, for this is equivalent to doubling the capacity
of the minor pipes. If the pipes are several thousand feet
long, and have a large proportionate domestic draught,
then a due increase should be given to the diameters.
499. Duplication Arrangement of Sub -Mains.
When the sub-mains can be distributed in parallel lines, at
several squares distance, and "gridironed" across by the
smaller service mains, as in v the plan, Fig. 113, or arranged
in some equivalent manner, then a most excellent system
will be secured. In such case, if an accident happens to a
pipe, or valve, or hydrant, in any central location, there are
at least two lines of sub-mains around that point, and the
supply will with certainty be maintained at points beyond.
Pipes are always liable to accident in consequence of
building excavations, sewerage excavations, sewer over-
flows, quicksand or clay slides, floods, and various other
causes that cannot be foreseen when the pipes are laid ; and
STOP-VALVE SYSTEM.
511
FIG. 118.
when new hydrants are to be attached, or large pipe con-
nections to be made, or repairs to be made, it is frequently
necessary to shut off the water. The advantage of dupli-
cate lines of supply to all points is apparent in such case.
When a city has become dependent on its pipes for its
water supply and protection from fire, it is absolutely neces-
sary that the supply be maintained, and the result may be
disastrous if it fails for an hour.
5OO. Stop-Valve System. It is equally advantage-
ous to have a sufficient number of stop-valves, or "gates,"
as they are frequently
termed, upon the pipe,
so the water may be shut
off from any given point
without cutting off the
supply from both a long
and a broad territory, or
even a very long length
of pipe. The sub-main
parallelogram system
shown in the plan, Fig.
113, permits of such an ar-
rangement of stop-valves,
chiefly of small diameters
and inexpensive, that an
accident at any point will
not leave that point with-
out a tolerable fire pro-
tection from both sides.
For instance, if it is
necessary to shut off in EDDY'S STOP-VALVE.
, . ._ (R. D. Wood & Co., Philadelphia.)
Section 2 a part of East
Fourth Street between Avenues A and D, the hydrants at
512 DISTRIBUTION SYSTEMS, AND APPENDAGES,
the corners of East Third and Fifth Streets will still be avail-
able. If the gates are placed at each branch from the sub-
mains, and at the intersections of the sub-mains, as they
should be, then an accident to a sub-main will not neces-
sitate the shutting off of any service-main joining it, for the
service-main supplies can be maintained from the opposite
ends. Wherever cross service-mains are required, as in
Avenues B and C, in Section 3 in the plan, they may pass
under the other service-mains whose lines they cross and
have gates at their end branches only, which admits of their
being readily isolated.
5O1. Stop-Valve Locations. A systematic disposi-
tion of the pipes generally should be adopted. If the pipes
are not placed in the centres of streets, they should be placed
with strict uniformity at some certain distance from the
centre of the street, and carefully aligned, and uniformly
upon the same geographical side, as, upon the northerly and
westerly side. The stop-valves should be disposed also,
with rigid system, as, always in the line of the street boun-
dary, the line of the curb, or some fixed distance from the
centre of the street. An accident may demand the prompt
shutting of any gate of the whole number, at any moment
of day or night ; and if, perchance, its curb-cover is hidden
by frozen earth or by snow, it is important to know exactly
where to strike without first journeying to the office and
searching for a memorandum of distances and bearings.
Searching for a gate-cover buried under frozen earth is a
tedious operation, and it is not always possible to uncover
every one of several hundred gates after every thaw and
every snow-storm in winter.
Strict adherence to a system in locating gates enables
new assistants to readily learn and to know the exact posi-
tion of them all.
STOP-VALVE DETAILS. 513
Strict adherence to system in locating pipes is requisite
for the strict location of gates, and pipes should be cut, if
necessary, to bring the gates to their exact locations. If a
gate is a half-length of pipe out of position, it may cost
several hours delay in digging earth frozen hard as a sand-
stone rock, to find the gate-cover.
502. Blow-off, and Waste Valves. When pipes are
located upon undulating ground, blow-off valves and pipes
will be required in the principal depressions of the mains
and sub-mains, to flush out the sediment that is deposited
from unfiltered water. The diameters of the blow-off pipes
may be about half the diameters of the mains from which
they branch. Smaller wastes will answer for the drainage
of the service-main sections for repairs or connections, and
these may lead into sewers, or wherever the waste-water
may be disposed of.
503. Stop- Valve Details. A variety of styles of stop-
valves are now offered by different manufacturers, and a
special advantage is claimed for each, so that no little prac-
tical sagacity is required on the part of the engineer to pro-
tect his works from the introduction of weak and defective
novelties, that may prove very troublesome.
He must observe that the valve castings are so designed
as to be strong and rigid in all parts, that there are no thin
spots from careless centring of cores ; that flat parts, if any,
are thickened up, or ribbed, so they will not spring ; that
the valve-disks are so supported as not to spring under
great pressures, and that they and their seats are faced with
good qualities of bronze composition and smoothly scraped,
ground, or planed, and that they will not stick in their
seats ; that the valve-stems are particularly strong and stiff,
with strong square or half-V threads, and that they and
their nuts are of a tough bronze or aluminum composition.
33
514 DISTRIBUTION SYSTEMS, AND APPENDAGES.
FIG. 119. FIG. 119a.
LUDLOW'S STOP-VALVE (Ludlow Manufacturing Co., Troy).
Figs. 114 to 119& illustrate the principal features of
valves that have been well introduced.
A majority of the good valves have double disks, that
are self-adjusting upon their seats, and their seats are
slightly divergent, so that the pressure of the screw can set
the valve-disks snug upon the seats.
The loose disks should have but a slight rocking move-
ment between their guides, and must not be permitted to
chatter when the valve is partially open.
The blow-off valves may be solid or single-disk valves,
but the valves in the distribution must be tight against
pressure from both and either sides, whether the difference
of pressure upon the two sides be much or little.
Valves exceeding twenty inches diameter are usually
placed upon their sides, except in chambers, and the disks
have lateral motions, or sometimes the valve-cases are so
VALVE CURBS.
515
arranged that the disks have vertical downward motions.
Otherwise the water in the valve-domes would be too much
exposed to frost in winter, as it would rise nearly to the
ground surface.
5O4. Valve Curbs. The stop-valve curbs are some-
times of chestnut or pitch-pine plank, with strong cast-iron
covers, and sometimes of cast-iron, placed upon a founda-
tion of bricks laid in cement.
The plank curbs are about eighteen by twenty-four
inches dimensions at top, flaring downward according to
FIG. 120.
the size of the valve, and they are often of such dimensions
as to admit a man, with room to enable him conveniently to
renew the packing about the valve-stem.
516 DISTRIBUTION SYSTEMS, AND APPENDAGES.
The cast-iron curbs are usually elliptical in section.
The writer has used in several cities, for the smaller gates,
up to twelve inches diameter, circular curbs (Fig. 120) of
beton coignet, with cast-iron necks and covers. The neck is
six inches clear diameter at the road surface, fifteen to
eighteen inches deep, according to the size of the valve, and
flares to the size of the cement curb, which is just large
enough to slip over the dome-flange of the valve-case. The
cement curb rests upon a foundation of brick or stone laid
in cement mortar.
When these are paved about, the whole surface exposed
is only seven and one-half inches diameter, and they are
not as objectionable in the streets as the larger covers.
All gate-curbs must be thoroughly drained, so that
water cannot stand in them, and freeze in winter.
5O5. Fire-Hydrants. The design of a fire-hydrant
that is a success in every particular is a great achievement.
It ranks very nearly with the design of a successful water-
meter.
Nearly every speculative mechanic, it would seem, who
has had employ in a machine-shop for a time, has felt it
his duty to design the much-needed successful hydrant ; as
so many doctors and lawyers have grappled with, and
believed for a time, that they had solved the great meter
problem.
Innumerable patterns of hydrants are urged upon water
companies and engineers, and are accompanied by an
abundance of certificates setting forth their excellence ; and
many of them have good points and will answer all practi-
cal purposes until an emergency comes, when they fail, and
the experiment winds up with a loss that would have paid
for a thousand reliable hydrants.
A considerable practical experience with hydrants, and
HYDRANT DETAILS.
517
FIG. 121.
an expert knowledge of the qualities demanded in the
design and materials of a hydrant, are necessary to enable
one to judge at sight of the value of a new pattern.
506. Post-Hydrants. In the smaller
towns and in the suburbs of cities, post-
Jiydrants, of which Fig. 121 illustrates one
pattern, are more generally preferred, as
they are more readily found at night, and
are usually least expensive in first cost.
They are placed on the edge of the
sidewalk, and a branch pipe from the
service main furnishes them with their
water. If the service main is of sufficient
capacity, the post-hydrant may have one,
two, three, or four nozzles. In cities where
steam fire-engines are used, a large nozzle
is added for the steamer supply, and if
there is a good head pressure, two nozzles
are usually supplied for attaching leading
hose.
For the supply of two hose streams, or
a steamer throwing two or more streams,
the hydrant requires a six-inch branch
pipe from the service main, and a valve of
equal capacity. The supply to post-hy-
drants has too often been throttled down,
when there was no head pressure to
spare, and the effectiveness of the hy-
drant very much reduced thereby.
507. Hydrant Details. In New
England and the Northern States, a
frost-case is a necessary appendage to MATHEW'S HYDRANT-
J -^ (R. D. Wood & Co.,
a post-hydrant, and it must be free to Philadelphia).
518 DISTRIBUTION SYSTEMS, AND APPENDAGES.
move up and down with the expansion and contraction of
the earth, without straining upon the hydrant base. In
clayey soils, these frost cases are often lifted several inches
in one winter season, and if the post is not supplied with
the movable case in such instances, it is liable to be torn
asunder.
A waste-valve must be provided in every hydrant that
will with certainty drain the hydrant of any and all water
it contains as soon as the valve is closed, and the waste
must close automatically as soon as the valve begins to
open.
The main valve must be positively tight, or great trouble
will be experienced with the hydrant in severe winters. A
moderate leakage, as in some stop-valves, cannot be per-
mitted. A free drainage must be provided to pass away
the waste water from the hydrant, or, if the hydrant is fre-
quently opened, for testing or use, the ground will soon be-
come saturated and the hydrant cannot properly drain.
If the valve closes "with" the pressure there must be
no slack motion of its stem, or when the valve is being
closed and has nearly reached its seat, the force of the cur-
rent will throw it suddenly to its seat and cause a severe
water-ram.
The screw motion of hydrant valves must be such that
the hydrant cannot be suddenly closed, or with less than
ten complete revolutions of the screw. The valves should
move slowly to their seats in all cases, as, if several hydrants
happen to be closed simultaneously, the water-ram caused
thereby may exert a great strain upon the valves, and the
shock will be felt to some extent throughout the whole
system of pipes. The sudden closing of a hydrant may
make a gauge, attached to the pipes, that is more than a
mile distant, kick up fifty or sixty pounds.
HYDRANT DETAILS.
519
FIG. 122.
If a hydrant branch is taken from a main-pipe or sub-
main, there should be a stop-valve between the main and
hydrant, so the hydrant may be repaired without shutting
off the flow through the main.
In 1874 the writer made some
measurements of the quantities of
water delivered, under different
heads, through Boston Machine
Co. Post Hydrants, which are sim-
ilar in form to the Mathews Hy-
drant (Fig. 121). The volume of
water was measured by passing it
through a 3-inch Union water-meter,
which was connected to each hy-
drant by a length of fire-hose.
The length of hose between the
hydrant and meter in each and
every experiment was 49 feet 10
inches. The bores of the hydrant
nozzles and of the hose and meter
couplings were two and one-quar-
ter inches diameter. The hydrant
branches were six inches in di-
ameter, and hydrant barrels four
and one-half inches diameter. The
lengths of hose given, following,
were in all cases beyond the meter,
and were attached to the meter.
The hydrant was filled with
water and pressure without flow, taken by a gauge just
previous to the beginning of each test.
The following tests, at different elevations, covers a range
of head pressures between 42 feet and 183 feet :
FLUSH HYDRANT.
520
DISTRIBUTION SYSTEMS, AND APPENDAGES.
TABLE No.107.
EXPERIMENTAL VOLUMES OF HYDRANT STREAMS.
REMARKS.
Pressure
before
test. Ibs.
Delivery
cu. ft.
per minute.
A. 42 Feet Head.
18.21
20.^76
H
q.372
u
12. <^O
tt
I 2 . 096
li- " " " 108 " Ilij " " "
ts
11.382
Open butt of 108 " n " " "
tt
15.342
B. HO Feet Head.
Open nozzle of meter, 2.\ inch diameter
47.74
4O.OOO
l|- inch nozzle attached to meter
24.666
ig- " " on 53 feet n inches of hose
21 .276
I*. " " " 108 " n^ " " "
<(
2O . 408
C. 136. S Feet Head.
CQ 24
43 Q74
a
24 . 3QO
ji " " on 55 feet \ inch of hose
a
23 ^26
D. 183.18 Feet Head.
T-J- inch nozzle on 55 feet 10 inches of hose
7Q H.
27 648
i " " " 108 " 4| " " "
oe. Q7/1
i| " " " 162 " 7 " " "
^l
24 648
Open butt of 162 " 7 " " "
37 672
5O8. Flush Hydrants. A style of flush hydrant, that
may be placed under a paved or flagged sidewalk, near the
edge, is shown in Fig. 122. This style may have one, two,
or three fixed nozzles.
Figs. 123 and 124 illustrate a style of hydrant with a
portable head. This style is manufactured under the
Lowry patent. It is designed to be placed at the intersec-
tions of mains, in the street, or in the line of a main, but
may be placed in the sidewalk. In either case it is placed
within an independent curb, and the cast-iron case rises
about to the surface. The portable head is of brass and
composition, nicely finished, as light as is consistent with
FIG. 123.
FIG. 124.
LOWRY'S FLUSH HYDRANT. (Boston Machine Co., Boston.)
522 DISTRIBUTION SYSTEMS, AND APPENDAGES.
strength, and is usually carried upon the steamer or the
hose carriage. It has any desired number of nozzles, from
one to eight, each of which has its independent supplemen-
tary valve.
In the centre of the portable head is a revolving key that
operates the main valve stem.
509. Gate Hydrants. A variety of metallic "gate"
hydrants have been introduced, from time to time, and had
a brief existence, but the majority of them have been soon
abandoned. The most minute particle of grit upon their
faces gives trouble, and they are much more likely to stick
than valves of good sole-leather or of rubber properly pre-
pared, and clamped between metallic plates. Gate hydrants
of good design and excellent workmanship, should be fully
successful with filtered water.
The rubber of valves requires to be very skillfully tem-
pered, or it will be too soft or too hard. It hardens, also,
as the temperature of the water lowers.
510. High Pressures. But a few years since the
maximum static strain upon hydrants, in public water
supplies, did not exceed that of a hundred and fifty feet
head, and the majority of the hydrants in each system had
not over one hundred feet pressures when the water was at
rest. Hand or steam fire-engines were necessities in such
cases, and the pipes were so small that often the engines
had to exert some suctions on the pipes to draw their full
supplies. Now the values of pressure that will permit six
or eight effective streams to be taken direct from the hy-
drants in any part of the system is more fully appreciated,
and direct pumping pressures equivalent to three or four
hundred feet head are not uncommon. The effect upon the
hydrants is, however, a greatly increased strain which they
must be able to meet.
AIR-VALVES. 523
511. Air- Valves. All water contains some atmos-
pheric air. When water has passed through a pumping-
engine into a force-main under great pressure, it absorbs
some of the air in the air-vessel. If, then, it is forced along
a pipe having vertical curves and summits at different
points, it parts with some of the air at those summits. In
time, sufficient air will accumulate at each summit to oc-
cupy a considerable part of the sectional area at that point,
and it will continue to accumulate until the velocity of the
water is sufficient to carry the air forward down the incline.
At such summits an air-valve is required to let off the
accumulated air, as occasion requires. Also, when the
water is drawn off from the pipes, as for repairs or any
other purpose, there is always a tendency to a vacuum at
the summits if no air is supplied there ; and if the pipes are
not thick and rigid, they may collapse in consequence of
the vacuum strain, or exterior pressure.
When pipes are being filled, there should always be
ample escape for the air at the summits, or the air contained
in the pipes will be compressed and recoil, again be still
more compressed and again recoil with greater force, shoot-
ing the column of water back and forth in the pipe with
enormous force, and straining every joint.
In the distribution, hydrants are usually located upon
summits, and in such case will perform the functions of
air-valves.
If a stop-valve is inserted in an inclined pipe, and is
closed during the filling of the section immediately below it,
it makes practically a summit at that point, and an air-
valve or vent will be required there.
An air and vacuum valve, for summits, may with advan-
tage be combined in the same fixture, the air-valve motion
being positive in action for the purpose of an air-valve,
524
DISTRIBUTION SYSTEMS, AND APPENDAGES.
f
FIG. 125.
opening against the pressure, but automatic as a vacuum-
valve, opening freely to the pressure of the atmosphere.
Fig. 125 is a com-
bined air and vacuum
valve designed by the
writer, and used in sev-
eral cities with success.
A two-inch air- valve
answers tolerably for
four, six, eight, and
ten inch pipes, but for
large pipes a special
branch with stop-valve
may be used.
Great care should
be exercised in filling
pipes with water, and
the water should not
be admitted faster
than the air can give
place to it by issue at
the air-valves, or open
hydrant nozzles, with-
out reactionary con-
vulsions.
512. Union of High and Low Services. Many
cities have high lands within their built-up limits that are
so much elevated above the general level that it is a matter
of convenience to divide the distribution into "high" and
" low services," and to give to each its independent reservoir.
In such case the benefit of the pressure of the high reser-
voir may be secured in the low system in case of a large
fire, by simply opening a valve in a branch connecting the
AIR VALVE.
COMBINED RESERVOIR AND DIRECT SYSTEMS.
525
two systems. A check-valve, Fig. 126, will be required in
the effluent pipe, or supply main from the lower reservoir
to prevent the flow back into the lower reservoir.
A weighted valve, automatic in action, may also be
placed in the branch connecting the two systems, and then
FIG. 126.
CHECK-VALVE.
in case of an accident to the supply pipe of the lower sys-
tem, or a malicious closing of its valve, the upper service
will maintain the supply at a few pounds diminished
pressure.
If the pumps are arranged so as to give a direct increased
pressure in the lower system for fire purposes, then a check-
valve in the branch connecting the two systems, opening
toward the high system, will be an excellent relief and pro-
tection against undue pressure.
513. Combined Reservoir and Direct Systems.
In the plan of a pipe system, Fig. 113, a pipe leads from the
pumps direct to the reservoir, and a second pipe leads direct
from the pumps into the distribution, so that water may be
sent either to the reservoir or to the distribution, at will.
526 DISTRIBUTION SYSTEMS, AND APPENDAGES.
A branch pipe connects these two pipes so as to supply the
distribution from the force main.
A check-valve opening toward the distribution is placed
in this branch. If a fire-pressure is put upon the distribu-
tion through the direct pipe this valve prevents the flow
back toward the reservoir, but upon the reduction of the
fire-pressure it comes into action and maintains the supply
to the distribution from the reservoir.
For additional security against unforseen contingencies,
another pipe may lead from the reservoir to one of the prin-
cipal sub-mains, as shown in the plan, when the relative
positions of the reservoir and distribution permits, and this
pipe may contain in the effluent chamber a check-valve
against fire-pressure and a weighted relief- valve to prevent
undue pressure.
In the reservoir plan, Fig. 58 (page 333), the force and
supply mains are shown to be connected by a pipe passing
along the side of the reservoir, so that the water may be sent
from the pumps direct into the distribution. The supply-
main has a check-valve in the effluent chamber in this case.
A combined reservoir and direct pressure system, sub-
stantially like that of Fig. 113, including high and low ser-
vices, was designed by the writer for one of the large New
England cities in 1872, and the same was constructed with the
exception of the high service reservoir, in the two following
seasons.
514. Stand-Pipes. Several of the American cities,
whose reservoirs are distant from their pumping stations,
have placed a stand-pipe upon their force-main, to equalize
the resistance against the pumps, as in St. Louis, Louis-
ville, and Milwaukee. Other cities use tall open-topped
stand-pipes without reservoirs, when no proper site for a
reservoir is readily attainable, as at Chicago and Toledo.
All the American stand-pipes now in use are of the
FRICTIONAL HEADS IN SERVICE PIPES. 527
single leg class. The city of Sandusky, Ohio, has now
(Nov. 1876) in process of construction a tank stand-pipe of
25 feet diameter and 208 feet height, surrounding a delivery
stand-pipe of 3 feet diameter and 225 feet height. This
tank is being built up of riveted metal plates, from designs
by J. D. Cook, Esq., chief engineer. In Europe, the stand-
pipes are more frequently double-legged, with connections
between the up and down legs at intervals of height.
The stand-pipes as generally used, serve as partial sub-
stitutes for relief- valves combined or acting in conjunction
with tall and capacious air-chambers. The surface of the
water in the stand-pipes vibrates up and down according to
the rate of delivery into them from the pumps, and the rate
of draught, if the main over which they are placed is con-
nected with the distribution. In northern cities it is neces-
sary that they be housed and protected from frost.
The Boston Highlands Stand-pipe (page 161) stands
upon an eminence 158 feet above tide, is of wrought-iron,
and is 80 feet high, and 5 feet interior diameter. It is
inclosed in a masonry tower.
The Milwaukee stand-pipe (page 25) rises to 210 feet
above Lake Michigan, and the Toledo stand-pipe (page 31)
to 260 feet above Maumee River.
515. Frictional Heads in Service-Pipes. The fol-
lowing shows the frictional head in clean, smooth service-
pipes, with given velocities, for each one-hundred feet length.
The numbers of the first column are the given velocities,
in feet per second. The second column gives the head,
which is necessary to generate the given velocities opposite.
In the first column, under each of the given diameters
from J inch to 4 inches, is the volume of flow, at its given
velocity ; in the next column the corresponding coefficient
of friction ; and in the next column the frictional head per
each one hundred feet length at its given velocity.
528
DISTRIBUTION SYSTEMS, AND APPENDAGES,
TABLE No. 1O8.
FRICTIONAL HEAD IN SERVICE PIPES* (in each 100 feet length),
1
Y 2 IN. DIAMETER
% IN. DIAMETER.
I IN. DIAMETER.
lYz IN. DIAMETER.
ll
1.
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If
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Feet.
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/
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/
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.01^0
.00992
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2.899
3.502
.0257
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1.812
2.265,
.0458
5 2 3
.00882
.00854
1.289,
1.636
.1030
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.00843
.00823
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1.8
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.00900
k.3kk
033 1
.00856
2.756
.0589
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2.005
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1.268
2.O
.062
.0164
.00862
8.136
.0368
.00830
3.m
.0654
.00810
2.kl6
.1472
.00790
1.570
2.2
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.0180
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6.091
.0405
.00811
&.902
.0719
.00790
2.851
.1619
.00775
1.86k
2.4
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.0196
.00810
6.950
.0442
.00792
k.53k
.0785
.00773
3.320
.1766
.00760
2,175
2.6
.105
.0213
.00788
7.935
.0478
.00773
5.193
.0850
.00758
3.821
.1914
.00745
2.520
2.8
.122
.0229
.00770
8.993
0515
.00756
5.891
.0916
k.356
.2061
.00730
2.8kk
3
.140
.0246
.00753
10.07
055 2
00745
6.66k
.0981
.00734
k.926
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3229
3- 2
,l6o .0262
00745
11.36
.0589
00737
7.501
.1046
.00726
5.5kk
.2356
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3.63k
3.4
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12.67
.0626
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8.337
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6.207
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k.05t>
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9.038
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6.900
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k.509
3-8
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15.62
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10.25
I2 43
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7.62k
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.00696
k.99k
4.0
4.2
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.275
.0328
344
.00722
.00719
17.21
18.89
.0736
0773
.00710
.00706
11.29
12.38
1309
.00702
.00698
8.376
9.182
2945
.3092
.00692
.00687
5.502
6.022
4.4
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.0360
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20.62
.0810
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13.51
1440
.00694 ! 10.02
3239
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6.571
4.6
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0377
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lk.70
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.00680
7.1k9
4.8
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2k.30
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.00696
15.9k
.00687 11.80
3534
.00677
7.751
5-
39
.0410
.00704
26.22
'.0920
.00693
17.22
1636
.00684 12.75
.3681
.00675
8.386
5-2
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.0426
.00701
28.2k
.0957
.00689
18.52
1701
.00681 13.73
.3828
.00671
9.017
5-4
455
.0442
.00698
30.32 ,
0993
.00686
19.88
1767
00678 lk.7k
3975
.00668! 9.680
5-6
49
0459
.00695
32.k7 f
.1030
.00683
21.29
1832
.00675 15.79
.4123
.00665
10.37
5.8
0475
.00692
3k.76
.1067
.00680
22.7k
1898
.00672 16.86
.4270
.00662
11.07
6.0
'.562
.0492
.00689
36.315
.1104
.00678
2k.26
1963
.00670
17.99
.4417
.00660
11.81
6.2
.600
.0508
.00686
39.88
.1141
.00675
25.79
2028
.00667
19.12
.4564
.00657
12.55
6.4
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.0524
.00683
kli67
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.00672
27.35
2094
.00664 20.28
47"
.00654
13.31
6.6
.680
.0541
.00681
U.09
.1214
.00669
28.96
2159
.00661 21.k7
4859
.00652; lk.ll
6.8
.722
0557
.00678
lfi.70
.1251
.00666
30.61
2225
.00659 2S-7*
.5006
.00650
lk.9k
7.0
765
0574
.00675
1,9.27
.1288
.00664
32.3k
2291
.00657
2k.01
5153
.00648
15.78
* This table does not include the resistances of the stop-cocks and short
bends in service pipes. Such resistances, as services are usually laid, reduce
the effective delivery of water fully fifty per cent.
jfli.. oc^-^- 7
X
FRICTIONAL HEAD IN SERVICE PIPES.
529
TABLE No. 1 O 8 (Continued).
FRICTIONAL HEAD IN SERVICE PIPES (in each 100 feet length).
1
1% IN. DIAMETER.
2 IN. DIAMETER.
3 IN. DIAMETER.
4 IN. DIAMETER.
=_
*o *-
2s.
|.a
bic feet
minute.
i
1l
11
.2
li
ibicfeet
minute.
"a
&
3
-I'S
tsj
ibic feet
minute.
9t
'5
1|
33 *
V
ul
1
ir
38
a
U
O
C*"
l
O
2T
Feet.
Feet.
Feet.
Feet.
1.4
.030
1.403 .00800
.668
1.875
.00763
.557
4- "3
.00724
.353
7.330 .00697
.255
1.6
1.8
.040
.050
1.603! .00786
1.804' -00769
.857 2.142
1.062 2.410
.00750
.00741
.715
.895
4.712
5-301
.00716
.00708
.456
.570
8-377
9-424
.00690 .SkSf
. 00684! .415
2.0
.062
2.004 -00757
1.290 2.678
.00731
1.090
5.891
.00700
.696
.00678 .505
2.2
.075
2.204 .00745
1.536
2.046
.00724
1.306
6.480
.00693
.833
11.52
.00672
.606
2.4
.090
2.405 .00733
1.799 3.214
.00717
1.539
7.069
.00687
.983
12.56
.00666
.715
2.6
.105
2.605 .00723
2.083 3.481
.00711
1.791
7.685
.00681
l.lkk
13.61
.00660
.839
2.8
3'
.122
.140
2.806 .00713
3.006 .00707
f Jftfj 3.794
2.711 4-018
.00704
.00692
2.057
I4WJ
8.247
8.846
.00675
.00670
1.315
1.498
14.66
15-71
.00655
.00650
.957
1.090
3-2
.l6o
3.206 .00700
3.05k 4.286
.00686
2.618
9-435
.00665
1.692
16.76
.00645
1.231
3.4
.ISO
3-407
.00604
3.418 4.554
.00681
2.934
10.02
.00661
1.899
17.80
.00641
1.381
3.6
.202
3.607 .00688
3.799 4.821
.00677
3.270 10.61
00657
.117
18.85
.00637
1.538
3.8
.225
3.808 .00685
4.215 5.089
.00674
3.628
IT. 20
.00654
2.347! 19.90
.00634
1.706
4.0
4-2
4-4
.250
275
.302
4.008
4.208
4.409
.00682
.00678
.00674
4.649 5.357
5.096 5.625
5.560 5.893
.00671
.00667
.00663
4.002 11.78
4.385: 12.37
4.784 12.96
.00651
.00647
.00644
2.588
2.836
3.098
20.94
21.99
23.03
.00631
.00628
.00625
1.889
2.065
2.255
4.6
33
! 4.609
.00670
6.040J 6.160
.00660
5.205 13.55
.00641
3.370
24.08
.00623
2.457
4.8
5.0
.360
.39
4.810
5.010
.00667
.00664
6.5471 6.428
6.7391 6.696
.00657
.00654
5.643 14.14
6.0941 14.73
.00638
.00636
3.653
3.951
33
.00620
.00618
2.662
2.880
5.2
.422
5.210
.00661
7.615: 6.064
.00651
6.561
15-32
.00633
4.253
27.23
.00615
3.099
5-4
5-6
455
.490
525
5-4"
5.611
5.812
.00658 8.175 7.232
.00655! 8.751 7.499
.00652 9.345 7.767
.00648
.00645
.00642
7.059
7.527
8.049
15-9I
16.50
17.09
.00630
.00627
.00624
4.565
4:886
5.167
28.27
30.32
30-37
.00612 3.326
.00609' 3.559
.00607 3.816
6.0
.562
6.012
.00650 9.970 8.035
.00640
8.587! 17.67
.00622
5.56k
.00605
4.059
6.2
.600
6.212
.00647 10.59
8.303
.00637
9.126 18.25
.00619
5.912 32.46
.00603
4.320
6.4
.640
6.413
.00645! 11.26
8,571
.00635
9.694 18.85
.00616
ejn
33-50
.00601
4.588
6.6
6.8
.680
.722
6.613
6.8l4
.00643' 11-93
.00641 12.63
8.838
9.I06
.00633
.00631
10.28
10.88
19.44
20.03
.00614
.00612
6646
7.032
34-55
35-6o
.00599 4.863
.00597 5.145
7.0
.765
7.014
.00639
13.34
9-374
.00629
11.49
20.62
.00610
7.427
36-65
.00595 5.310
34
CHAPTER XXIII.
CLARIFICATION OF WATER.
516. Rarity of Clear Waters. A small but favored
minority of the American cities have the good fortune to
find an abundant supply of water for their domestic pur-
poses, within their reach, that remains in a desirable state
of transparency and limpidity.
The origin and character of the impurities that are
almost universally found in ^suspension in large bodies of
water, have been already discussed in the chapters devoted
to " Impurities of Water" (Chap. VIII), and to " Supplies
from Lakes and Rivers" (Chap. IX) ; so there remains now
for investigation only the methods of separating the foreign
matters before pointed out.
517. Floating Debris, The running rivers, that are
subject to floods, bring down all manner of floating debris,
from the fine meadow grasses to huge tree-trunks, and
buildings entire. These are all visible matters, that remain
upon the surface of the water, and their separation is
accomplished by the most simple mechanical devices.
Coarse and fine racks of iron, and fine screens of woven
copper wire are effectual intercepters of such matters and
prevent their entrance into artificial water conduits.
518. Mineral Sediments. Next among the visible
sediments may be classed the gravelly pebbles, sand, disin-
tegrated rock, and loam, that the eddy motions continually
ORGANIC SEDIMENTS. 531
toss up from the channel bottom, and the current bears
forward.
These are not intercepted by ordinary screens, but are
most easily separated from the water by allowing them
quickly to deposit themselves, in obedience to the law of
gravitation, in a basin where the waters can remain quietly
at rest for a time.
When the water is received into large storage reservoirs,
it is soon relieved of these heavy sedimentary matters, by
deposition ; and a season of quietude, even though but a few
hours in duration, is a valuable preparation for succeeding
stages of clarification.
Next are more subtle mineral impurities, consisting of
the most minute particles of sand and finely comminuted
clay, which consume a fortnight or more, while the water is
at rest, in a confining basin, in their leisurely meanderings
toward the bed of the basin.
If these mineral grains are to be removed by subsidence
for a public water supply, the subsidence basin must
usually be large enough to hold a three- weeks supply, and
must be narrow and deep, so the winds will stir up but a
comparatively thin surface stratum, and also so the exposed
water will not be heated unduly in midsummer.
519. Organic Sediments. Next are the organic frag-
ments, including the disintegrating seeds, leaves, and stalks
of plants, the legs and trunks of insects and Crustacea, and
the macerated refuse from the mills.
All these have so nearly the same specific gravity as the
water, that they remain in suspension until decomposition
has removed so much of their volatile natures that the
mineral residues can finally gravitate to the bottom.
If these are to be removed by subsidence, the basin must
hold several months supply, at least, and be so formed
532 CLAKIFICATION OF WATER.
and protected as to neither generate or receive other im-
purities.
In addition, are the innumerable throngs of living
creatures that people the ponds and streams, and their
spawns. These cannot be removed by subsidence during
their active existence, and reproduction maintains always
their numbers good.
520. Organic Solutions. Still more subtle than all
the above impurities, that remain in suspension, are the
dissolved organic matters that the water takes into solution.
These include the dissolved remains of animate creatures,
dissolved fertilizers, and dissolved sewage.
All the former may be treated mechanically with toler-
able success, but the latter pass through the finest filters
and yield only to chemical transformations.
521. Natural Processes of Clarification. Nature's
process for removing all these impurities, to fit the water
for the use of animals, is to pass them through the pores of
the soil and fissures of the rocks. The soil at once removes
the matters in suspension, and they become food for the
plants that grow upon the soil, and are by the plants recon-
verted into their original elements. The minerals of the
soil reconvert the organic matters in solution into other
combinations and separate them from the water.
522. Chemical Processes of Clarification. Arti-
ficial chemical processes, more or less successful in their
action, have been employed from the remotest ages to sep-
arate quickly the fine earthy matters from the waters of
running streams. The dwellers on the banks of streams,
who had no other water supply, treated them, each for
themselves, and in like manner have others treated the rain
waters which they caught upon their roofs, when they had
no other domestic supplies.
PROCESSES OF CLARIFICATION. 533
Many centuries ago the Egyptians and Indians had dis-
covered that certain bitter vegetable substances which grew
around them were capable of hastening the clarification of
the waters of the Nile, Ganges, Indus, and other sediment-
ary streams of their countries.
The Canadians have long been accustomed to purify
rain-water by introducing powdered alum and borax, in
the proportions of 3 ounces of each to one barrel (31 J- gals.)
of water ; and alum is used by dwellers on the banks of
the muddy Mississippi to precipitate its clay. Arago ob-
served also the prompt action of alum upon the muddy
water of the Seine. One part of a solution of alum in fifty
thousand parts of water results in the production of a floc-
culent precipitate, which carries down the clayey and
organic matters in suspension, leaving the water perfectly
-clear.
Dr. Gunning demonstrated by many experiments that
the impure waters of the river Mans, near Rotterdam, could
be fully clarified and rendered fit for the domestic supply
of the city, by the introduction of .032 gramme of per-
chloride of iron into one liter of the water. The waters of
the Maas are very turbid and contain large proportions of
organic matter, and they often produce in those visitors who
-are not accustomed to their use, diarrhoeas, with other un-
pleasant symptoms.
Dr. Bischoff, Jr., patented in England, in 1871, a process
of removing organic matter from water by using a filter of
spongy iron, prepared by heating hydrated oxide of iron
with carbon. The water is said to be quite perceptibly
impregnated with iron by this process, and a copious pre-
cipitate of the hydrated oxide of iron to be afterwards
separated.
Horsley's patent process for the purification of water
534 CLARIFICATION OF WATER.
covers the use of oxalate of potassa, and Clark's the use of
caustic lime.
Mr. Spencer has used in England with great success, in
connection with sand filtration, the crushed grains of a car-
bide of iron, prepared by roasting red hematite ore, mixed
with an equal part of sawdust, in an iron retort. This he
mixes with one of the lower sand strata of a sand filter, and
its office is to decompose the organic matters in solution in
the water. The carbide is said to perform its office thor-
oughly several years in succession without renewal. Mr.
Spencer's process may be applied on a scale commensurate
with the wants of the largest cities, and has been adopted
in several of the cities of Great Britain.
Dr. Medlock was requested by the Water Company of
Amsterdam to examine the water gathered by them from
the Dunes near Haarlem, for delivery in the city. The
water had a peculiar " fish-like" odor, and after standing
awhile, deposited a reddish-brown sediment.
Under the microscope, the deposit was seen to consist of
the filaments of decaying algse, confervse, and other micro-
scopic plants, of various hues, from green through pale-
yellow, orange, red, brown, dark-brown, to black.
The Doctor found the open water channels lined with a
luxuriant growth of aquatic plants, and the channel-bed
covered with a deposit of black decaying vegetal matter.
He discovered also that the reddish-brown sediment was-
deposited in greatest abundance about the iron sluice-gates.
Copper, platinum, and lead, in finely-divided states, were
known by him to have the power of converting ammonia
into nitrous acid, and he was led to suspect that iron pos-
sessed the same power. Experiments with iron in various
states, and finally with sheet-iron, demonstrated that strips
of iron placed in water containing ammonia, or organic
CHARCOAL PROCESS. 535
matter capable of yielding it, acted almost as energetically
as the pulverized metal. The organic matters of the Thames
water in London, and the Rivington Pike water in Liver-
pool, as well as the Dune water in Amsterdam, were found
to be completely decomposed or thrown down by contact
with iron, and the iron acted effectually when introduced
into the water in strips of the sheet metal or in coils of wire.
This simple and easy use of iron may be employed in sub-
sidence basins or reservoirs on the largest scale for towns,
as well as on a smaller scale for a single family.
The results of these experiments with iron were consid-
ered of such great hygienic and national importance by Dr.
Sheridan Muspratt that he has put an extended account of
them on record.*
523. Charcoal Process. The charcoal plate niters
prepared under the patent of Messrs. F. H. Atkins & Co.,
of London, have not been introduced here as yet, so far as
the writer is informed.
The valuable chemical and mechanical properties of
animal charcoal for the purification of water have long been
recognized, and it was the practice in the construction of the
early English filter-beds, as prepared by Mr. Thorn, to mix
powdered charcoal with the fine sand.
If there is either lime or iron in the water, as there is in
most waters, the chemical action results in the formation of
an insoluble precipitate upon the grains of charcoal, when
they become of no more value than sand, and their action
is thenceforth only mechanical. Messrs. Atkins & Co. have
devised a method of overcoming this difficulty, in part at
least, by forming the charcoal into plates, usually one foot
square and three inches thick, and so firm that their coated
surfaces can be scraped clean. These plates may be set in
* Muspratt's Chemistry, p. 1085, Vol. II.
536
CLARIFICATION OF WATER
FIG. 129.
CHARCOAL-PLATE FILTERS.
frames, Fig. 129, as lights of glass are set in a sash, and the
water be made to flow through them. They are compound-
ed for either slow or quick filtration ; the detise plates (a
square foot) passing 30 to 40 imperial gallons per diem, the
porous 80 to 100 gallons, and the very porous 250 to 300
gallons per diem, when clean. The water may be first
passed through sand, for the removal of the greater part of
the organic matters.
The use of charcoal has heretofore been confined almost
entirely to the laboratory, so far as relates to the purifica-
tion of water, and animal charcoal has been found very
much superior to wood and peat coals. Its success has
undoubtedly been due largely to its intermittent use and
frequent cleanings and opportunities for oxidation. Its
power of chemical action upon organic matter is very
quickly reduced, and it must be often cleaned to be
INFILTRATION BASINS.
effectual. Some very interesting and valuable experiments
to test the purification powers of charcoal upon foul waters,
were described to the members of the Institution of Civil
Engineers, by Edward Byrne, in May, 1867.
524:. Infiltration. If any water intended for a do-
mestic supply is found to be charged with organic matter
in solution, the very best plan of treatment, relating to that
water, is to let it alone, and take the required supply from
a purer source.
The impurities in suspension in water may best be
treated on Nature's plan, by which she provides us with the
sparkling limpid waters of the springs that bubble at the
bases of the hills and from the fissures in the rocks.
525. Infiltration Basins. In the most simple natural
plan of clarification, a well, or basin, or gallery, is excavated
in the porous margin of a lake or stream, down to a level
below the water surface, where the water supply will be
maintained by infiltration.
All those streams that have their sources in the mount-
ains, and that flow through the drift formation, transport in
flood large quantities of coarse sand and the lesser gravel
pebbles. These are deposited in beds in the convex sides
of the river bends, and the finer sands are spread upon them
as the floods subside. From these beds may be obtained
supplies of water of remarkable clearness and transparency.
The volume of water to be obtained from such sources
depends, first, upon the porosity of the sand or gravel be-
tween the well, basin, or gallery, and the main body of
water, the distance of percolation required, the infiltration
area of the well or gallery, and the head of water under
which the infiltration is maintained.
A considerable number of American towns and cities
have already adopted the infiltration system of clarification
538 CLARIFICATION OF WATER.
of their public water supplies, and although it is not one
that can be universally applied, it should and will meet
with favor wherever the local circumstances invite its use.
Attention has not as yet become fairly attracted in America
to the benefits and the necessities of filtration of domestic
water supplies, and many of the young cities have been
obliged to make an herculean effort to secure a public water
supply, having even the requisite of abundance, and they
have been obliged to defer to days of greater financial
strength the additional requisite of clarification. A knowl-
edge of the processes of clarification, which are simple for
most waters, is being gradually diffused, and this is a sure
precursor of the more general acceptance of its benefits.
In some of the small western and middle State towns,
the infiltration basins have heretofore taken the form of one
or more circular wells, each of as large magnitude as can
be economically roofed over, or of narrow open basins. In
the eastern States the form has usually been that of a cov-
ered gallery along the margin of the stream or lake, or of a
broad open basin. Some of these basins are intended quite
as much to intercept the flow of water from the land side
toward the river as to draw their supplies from the river,
and the prevailing temperatures and chemical analyses of
the waters, as compared with the temperatures and analyses
of the river waters, give evidence that their supplies are in
part from the land.
A thorough examination of the substrata, on the site of
and in the vicinity of the proposed infiltration basin, down
to a level eight or ten feet below the bottom of the basin,
will permit an intelligent opinion to be formed of its percola-
tion capacity.
526. Examples of Infiltration. Pig. 130 illustrates
a section of the infiltration gallery at Lowell, Mass. This
EXAMPLES OF INFILTRATION.
539
gallery is a short distance above the city and above the
dam of the Locks and Canal Co. in the Merrimac River,
that supplies some 10,000 horse-power to the manufacturers
of the city. The gallery is on the northerly shore of the
stream, parallel with it, and lies about one hundred feet
from the shore.
Its length is 1300 feet, width 8 feet, and clear inside
height, 8 feet. Its floor is eight feet below the level of the
crest of the dam. The side walls have an average thickness
of two and three-fourths feet, and a height of five feet, and
are constructed of heavy rubble masonry, laid water-tight
in hydraulic mortar.
LOWELL INFILTRATION GALLERY.
The covering arch is semicircular, of brick, one foot
thick, and is laid water-tight in cement mortar.
Along the bottom, at distances of ten feet between
centres, stone braces one foot square and eight feet long,
are placed transversely between the side walls to resist the
exterior thrust of the earth and the hydrostatic pressure.
540 CLARIFICATION OF WATER.
The bottom is covered with coarse screened gravel, one foot
thick, up to the level of the top of the brace stones.
The required depth of excavation from the surface of the
plain averaged about sixteen feet.
The Merrimac Kiver is tolerably clear of visible impuri-
ties during a large portion of the year, but during high-
water carries a large quantity of clay and of a silicious sand
of very minute, microscopic grains.
An inlet pipe, thirty inches in diameter, connects the
lower end of the gallery directly with the river, for use in
emergencies, and to supplement the supply temporarily at
low- water in the river, when it is usually clear. At the ter-
minal chamber of the gallery into which the inlet pipe leads,
and from which the conduit leads toward the pumps, are
the requisite regulating gates and screens.
This gallery was completed in 1871, and during the
drought and low water of the summer of 1873, a test devel-
oped the continuous infiltration capacity of the gallery to
be one and one-half million gallons per twenty-four hours,
or about one hundred and fifty gallons for each square foot
of bottom area per twenty-four hours.
At Lawrence, Mass., is a similar infiltration gallery along
the eastern shore of the Merrimac Kiver, from which the
city's supply is at present drawn.
The infiltration gallery for the supply of the town of
Brookline, Mass., completed in 1874, lies near the margin
of the Charles River. The bottom is six feet below the
lowest stage of water in the river, its breadth between walls
four feet, and length seven hundred and sixty-two feet. The
side walls are two feet high, laid without mortar, and the
covering arch is semicircular, two courses thick, and tight.
During a pump test of thirty-six hours duration, this
gallery supplied water at a rate of one and one-half million
EXAMPLES OF INFILTRATION. 541
gallons in twenty-four hours, or four hundred and ninety
gallons per square foot of bottom area per twenty-four
hours. The ordinary draught up to the present writing is
about one-third this rate.
The pioneer American infiltration basins were constructed
for the city of Newark, N. J., under the direction of Mr.
Geo. H. Bailey, chief engineer of the Newark water-works.
These basins are somewhat more than a mile above the
city, on the bank of the Passaic River. There are two
basins, each 350 feet long and 150 feet wide, distant about
200 feet from the river. They are revetted with excellent
vertical-faced stone walls, and everything pertaining to
them is substantial and neat. An inlet pipe connects them
with the river for use as exigencies may require.
At Waltham, Mass., a basin was excavated from the
margin of the Charles Eiver back to some distance, and
then a bank of gravel constructed between it and the river,
intended to act as a filter.
The excavation developed a considerable number of
springs that flowed up through the bottom of the basin,
and these are supposed to furnish a large share of the
water supply.
At Providence, two basins have been excavated, one on
each side of the Pawtuxet River. These are near the mar-
gin of the River, and are partitioned from the floods by
artificial gravelly levees.
At Hamilton and Toronto, in Canada, basins have been
excavated on the border of Lake Ontario. The Hamilton
basin has, at the level of low-water in the lake, a water area
of little more than one acre.
At Toronto, the infiltration basin lies along the border
of an island in the lake, nearly opposite to the city. It is
excavated to a depth of thirteen and one-half feet below
542 CLARIFICATION OF WATER.
low- water in the lake, has an average bottom width of 26J
feet, side slopes 2 to 1, and length, including an arm of
390 feet, of 3090 feet. This basin is distant about 150 feet
from the lake.
The top of the draught conduit, which is four feet diam-
eter, is placed at six and one-half feet below low-water, or
the zero datum of the lake ; and the water area in the basin,
if drawn so low as the top of the conduit, will then be 3.75
acres, and when full to zero line is 5.64 acres, the average
surface width being then eighty feet.
During a six days test this basin supplied about four
and one-quarter million imperial gallons per twenty -four
hours under an average head of five feet from the lake, or
at the rate of fifty-two imperial gallons per square foot of
bottom area per twenty-four hours.
At Binghamton, 1ST. Y., two wells of thirty feet diameter
each, were excavated about 150 feet from the margin of the
Susquehanna River, one on each side of the pump-house.
These wells are roofed in.
At Schenectady there is a small gallery along the margin
of the Mohawk River.
Columbus opened her works with a basin on the bank
of the Scioto, and has since added a basin with a process
of sand filtration.
Other towns and cities have formed their infiltration
basins according to their peculiar local circumstances.
These basins generally clarify the water in a most satis-
factory manner, and accomplish all that can be expected
of a mechanical process, but they have not always delivered
the expected volumes of water; but perhaps too much is
sometimes anticipated through ignorance of the true nature
of the soil.
527. Practical Considerations. The experience with
PRACTICAL CONSIDERATIONS. 543
the American and European infiltration basins shows that
when judiciously located they should supply from 150 to
200 U. S. gallons per square foot of bottom area in each
twenty-four hours continuously. This requires a rate of
motion through the gallery inflow surface, of from twenty
to twenty-five lineal feet per twenty-four hours.
This inflow is dependent largely upon the area of shore
surface through which the water tends toward the basin,
and the cleanliness and porousness of that surface.
We have not here the aid of Nature's surface process, in
which the intercepted sediment is decomposed by plant
action, and the pores thrown open by frost expansions, but
are dependent upon floods and littoral currents to clean off
the sediment separated from the intiltering water. If the
infiltering surface is not so cleaned periodically by currents,
it becomes clogged with the sediment, and its capability of
passing water is greatly reduced.
A uniform sized grain of sand or gravel offers greater
percolating facilities than mixed coarse and fine grains.
The proportion of interstices in uniform grains is from thirty
to thirty- three per cent, of the bulk, and the larger the grains
the larger the interstices and the more free the flow. On
the other hand, the smaller the grains, or the more the ad-
mixture of smaller with predominating grains, the smaller
the interstices, and the less the flow, but the more thorough
the clarification and the sooner the pores are silted with
sediment.
If there is much fine material mixed with the gravel,
water will percolate very slowly, and a larger proportional
infiltration area will be required to deliver a given volume
of water.
It will be remembered that we found gravel ( 351) with
due admixtures of graded fine materials to make the very
544 CLARIFICATION OF WATER.
"best embankment to retain water, even under fifty or more
feet head.
The best bank in which to locate an infiltration basin is
one which is made up of uniform silicious sand grains of
about the size used for hydraulic mortar, and which has a
thin covering of finer grains next the body of water to be
filtered. The silting will in such case be chiefly in the sur-
face layer, and the cleaning by flood current then be most
effectual.
The distance of the basin from the body of water is gov-
erned by the nature of the materials, being greater in coarse
gravel than in sand. It should be only just sufficient to
insure thorough clarification when the surface is cleanest.
A greater distance necessitates a greater expense for greater
basin area to accomplish a given duty, and a lesser distance
will not always give thorough clarification.
The distance should be graduated in a varying stratum,
so that the work per unit of area shall be as uniform as
possible.
528. Examples of European Infiltration. Mr. Jas.
P. Kirkwood, C.E., in his report* to the Board of Water
Commissioners of St. Louis, by whom he was commissioned
to examine the filtering processes practised in Europe, as
applied to public water supplies, has given most accurate
and valuable information, which those who are interested in
the subject of filtration will do well to consult.
From Mr. Kirkwood' s elaborate report we have con-
densed some data relating to European infiltration galleries.
Perth, in Scotland, has a covered gallery located in an
island in the River Tay. Its inside width is 4 feet, height
8 feet, and length 300 feet. Its floor is 2 j feet below low-
water surface in the river. Its capacity is 200,000 gallons
* Filtration of River Waters, Van Nostrand, New York, 1869.
1
EUROPEAN INFILTRATION. 545
per diem, and rate of infiltration per square foot of bottom
area, 182 gallons per diem.
Angers, in France, has a covered gallery located in an
island in the River Loire. This gallery has two angles of
slight deflection, dividing it into three sections. The two
end sections are 3'-4" wide and the centre section 6-0" wide.
The floors of the two end sections are 7 below low- water in
the river, and of the central section 9J feet below. The
combined length of these galleries is 288 feet, and their de-
livery 187 gallons per diem per square foot of bottom area.
These were constructed in 1856, and rest on a clayey
substratum ; consequently the greater part of their inflow-
must be through the open side walls.
More recently, these have been reinforced by a new
gallery, with its floor 5J feet below low- water surface in the
river, and not extending down to the clay stratum. This is
5 feet wide and 8 feet high, and delivers 300 gallons per
diem per square foot of bottom area.
Lyons, in France, has two covered galleries along the
banks of the Rhone, the first 16-6" wide and 394 feet long.
The second is 33 feet wide, except at a short section in the
centre, where it is narrowed to 8 feet, and is 328 feet long.
There are also two rectangular covered basins. The com-
bined bottom areas of the two galleries is 17,200 square
feet, and of the two basins 40,506 square feet. The total
delivery at the lowest stage of the river is nearly six mil-
lion gallons per diem, or 100 gallons per square foot of
bottom area. The capacity of the 33-foot gallery alone is,
however, 147 gallons per square foot of bottom area. About
6J feet head is required for the delivery of the maximum
quantity. The average distance of the galleries from the
river is about 80 feet, and the two basins are behind one of
the galleries.
35
546 CLARIFICATION OF WATER.
At Toulouse, France, three covered galleries extend
along the bank of the Garonne. The first two, after being
walled, were filled with small stones.
The new gallery has its side-walls laid in mortar, is cov-
ered with a semicircular arch, is 7-6" wide, 8-8" high, and
1180 feet long. Its floor is 8'-7" below low- water surface in
the river. Its total capacity is a little in excess of 2% mil-
lion gallons, or 228 gallons per diem, per square foot of
bottom area.
For the supply of Genoa, in Italy, which lies upon the
Mediterranean, a gallery has been constructed, in a valley
of a northern slope of the Maritime Alps, at an altitude of
1181 feet above the sea. This gallery extends in part
beneath the bed of the River Scrivia, transversely from side
to side, and in part along the banks of the stream. The
width is 5 feet, height 7 to 8 feet, and length 1780 feet.
The extraordinarily large delivery, per lineal foot, is
6412 gallons per diem.
The waters are conveyed down to Genoa in cast-iron
pipes, with relieving-tanks at intervals.
529. Example of Intercepting Well. The great
well in Prospect Park, Brooklyn, L. I., is a notable instance
of intercepting basin, such as is sometimes adopted to inter-
cept the flow of the land waters toward a great valley, or
the sea, or to gather the rainfall upon a great area of sandy
plain.
This portion of Long Island is a vast bed of sand, which
receives into its interstices a large percentage of the rainfall.
The rain-water then percolates through the sand in steady
flow toward the ocean. Although the surface of the land
has considerable undulation, the subterranean saturation is
found to take nearly a true plane of inclination toward the
sea, and this inclination is found by measurements in
FILTER-BEDS. 547
numerous wells to be at the rate of about one foot in 770 ft.,
or seven feet per mile. So if a well is to be dug at one-half
mile from the ocean beach, water is expected to be found
at a level about three and one-half feet above mean tide ;
or, if one mile from the beach, at seven feet above mean
tide, whatever may be the elevation of the land surface.
If in such subsoils a well is excavated, and a great draught
of water is pumped, the surface of saturation will take its
inclination toward the well, and the area of the watershed
of the well will extend as the water surface in the well is
lowered. If the well has its water surface lowered so as to
draw toward it say a share equal to twenty-four inches of
the annual rainfall on a circle around it of one-quarter mile
radius, then its yield should be at the rate of very nearly
one-half million gallons of water daily.
The Prospect Park well, Fig. 131 (p. 102), is 50 ft. in diam-
eter. A brick steen or curb of this diameter, resting upon
and bolted to a timber shoe, edged with iron, was sunk by
excavating within and beneath it, fifty-nine feet to the sat-
uration plane, and then a like curb of thirty -five feet diam-
eter was sunk to a further depth of ten feet. The top of the
inner curb was finished at the line of water surface. A
platform was then constructed a few feet above the water
surface, within the large curb, to receive the pumping
engine. The boilers were placed in an ornate boiler-house
near the well.
On test trial, the well was found to yield, after the water
surface in the well had been drawn down four and one-half
feet, at the rate of 850,000 gallons per twenty-four hours.
53O. Filter-beds. A method of filtration, more arti-
ficial than those above described, must in many cases be
resorted to for the clarification of public water supplies.
The most simple of the methods that has had thorough
648
CLARIFICATION OF WATER.
FIG. 132.
trial, consists in passing the water downward, in an arti-
ficial basin specially constructed for the purpose, through
layers of fine sand, coarse sand, fine gravel, coarse gravel,
and broken stone, to collecting drains placed beneath the
whole, Fig. 132.
FILTER-BEDS. 549
The basins in such cases are usually from 100 to 200
feet wide, and from 200 to 300 feet long, each. Each basin
is made quite water-tight, the horizontal bottom or floor
being puddled, if necessary, and sometimes also covered
with a paving of concrete, or layer of bricks in cement
mortar. The sides are revetted with masonry, or have
slopes paved with substantial stone in mortar, or with
concrete.
A main drain extends longitudinally through the centre
of the basin, rests upon the floor, and is about two feet
wide and three feet high. From the main drain, on each
side, at right-angles, and at distances of about six feet
between centres, branch the small drains. These are six or
eight inches in diameter, of porous, or, more generally, per-
forated clay tiles, resting upon the bottom or floor, and they
extend from the central drain to the side walls, where they
have vertical, open-topped, ventilating, or air-escape pipes,
rising to the top of the side walls.
These pipes and the central drain form an arterial sys-
tem by which water may be gathered uniformly from the
whole area of the basin.
This arterial system is then covered, in horizontal layers,
according to the suitable materials available, substantially
as follows, viz.: two feet of broken stone, like "road
metal ;" one foot of shingle or coarse-screened gravel ; one
foot of pea-sized screened gravel ; one foot of coarse sand ;
and a top covering of one and one-half to three feet of fine
sand.
This combination is termed a filter-bed, and over it is
flowed the water to be clarified.
Provision is made for flowing on the water so as not to
disturb the fine sand surface. This inflow duct is often
arranged in the form of a tight channel on the top of the
550 CLARIFICATION OF WATER.
covering of the central gathering drain, and the water flows
over its side walls, during the filling of the "basin, to right
and left, with slow motion.
The depth of water maintained npon the filter-bed is
four feet or more, according to exposure and climatic effects
upon it.
At the outflow end of the central gathering drain is an
effluent chamber, with a regulating gate over which the
filtered water flows into the conduit leading to the clear-
water basin. The water in the effluent chamber is connected
with the water upon the filter-bed through the drains and
interstices of the bed ; consequently, if there is no draught,
its surface has the same level as that upon the bed, but if
there is draught, the surface in the chamber is lowest, and
the difference of level is the head under which water flows
through the filter-bed to the effluent chamber.
The regulating gate in the effluent chamber controls the
outflow there to the clarified water basin, and consequently
the head under which filtration takes place, and the rate of
flow through the filter-bed.
531. Settling and Clear- water Basins. When the
water is received from a river subject to the roil of floods, it
should be received first into a settling basin, where it will
be at rest forty-eight hours or more, so that as much as
possible of the sediment may be separated by the gravity
process, before alluded to. Its rest in large storage basins
prepares it very fully for introduction to the filter-bed,
which is to complete the separation of the microscopic
plants, vegetable fibres, and animate organisms, that can-
not be separated by precipitation.
Since the domestic consumption of the water at some
hours of the day is nearly or quite double the average con-
sumption per diem, the clarified water basin should be
FILTER-BED SYSTEM. 551
large enough to supply the irregular draught and permit
the flow through the niter to be uniform.
This system of clarification in perfection includes three
divisions, viz. : the Settling Basin, the Filter-bed, and the
Clear-water Basin.
The settling and clear- water basins may be constructed
according to the methods and principles already discussed
for distributing reservoirs (Chap. XYI). The capacity of
each should be sufficient to hold not less than two days
supply, and the depth of water should be not less than
ten feet, so that the water may not be raised to too high
a temperature in summer, and that its temperature may
be raised somewhat in winter before it enters the distribu-
tion-pipes.
532. Introduction of Filter-bed System. Pough-
keepsie, on the Hudson, was the first American city to
adopt the filler-bed system of clarification of her public
water-supply.
The Poughkeepsie works were constructed in 1871, to
take water from the Hudson Eiver. During the spring
floods, the river is quite turbid. These filtering works con-
sist of a small settling basin and two filter-beds, each^73^ ft.
wide and 200 ft. long. Each bed is composed of
24 inches of fine sand.
6 " " -inch gravel.
6 " " |-inch gravel.
6 " " i-inch broken stone.
24 " " 4 to 8-inch spalls.
72 " total.
The floors on which the beds rest are of concrete, twelve
inches thick.
The clear- water basin is 28 by 88 feet in plan, and 17 ft.
deep.
552 CLARIFICATION OF WATER.
Water is lifted from the river to the settling basin by a
pump, and it flows from the clear-water basin to the suction
chamber of the main pump, giving some back pressure.
From thence it is pumped to the distributing reservoir.
The filter-beds are at present used but a portion of the
year, subsidence in the main reservoir being sufficient to
render the water acceptable to the consumers.
In the recent construction of the new water supply for
the city of Toledo, 20,000 square feet of filter-bed was at
first prepared to test its efficiency in the clarification of the
turbid Maumee River water. The great demand for water
has, however, made the construction of additional filter area
and large subsidence basins a necessity, the consumption
having already (1876) reached nearly 3,000,000 gallons per
diem. Anticipating the necessity, Chief Engineer Cook has
devised and is experimenting with a series of chambers, to
contain filtering materials through which the water is to be
flowed with an upward current.
When our American water consumers are more familiar
with this filter-bed system of clarification, now in such gen-
eral use in England and Scotland and on the Continent, its
use will be oftener demanded. Subsidence, as we have
4
before remarked, does not completely clarify the water,
even in a fortnight's or three weeks' time, but a good sand
filter, if not overworked, intercepts not only the visible sedi-
ment and fine clay, but the most minute vegetable fibres
and organisms and the spawn of fish, and it is highly im-
portant that these should be separated before the water is
passed to the consumer.
533. Capacity of Filter-Beds. Experience indicates
that the flow through a filter-bed, such as we have above
described, should not exceed the rate of 17 feet lineal per
diem, or be reduced by silting of the sand layer to less than
i
CLEANING OF FILTER-BEDS. 553
6.5 feet per diem. It must not be so rapid as to suck the
sand grains or clay particles or the intercepted fibres
through the bed, or its whole purpose will be entirely
defeated.
A rate of about one-half inch per hour, or twelve lineal
feet per diem, when the filter is tolerably clean, is generally
considered the best. This gives the filter-bed a capacity of
twelve cubic feet, or 89.76 gallons, per square foot of sur-
face per twenty-four hours, and requires, in work, about
12,000 square feet of filtering surface for each million gal-
lons of water to be filtered per diem.
534. Cleaning of FUter-Beds. The filter-beds upon
the English streams require cleaning about once a week,
when the rivers are in their most turbid condition, and
ordinarily once in three or four weeks.
The process of cleaning consists of removing a slice of
about one-half inch thickness from the surface of the fine
sand layer, and the stirring or loosening up of the sand that
is packed hard by the weight of the water, when the clog-
ging of the filter prevents or hinders greatly its flow. This
requires the water to be drawn off from the bed to be cleaned,
and of course puts the portion of filter area being cleaned
out of service. According to the usual practice, the water is
drawn down only about a foot below the sand surface for
the cleaning ; but there is a great advantage, though an in-
convenience, in drawing the water entirely out of the bed,
for this admits the air to oxidize the organic matters that
are drawn into the filter, which is of great importance.
To provide for cleaning, the required area for service
should be divided into two or more independent beds, and
then one additional bed should be provided also, so that
there shall always be one bed surplus that may be put out
of use for cleaning.
554
CLARIFICATION OF WATER.
The greater the number of equal divisions the less will
be the surplus area to be provided, and on the other hand,
each division adds something to the cost, so that both con-
venience and finance are factors controlling the design as
well as the form and extent of lands available.
As a suggestion merely, it is remarked that the divisions
may be approximately as follows, for given volumes, de-
pendent on the turbidness of water and local circumstances :
3 '
80
x 150 '
3 "
100
X 1 80 '
4 "
100
X 1 80 '
4 "
100
x 240 '
4 "
1 20
x 270 '
5 "
1 20
x 270 '
TABLE No. 1O9.
DIMENSIONS OF FILTER-BEDS FOR GIVEN VOLUMES.
For i million gallons per diem, 3 beds 60 feet x 100 feet.
2
3
4|
6
8
10
535. Renewal of Sand Surface. When the repeated
pairings from the surface have reduced the top fine-sand
layer to about twelve inches thickness, a new coat should
be put on restoring it to its original thickness.
If good fine sand is difficult of procurement, the pairings
may perhaps be washed for replacing with economical
result.
This is sometimes accomplished by letting water flow
over the sand in an inclined trough of plank, having cleats
across it to intercept the sand, or by letting water flow up
through it in a wood or iron tank. In the latter case water
is admitted under pressure through the bottom of the tank,
and the sand rests upon a grating covered with a fine wire
cloth, placed a short distance above the bottom of the tank.
The current is allowed to flow up through the sand and over
the top of the tank until it runs clear.
BASIN COVERINGS. 555
536. Basin Coverings. The British and Continental
filter-beds are rarely roofed in, although the practice is
almost universal of vaulting over the distributing reservoirs
that are near the towns.
The intensity of our summer heat and intensity of winter
cold in our northern and eastern States, makes the roofing
in of our filter-beds almost a necessity, though we are not
aware that this has been done as yet in any instance.
I The use of the shallow depth of four feet of water, so
common in the English filters, would be most fatal to open
filters here, for the water would frequently be raised in
summer to temperatures above 80 Fah. and sent into the
pipes altogether too warm, with scarce any beneficial
change before it reached the consumer. Such tempera-
tures induce also a prolific growth of algcB upon the sides
of the basin, and upon the sand surface when it has become
partially clogged, and soon produce a vegetable scum upon
the water surface also. As these vegetations are rapidly
reproduced and are short-lived, their gases of decomposi-
tion permeate the whole flow, and render the water ob-
noxious.
Depth of water and protection from the direct heating
action of the sun are the remedies and preventatives for
such troubles. A free circulation of air and light must,
however, be provided, and also the most convenient facili-
ties for the cleansing and renewal of the bed.
In Fig. 132 is presented a suggestion for a roof-covering
that will give the necessary protection from sun and frost, and
the requisite light, ventilation, and convenience of access.
The side walls are here proposed to be of brick, and the
truss supporting the roof to be of the suspended trapezoidal
. class. The confined air in the hollow walls, and the saw-
dust or tan layer over the truss, are the non-conductors that
556 CLARIFICATION OF WATER.
assist in maintaining an even temperature within the basin,
and resist the effects of intense heat and intense cold.
The Parisian reservoirs at Menilmontant, and the splen-
did new structure at Moutrouge, are covered with a system
of vaulting, after the manner practised by the Romans, and
this system is also followed by the British engineers in their
basin covers.
A substantial cover over a filter basin will reduce the
difficulties with ice to a minimum, and remove the risk of
the bed being frozen while the water is drawn off for clean-
ing in winter. In such case, if the water is drawn imme-
diately from a deep natural lake, or a large impounding
reservoir, the only ice formation will be a mere skimming
over of the surface in the severest weather, and the inflow
of water, at a temperature slightly above freezing, will tend
constantly to preserve the surface of the water uncongealed,
and the sand free from anchor ice.
FIG. 133.
PUMPING ENGINE No. 3, BROOKLYN.
CHAPTER XXIV.
PUMPING OF WATER.
537. Types of Pumps. The machines that have been
used for raising water for public water supplies in the United
States present a variety of combinations, but their water
ends may be classified and illustrated by a few type forms.
Our space will not permit a discussion of the theories
and details of their prime movers, nor more than a general
discussion of the details of the pumps, with their relations
to the flow of water in their force mains.
The horizontal double-acting piston pump of the type,
Fig. 134, is an ancient device, and in its present form re-
mains substantially as devised by La Hire, and described
in the Memoirs of the French Academy in 1716. This was
at one time a favorite type, and was adopted for the most
prominent of the early American pumping works, as at
Philadelphia, Eichmond, New Haven, Cincinnati, Mon-
treal, etc.
Several modifications of the vertical plunger pump, after
the modern Cornish pattern (Fig. 135), were later intro-
duced at Jersey City, Cleveland, Philadelphia, Louisville,
etc., and in 1875 at Providence.
The vertical bucket pump (Fig. 133), in various modifi-
cations (referring to the water end only), was introduced at
Hartford, Brooklyn, New Bedford, etc.
The bucket-plunger pump (Fig. 136, water end), has
been more recently introduced at Chicago, St. Louis, Mil-
waukee, Lowell, Lynn, Lawrence, Manchester, etc.
558
PUMPS.
A vertical acting differential plunger pump, having one
set of suction and one set of delivery valves, each arranged
in an annular ring around the plunger chamber, has re-
cently been invented by at least two engineers, independ-
ently of each other, and with similar disposition of parts.
This, like the bucket and plunger pump, is single-acting in
suction and double-acting in delivery. This pump gives
promise of superior excellence
The double-acting horizontal plunger pump (page 223),
itself an ancient and admirable invention, was first intro-
duced in combination with the Worthington duplex engine
about the year 1860, and has since been adopted at Harris-
burg, Charlestown, Newark, Salem, Baltimore, Toledo,
Toronto, Montreal, etc.
FIG. 134.
HORIZONTAL DOUBLE-ACTING PISTON PUMP.
Kotary, and gangs of small piston pumps have been in-
troduced to some extent, in direct pressure systems, in some
of the small Western towns.
EXPENSE OF VARIABLE DELIVERY of WATER. 559
538. Several of the earliest pumps * of magnitude worthy
of note were driven by overshot, or breast water-wheels, as
at Bethlehem, Pa., Fairmount Works, Philadelphia, New
Haven, Richmond, and Montreal. Turbines have, how-
ever, taken the places of the horizontal wheels at Phila-
delphia and Richmond, and in part at Montreal, and tur-
bines give the motion at Manchester, Lancaster, Bangor,
and at other cities.
Fig. 143 shows the latest improved form of the G-eyelin-
Jonval turbine, which has been used very successfully in
several of the large cities for driving pumps.
The greater number of the pumping machines now in
use are actuated by compound steam-engines.
A considerable number of the large pumping machines
have their pump cylinders in line with their steam cylin-
ders, and their pump rods in prolongation of their steam
piston rods.
539. Expense of Variable Delivery of Water.
It is important that the delivery of water into the force-main
from the pumping machinery be as uniform as possible,
and constant,
If the delivery of water is intermittent or variable, and
the flow in the main equally variable, then power is con-
sumed at each stroke in accelerating the flow from the
minimum to the maximum rate.
The ms viva^ of the column of water in the force-main,
surrendered during the retardation at each stroke, is neutral-
* Bethlehem, Pa., constructed in 1762 the first public water supply in the
United States in which the pumps were driven by water-power. Philadelphia
constructed, in 1797, on the Schuylkill River, a little below Fairmount, the
first public water- works in the United States driven by steam-power. In 1812
steam-pumps were started at Fairmount, and the old works abandoned. In
April, 1822, the hydraulic- power pumps were started at Fairmount.
f Vide " principle of ms viva," in Moseley's " Mechanics of Engineering,"
p. 115, New York, 1860, and Poncelet's Mecanique Industrielle, Art. 135,
Paris, 1841.
560 * PUMPS.
ized by gravity, and no useful effect or aid to the piston of
the pump is given back, as useful work is given during the
retardation of the fly-wheel of an engine.
If, as when the pump is single-acting, motion is gener-
ated during each forward stroke, and the column comes to
rest during the return stroke of the piston, or between
strokes of the piston, the power consumed (neglecting fric-
tion) to generate the maximum rate of motion, equals the
product of the weight of the column of water into the height
to which such maximum rate of motion would be due if the
column was falling freely, in vacuo, in obedience to the in-
fluence of gravity.
Let Q be the volume of water to be set in motion, in
cubic feet, w the weight of a cubic foot of water, in pounds
(= 62.5 Ibs), ^i the equivalent height, in feet, to which the
(t) 2 \
= ^-), and PI the power required to
&g'
produce the acceleration ; then
p l Q x w x hi. (1)
If the velocity is checked and then accelerated during
each stroke, without coming to a rest, let v be the maximum
velocity, in feet per second, and Vi the minimum velocity ;
then the power consumed in or necessary to produce the
acceleration is
In illustration of this last equation, which represents a
smaller loss than the first, assume the force-main, with air-
vessel inoperative, to be 1000 feet long and 2 feet diameter,
and the maximum and minimum velocities of flow to be
5 feet and 4 feet per second respectively.
The weight of the contents of the main into its accelera-
tion will be (.7854d 2 x 1) x w x \- - -^ j- = 3142 cu. ft. x
* *)
EXPENSE OF VARIABLE DELIVERY OF WATER. 561
62.5 Ibs. x .14 ft. = 27492.5 foot-lbs. If there are ten strokes
per minute, 274925 foot Ibs. = 8J HP will be thus con-
sumed. If the main is twice, or four times as long, the
power consumed will be doubled, or quadrupled.
The power required to accelerate the motion of the
column is in addition to the dynamic power P l in foot-lbs.,
required to lift it through the height H, of actual lift.
For the equation of lifting power per second, when Q is
the volume per second (neglecting friction), we have
P, = Q x w x If, (3)
or for any time,
P l = QxtxwxH. (4)
The frictional resistance to flow in a straight main is
proportional, very nearly to the square of the velocity of
flow (to mv 2 ), and is computed by some formula for frictional
head 7i", among which for lengths exceeding 1000 feet is
in which 7i" is the vertical height, in feet, equivalent to the
frictional resistance.
I " length of main, in feet.
d " diameter of the main, in feet.
m is a coefficient, which may be selected from
Table 61, page 242, of values of m.
The equation of power p", to overcome the frictional
head, is
The equation of power required, expressed in horse-
powers \_H.P.} of 33,000 foot-pounds per minute, each, for
dynamic lift, and frictional resistance to flow combined, is
33,000
36
562
PUMPS.
The several resistances above described are all loads
upon the pump-piston, and their sum, together with the
frictions at angles and contractions, is the load, from the
flow in the main which the prime mover has to overcome.
When the delivery of the water into the main is constant
and uniform, these resistances are at their minimum.
54O. Variable Motions of a Piston. If we analyze
the rates of motion during the forward stroke of a piston
moved by a revolving crank with uniform motion, whose
length or radius of circle is 1 foot, we find the spaces or dis-
tances moved through in equal times by the piston, while
the crank-pin passes through equal arcs, to be as in the fol-
lowing table.
TABLE No. HO.
PISTON SPACES, FOR EQUAL SUCCESSIVE ARCS OF CRANK MOTION, n^.
Arcs
"i
22*
33*
45
56*
67*
7 8|
90
Space, ft. .
.0223
.0648
.1034
1384
1655
.1849
.1946
.1981
Arcs
I0li
na|
4i
135
i 4 6i
iS7l
i68|
180
Space, ft. .
.1921
.1806
.1609
1375
.1104
.0814
.0488
.0163
The spaces are equal to the above, but in inverse order
during the return stroke. To compute spaces for other
lengths of crank, and the same arcs, multiply the given
lengths of crank in feet by the above spaces.
The sum of the motions of the piston while the pin moves
through the first 90 is 1.072 feet, and while through the
second 90 is .928 feet; therefore the motion of the piston
is faster during the first and fourth parts of the revolution
than during the second and third.
The motion of the piston is accelerated through .5218 of
its forward and .4782 of its return stroke, and is retarded
during the remaining parts of its forward and backward
FIG. 135.
CORNISH PUMP, JERSEY CITY.
564
PUMPS.
motions ; and with the usual length of connecting rod, it
attains a maximum velocity equal to about 1.625 times its
mean velocity.
If the pump is single acting, then no delivery of water
takes place during the return stroke, and this is the most dif-
ficult case of intermittent motion to provide for in the main.
541. Ratios of Variable Delivery of Water. If we
analyze the ratios of movement of a single, and the sums of
ratios of movement of two or three coupled double-acting
pump pistons, when the two crank-pins are 90 apart, and the
three pins 60, we find the ratios, during the forward motion
of piston No. 1, for given arcs, approximately as in the
following table :
TABLE No. 111.
RATIOS, AND SUMS OF RATIOS, OF PISTON MOTIONS FOR EQUAL
SUCCESSIVE ARCS OF CRANK MOTION, nj.
Arcs
Hi
22*
33f
45
5^
67!
78|
90
i piston
2 pistons .
.0
.1620
.0423
.2293
.0840
.2550
.1180
.2607
.1490
.27S3
.1653
.2730
.1906
.2567
.1967
.2766
1953
.1960
3 pistons
.3426
.3700
.3866
.3896
3776
3577
.3640
3853
3930
Arcs
I2-* 3
id6 l
I c 7 1
168'
180
i piston
18^3
0660
2 pistons
.22Q3
*/~*
.2680
.1960
3 pistons
.3810
3613
.3200
3777
3893
.3856
.3700
3740
....
The variations of motion, and of delivery of water, on
each side of the mean rate of delivery is with one piston
about 10 per cent., with two pistons about 5\ per cent., and
with three pistons about 2J per cent., or in other words, the
ratios of excess of delivery are .10, .055, .025, and the ratios
of deficiency have like values.
542. Office of Staiid-Pipe and Air- Vessel. It is
the office of the stand-pipe and air-vessel to take up the
CAPACITIES OF AIR-VESSELS. 565
excess, and to compensate for the deficiency of delivery by
the pump pistons, plungers, or buckets. These are most
effective when nearest to the pump cylinders.
The excess of delivery enters the open-topped stand-pipe
and raises its column of water, and the column is drawn
from and falls to supply the deficiency. Work is expended
to lift the column, and this work is given to the advancing
water in the main when the column falls again, but when
the piston is again accelerated it has the labor of checking
the motion of the falling column in the stand-pipe.
The air-vessel on the force main is practically a shorter,
closed-top stand-pipe containing an imprisoned body of
air. The excess of delivery of water from the pumps enters
the air-vessel and compresses the air, and the expansion of
the air forces out water to supply the deficiency. The reduc-
tion at each stroke of the mean volume of the air in the
vessel is directly proportioned to the excess of water deliv-
ered and received into the air-vessel, which is; for different
pumps, proportional to their variations, or if coupled or
working through the same air-vessel, to the algebraical
sums of their variations.
543. Capacities of Air- Vessels. The cubical capa-
city of an air-vessel for one pair of double-acting pumps is
usually about five or six times the combined cubical capa-
city of the water cylinders ; but we shall see that the capa-
city of the cylinders alone is not the full basis on which the
capacity of the vessel is to be proportioned.
If the air-vessel is filled with air under the pressure of
the atmosphere only, and then is subjected to a greater
pressure of water, it will not remain full of air, for the air
will be compressed, and, according to Mariotte's law,* its
* Vide Lardner's Hydrostatics and Pneumatics, p. 158. London, 1874.
566 PUMPS.
volume will "be inversely proportional to the pressure under
which it exists, provided the temperature remains the same.
Thus, if the vessel was filled under a pressure of 15 Ibs. per
square inch, and the water pressure is six times greater or
90 Ibs. per square inch, and the temperature is unchanged,
then the air-vessel will be but one-sixth full.
It is the reduced volume of air in the vessel that is com-
pressed to take up the excess of water delivered by the
pumps ; therefore the degree of pressure should be a factor
in the equation of capacity of air-vessel, as well as the ratio
of excess of delivery during a half stroke.
Let q be the volume of delivery of a pump piston dur-
ing its forward stroke, r the ratio of excess ; or if two or
more pistons are coupled, the algebraic sum of ratios of
excess of delivery of water during the forward stroke of
No. 1 piston, n the maximum pressure of water in atmos-
pheres (= 14.7 Ibs. per square inch each), and /an experi-
ence coefficient whose value will ordinarily be about 15,
then the equation for cubical capacity, (?, in cubic feet, of
air-vessel is,
C = qxrxnxf, (8)
or if p is the maximum water pressure, in pounds per square
inch, then the equation, when/ = 15, may take the form
C = pqr. (9)
If the water is to be permitted to abstract an appreciable
portion of the air from the air-vessel, that is, if the air-vessel
is not to be frequently recharged, then the coefficient in the
above equation should be greater than 15. If the air-vessel
is to be recharged often, mechanically, with volumes of air
greater than the atmospheric pressure would supply, then
the coefficient may be some less than 15.
FIG. 136.
LYNN PUMPING ENGINE. - (E. D. Leavitt, Jr.'s, Patent.)
568 PUMPS.
The larger the water surface in contact with the air in
the air-vessel, the faster the air is absorbed by the water ;
therefore it is advisable to give considerable height in pro-
portion to diameter to the air-vessel, and a disk of wood or
other nearly or quite impervious material, one or two inches
less in diameter than the air-vessel, may be allowed to lie
on the water in the vessel, and thus still more reduce the
surfaces of contact of air and water.
544. Valves. Pumps that have to lift water to heights
greater than thirty feet, are usually of necessity, or for
convenience of access, placed between the water to be
raised and the point of delivery. When so situated they
perform two distinct operations, one of which is to draw the
water to them, and the other to force it up to the desired
elevation. When the pump piston or plunger advances,
FIG. 137.
the water in front of it is pressed forward, and at the same
time the pressure of the atmosphere forces in water to fill
the space or vacuum that it would otherwise leave behind
it. The return of the water must be prevented, or the work
done by lifting it will be wasted. Valves which open freely
to forward motion of the water and close against its return,
are, therefore, a necessity, both upon the suction and the
delivery sides of the pump.
All valves break up and distort, in some degree, the ad-
vancing column of water. Such distortions and divisions
VALVES. 569
cause frictional resistance, which consumes power. The
valve that admits the passage of the column of water by or
through it with the least division or deflection from its direct
course, neutralizes least of the motive power. Short bends
and contractions in water passages, that consume a great
deal of power or equivalent head, often occur in their worst
degree in pump valves.
The piston valve which moves entirely out of the water-
passage, and permits the flow of water in a single cylindrical
column, such for instance as was used in the Darlington
and Junker water -engines,* is perhaps least objectionable
in the matter of frictional resistance to the moving water,
but is often inconvenient to use. The single flap- valve
(Fig. 137), with area at 30 lift exceeding the sectional area
of the pump cylinder, gives also a minimum amount of fric-
tional resistance.
The single annular form of column, while passing through
the valve, is less objectionable than any of the other divi-
sions of the water, and annular valve openings have been
the favorite forms in nearly all the large pumping ma-
chines.
In some of the earlier pumps the suction was through a
single valve with two annular openings, after the Harvey
and West model, or, as more familiarly known, the Cornish
double-beat valve, similar to Fig. 138, illustrating the valves
used in the Brooklyn engines.
When pumps began to be built of great magnitude,
requiring large capacities for flow, and the valves were
increased in size to two feet diameter and upward, the
valves were found to strike very powerful blows as they
* Vide illustration of a water-engine in Rankine's "Steam Engine," p. 140,
London, 1873, and Lardner's Hydrostatics and Pneumatics, p. 312. London,
1874.
570
PUMPS.
FIG. 138.
came upon their seats, and to make the whole machine, the
"building, and the earth around the foundations tremble.
This annoyance led to dividing the valves into nests of
five or more valves of similar double-beat form. In London
and other large English cities the valves have of late been
of the four-beat class, or Husband's model.
In many pumps the valves have of late been divided into
nests of twelve or more rubber-disks (Fig. 139) in each set,
seating upon grated openings in a flat valve-plate. Each
subdivision increases the frictional resistance, but reduces
the force of the blow, or water-hammer., when the valve
strikes its seat.
The suction and delivery valves of the piston pumps
(Fig. 134) were usually of the flap or hinged pattern. These
piston-pumps had sometimes, though rarely, their cylinders
placed vertically, as at the Centre Square Works erected in
MOTION OF WATER THROUGH PUMPS.
571
Philadelphia in 1801, and at the Schuylkill Works erected
in the same city in 1844. They were inclined ten or twelve
degrees from the horizontal at Montreal.
The horizontal plunger,
or " Worthington " pumps
(page 223), have uniformly
been fitted with nests of rub-
ber disk valves.
The best of the modern
steam fire-engines are fitted
with nests of rubber disk
valves, showing that this
class of valve is a favorite
when the pressure is great and the motion is rapid.
The rubber disk valve (Fig. 139) was sketched from an
Amoskeag fire-steamer valve.
545. Motion of Water Through Pumps. Water is
so heavy and inelastic that large columns of it cannot be
quickly started or stopped, without the exertion or opposi-
tion of great power to overcome its inertia, or vis viva.
There is therefore an advantage, as respects the even and
moderate consumption of power, when the piston or plunger
motion is reciprocal, in making the strokes long, and few
per minute.
The case is entirely different with an elastic fluid like
steam. The tendency of the most successful modern steam
engineering has been toward quick strokes and high steam
pressures, and with high degrees of expansion in the larger
engines.
The "indoor" ends of the beams of the best Cornish
pumping-engines are longer than the " outdoor" ends, and
it is claimed as one of their special advantages that the in-
door or steam stroke that lifts the plunger pole can be made
572 PUMPS.
with rapidity, while the outdoor stroke, or fall of the
plunger by its own weight, can "be gradual, and thus the
water be pressed forward at a nearly steady and uniform
rate. The single-cylinder, single-acting, non-rotative Cor-
nish engine is admirably adapted to the work to which
it was early applied by Watt and Boulton namely, the
raising of water from the deep pits of mines by suc-
cessive lifts to the surface adits, where it flowed freely
away ; but when applied to long force-mains of water-
supplies, a stand-pipe near the pump becomes a necessity
to neutralize the straining and laborious effects of the inter-
mittent action.
546. Double- Acting Pumping-Engines. The de-
sire to overcome the objectionable intermittent delivery of
the single-acting pump, as well as the influence of the sharp
competition among engine-builders, that forced them to
study methods of economizing the first cost of the machines
while maintaining their capacity and economy of action,
led to the introduction, for water-supply pumping, of the
compound or double cylinder, double-acting, rotative or
fly-wheel engine. This last class of engines was brought to
a high state of perfection by Mr. Wicksted and Mr. Simp-
son at the London pumping stations. Some admirable
pumping machines of this class have been constructed for
American water-works from designs of Messrs. Wright,
Cregeir, Leavitt, and others.
547. Geared Pumping-Engines. Geared compound
pumping-engines, one style of which (the Nagle) is shown in
side and end elevations* in Figs. 140 (p. 377) and 141 (p. 573),
are well adapted both for direct pumping, and also where
the reservoir and direct systems are combined. Advantage
* From the design adopted for the Providence High Service, and working
with direct pressure.
FIG. 141.
A. F. NAGIE.
CROSS SECTIONAL ELEVATION.
NAGLE'S GEARED PUMPING ENGINE.
574 PUMPS.
may here be taken of high pressure of steam, rapid steam
piston stroke, and large degree of steam expansion, while
the water piston moves relatively slow with a minimum
number of reversals.
548. Costs of Pumping Water. The following table
(p. 575) gives the running expenses for pumping water in
various cities.
549. Duty of Pumping Engines. The duty or
effective work of a steam pumping-engine, as now usually
expressed, is the ratio of the product, in foot-pounds, of
the weight of water into the height it is lifted, to one hun-
dred pounds of the coal burned to lift the water.
This standard is an outgrowth from that established
by Watt, about the year 1780, for the purpose of compar-
ing the performances of pumping-engines in the Cornish
mines, when Messrs. Boulton and Watt first introduced
their improved pumping-engines upon condition that their
compensation was to be derived from a share of the saving
in fuel. Watt first used a bushel of coal as the unit of
measure of fuel, equal to about 94 pounds, and afterward
a cwt. of coal, equal to 112 pounds. More recently, in
European practice, and generally in American practice,
100 pounds of coal is the unit of measure of fuel. In some
recent refined experiments, the weight of ashes and clinkers
is deducted, and the unit of measure of fuel is the combus-
tible portion of 100 pounds of coal. The use of these sev-
eral units, differing but slightly from each other in value,
leads to confusion or apparent wide discrepancies in results,
when the performances of different pumping-engines are
compared, unless the results are all reduced to an uniform
standard.
To construct an equation in conformity with the more
generally accepted standard of duty, let Q be the volume
r
COSTS OF PUMPING WATER.
575
10
**
00
H
u
S
O
S
*}93J 001 -
M moo N
ssiiu oj pgsn
JBOO jo spunoj
c 9 nniui S lu? I &^^^!^38S3;s;&*fri?&8?8>K%5:
mxio }so &Z 5- 3 ^2 ^^S ^S" 2 2 &
s n 'mo
auo jSuidiund
JO }SOO'
10 O vo ro r> * m ro M inoo \o <> ?> M r in ir>oo Mvo 1 fO I/I'M
oo 6^ 10^0 4-iot^tN.md *-* iocp C^IM rot^coio^iot^
CM
W
J I
W 2
I
{H ^
SUBS -nji
'saiiddns puB
S9j'o;s s^uara
jpjsooj_
-ua 0}
puB
uara
-3uiSu9 jo S^B^VV
SIBOO jo 5503
! O ^C ro
tx\c ^- ci ci 10 ir> ci
od oo 10 t^ <5s txod oo" ^-06
jo spunoj
JB9X Snunp
paduind saoi
;33j ai yiq
1
::
-gdddj/
:
liifi
26 * ^sa
M' 4co
m . \o t*>
il
Philadelphia
New Haven
Montreal
676 PUMPS.
of water delivered in any given time into the force-main, in
gallons ; w the weight * of a gallon of water in pounds
(= 8.34 Ibs. approximately) ; H the dynamic height of lift ;
Ti the height equivalent to the Motional resistance "between
pumps and reservoir, including resistances of flow, valves,
bends, etc., in the force-main, but not the work due to in-
termittent motion of pumps, or to bends and frictions within
the pump iiself ; W the weight, in pounds, of coal passed
into the furnace in the given time ; and D the duty per 100
pounds of coal ; then
D _Q x w x (H+ 7i)
:enr~
Sometimes the value of Q is expressed in cubic feet, in
which case w is the weight in pounds of a cubic foot of
water (= 62.33 Ibs. approximately).
If it is preferred to use the area of plunger, its mean rate
of motion in the given time, and the pressure against which
it moves, as factors in the calculation, then the equivalent
equation of duty D, takes the form,
__cA xVx t x (P+p)
~~~
in which A is the area, in square feet, of the piston or
bucket, and c its coefficient of effective delivery, which
varies from .60 to .98, according to design or condition of
the valves and velocity of flow through them ; V the mean
rate of motion, in feet per minute, of the plunger or bucket ;
t the given time, in minutes ; P the pressure, in pounds,
due to the dynamic head ; p the pressure in pounds due to
the resistances in the force-main ; and W the weight of
* Vide Table 38 for weights of water per cubic foot, at different temperatures.
DUTY OF PUMPING ENGINES. 577
coal, in pounds, passed into the furnace in the given
time.
If W is taken for denominator in the equation instead of
.01 TF, then the result gives the duty per pound of coal.
The numerator in each equation refers to the foot-pounds
of work done by the plunger or bucket of the pump in effec-
tive delivery of water into and efflux from the force-main,
and the denominator refers to the foot-pounds of work con-
verted from the heat in the coal, and effectively applied by
the combination of boiler and steam engine.
The coefficient c and the terms Ji and p in equations 10
and 11 are ordinarily appreciably variable with variable
rates of plunger or bucket motion. Preliminary to a general
duty test of a pump the values of c for different velocities
or rates of piston motion, from minimum to maximum,
should be determined by a reliable and accurate weight or
weir test, and the value of 7i or p be accurately determined
for similar conditions by an accurate gauge or pressure test,
and a scale, per unit of velocity prepared for each, so that
values may be read off for the actual rates of piston motion
during the general test.
The main parts or divisions which make up a steam
pumping engine, are :
1. Boilers (including grates, heating surfaces, steam and
water spaces, and flues).
2. Steam engine (including steam pipes, cylinders, valves,
pistons, and condensing apparatus).
3. Pump (including water passages, cylinders, plunger
bucket, and valves).
In comparisons of data, for the selection or design of the
of such a combination, the classes of each part should
considered in detail, independently, with prime costs,
37
578 PUMPS.
since if either part gives a low duty alone, the duty of the
combination will suffer in consequence.
Attention will be given especially to the evaporative
power of the boiler and its duty, or ratio of effective to
theoretical pressure delivered into the steam pipe ; the effec-
tive piston pressure capabilities or duty of the steam cylin-
der, over and above its condensations, enhanced by slow
motion, leakages of steam, arid frictions ; and the fractional
resistances of the pump piston or plunger, and valves, and
reactions in the water passages.
Each pound of good coal, according to the dynamic
theory of heat, contains in its combustible part about 12,000
heat units, which are developed into a force by the burning
of the coal to produce steam, and this force is capable of
performing a definite amount of work. From sixteen to
twenty per cent, of these heat units are, ordinarily, lost by
escape up the chimney ; sixteen to twenty per cent addi-
tional are lost by condensation of the steam in the pipes
and cylinders, and by leakage past the piston or valves into
the condenser, and about fifty per cent, of their equivalents
escape with the exhaust steam into the condenser. Only
about ten or twelve per cent, of these heat units are ordi-
narily transformed into actual useful work done by the
steam.
If the engine has many rubbing surfaces, or binds at
any bearing, or if the pumps have crooked water passages,
many divisions of the jet in the valves, frequent and rapid
startings and checkings of the water column, or if its binds
at any bearing, then each of these resistances consume a
portion of the remaining ten or twelve per cent, of useful
work of the steam.
Stability and substantiality are matters of the utmost
importance to be considered in the selection of a class or
ECONOMY OF A HIGH DUTY.
579
manufacture of pumping engines. By these terms, in this
connection, we mean the capability of endurance of contin-
uous action at the standard rate and work, without stoppage
for repairs, and with the minimum expenditure for repairs.
This power of continuous work at a maximum rate is of
far greater value, ordinarily, than an extremely high duty,
if stability is sacrificed in part for the attainment of a high
duty, for the comfort and safety of the city may be jeopard-
ized by a weakness in its pumping engine. Stability being
first attained, then duty becomes an element of excellence
and superiority.
FIG 142.
GEYELIN'S DUPLEX-JONVAL TURBINE (R. D. WOOD & co., PHILA.)
550. Special Trial Duties. The following table (page
580) gives the duty results obtained by special trials of
various engines, under the direction of experts.*
551. Economy of a High Duty. The financial value
of a high duty is too often overlooked.
* Vide report of Messrs. Low, Roberts and Bogart ; in Journal of American
Society of Civil Engineers. Vol. IV, p. 142.
580
PUMPS.
}99J UI -QH OIUmiA'Q
I9VBM JO }U9tH
-9inSB9UI pUB
yi\ oiureuA'p Ag
vo H vo cr>
IO O N H
oo ^ tx
w ON -*
i
in 4
t^'OO *t^
tx in H
drand
-^- IH
oo w ro i
VO t^ ^ <
ut aariss9Jd
ui
Ag
li
lBoojo*q^J9d'(
eiej09jn^BJ9dui91
PJBPUB^S o; pgonp
-9j 'jg^BM. jo spuno j
UB9A
"
Vertical bucket and
double-beat valves
It t( ((
Horizontal plunger, disk valves,.
Doub. act. piston, flap valves
" rubber bar val
Horizontal piston, disk valves
vert
ori
No. i,
No, i,
beam
No. 2,
No. 2,
No, 3,
No. 3,
Mt. Pr
Cornish
Leavitt, rotativ
Simpson, "
Leavitt, "
Compound beam
Worthington, ho
compound, dir
McAlpine, beam
Corliss, radial ho
Worthington, ho
compound
Nagle, geared
Worthingto
mpoun
Ph
a *
r
ESC
COSTS OF PUMPING WATER.
581
Engines of substantial construction can now be readily
obtained, that, when working continuously at their stand-
ard capacities, will give duties of from 75 to 100 million
foot-pounds per 100 pounds of coal. When they are real-
izing less than their maximum duties, money, or its equiva-
lent, goes to waste.
We have just seen ( 549) that duty is a ratio of effec-
tive work. If we divide the dynamic work to be done by
this ratio, then we have the pounds of coal required to do
the work when the given duty is realized.
Let D be the given duty in foot-pounds per 100 pounds
of coal ; Q the volume of water delivered into the force-main
in gallons ; w the weight of a gallon of water, in pounds
(= 8.34 Ibs., approximately) ; If the actual height of lift ;
7i the height equivalent to the frictional resistances in the
main ; and TFthe weight of coal required, in pounds ; then
we have for equation of weight of coal,
W= IOOQ x w x (ff+7i)
D
(12)
When Q and D are in even millions, the computation
will be shortened by taking one million as the unit for those
quantities.
Let us assume that we have one million gallons of water
to lift 100 feet high in twenty -four hours, then the pounds
of coal required at various duties will be approximately
as follows :
TABLE No. 114.
COMPARATIVE CONSUMPTIONS OF COAL AT DIFFERENT DUTIES.
"Duty, in millions
105
too
ne
64
80
75
70
Pounds of coal
794
834
8?8
981
III2
IIQI
Duty, in millions
Pounds of coal ....
6 5
i 2 go
60
55
So
1668
45
4
3
2780
20
582
PUMPS.
The relative costs per annum, in dollars, for lifting
various quantities of water daily 100 feet high, at different
duties, will be approximately as in the following table,
on the assumption that the coal costs $8 per ton of 2000
pounds, when delivered into the furnace.
TABLE No. 1 15.
FUEL EXPENSES FOR PUMPING, COMPARED ON DUTY BASES.
Duty in
Number of millions of gallons pumped daily, one hundred feet high.
(Coal in furnace at $8 per ton.)
millions of
foot-pounds.
1
2
3
4
6
8
10
Cost of coal per annum, in dollars.
100
$1277-86
$2556
$3834
$5111
$7667
$10223
$12779
90
1419.85
2840
4260
5679
8519
H359
14198
80
1597.32
3195
4792
6389
9584
12778
15973
70
1825.51
3651
5477
7302
10953
14604
18255
60
2129.76
4260
6389
8519
12779
17038
21298
50
2555.72
CHI
7667
10223
15334
20446
25557
40
3194.65
6389
9584
12769
19168
25537
31946
30
4259-53
8519
12779
17038
25557
34076
42595
20
6389.30
12768
19168
25537
39336
5H74
63893
If the lift is 150 feet, then the annual cost will be one
and one-half times the above amounts respectively, if 200
feet, twice the above amounts, etc.
If we have four million gallons per day to pump 100 feet
high, then the cost of coal per annum for a 100 million
duty engine will be about $5000, and with a 20 million duty
engine about $25000. If we have to pump the same water
200 feet, the coal for the first engine will cost about $10,200
and with the second engine $51,000. These sums capital-
ized represent the relative financial values of the engines,
so far as relates to cost of fuel.
If pumping-engines are sufficiently strong, of good me-
chanical workmanship, and simple in arrangement of parts,
then the cost of attendance, lubricants, and ordinary re-
pairs, while doing a given work, will be substantially the
COSTS OF PUMPING WATER. 583
same for different makes or designs. Beyond this the rela-
tive merits of machines of equal stability, independent of
prime cost, are nearly in the inverse order of the amount of
fuel they require to do a given work.
But the first costs of the complete combination should
be made a factor in the comparison, including costs of foun-
dations and extra costs of buildings, standpipes, etc., if re-
quired, as in the case of Cornish engines. Then the relative
economic merits are inversely as the products of costs into
reciprocals of duties, or directly as duty divided by cost.
Let C d be the cost in dollars of the complete pumping-
engine, including foundations, pump- wells, etc., and D the
duty in millions, then the most economic engine, so far as
relates to cost of fuel, will be that which has the least
product of O d x JY or -^, and the relative result will be very
)
nearly the same if the cost of engine is capitalized.
Let % be the per cent., or rate of interest at which the
cost is capitalized, then the most economic engine, as to
prime cost and duty, will be that which has the least pro-
(71 1 Q
duct of -~ x jy, or -, x ~.
Let us assume that we have five million gallons of water
to lift 100 feet high per day, and that a standard engine of
suitable capacity to do the work, realizing one hundred mil-
lion duty, will cost $65,000.
With this standard let us compare, financially, engines
of less first cost and giving less duties, as in the following
table, in which the ratio of the standard is taken equal
unity.
584
PUMPS.
TABLE No. 11 6.
COMPARISON OF VALUES OF PUMPING-ENGINES OF VARIOUS PRIME
COSTS AND DUTIES ON FUEL BASES.
COST = Q.
DUTY = D.
C x X - Cd
RATIO.
$65,000
IOO M.
650.0
6o,OOO
9 o "
666.6
.025
5O,OOO
75 "
666.6
.025
45,000
60 "
750.0
153
35,000
5 "
700.0
.077
25,000
30 "
833.3
.282
By the column of ratios in the table we learn that the
$25,000 engine will really cost twenty-eight per cent, more
per annum than the $65,000 engine, for the same work, and
that the purchase of the assumed standard engine, if it has
stability equal to that of the lower-priced engine, will lead
to the most profitable results.
In the table, the $50,000 pumping-engine giving a seventy-
five million duty, is seen to have a financial value almost
identical with that of the assumed standard engine. If it
is also freer from liability to breakage or interruption, if it
requires less labor or less skill in attendance, if it is easier
in adjustment to varying work when variable work is to
be performed, or if it is better adapted mechanically to the
special work to be performed, then the practical over-
balances the financial advantages, and it is obviously en-
titled to preference in the selection, and good judgment will
lead to the purchase of this rather than of the assumed
standard engine.
FIG. 143.
TURBINES AND PUMPS, MANCHESTER.
OHAPTEE XXV.
SYSTEMS OF WATER SUPPLY.
552. Permanence of Supply Essential. Let the
projector of a public water supply first make himself famil-
iar with the possible scope and objects of a good and ample
system of water supply, and become fully conscious of how
intimately it is to be connected with the well-being of the
people and their active industries in all departments of their
arts, mechanics, trade, and commerce, as well as in their
culinary operations, and let him also appreciate the conse-
quences of its failure, or partial failure after a season of
success.
When the people have become accustomed to the ready
flow from the faucets, at the sinks and basins, and in the
shops and warehouses, then, if the pumps cease motion or
the valve is closed at the reservoir, the household oper-
ations, from laundry to nursery, are brought to a stand-
still engines in the shops cease motion, hydraulic hoists
and motors in the warehouses cease to handle goods, rail-
way trains, ocean steamers, and coasters delay for water,
and a general paralysis checks the busy activity of the
city. What a thrill is then given by an alarm of fire, be-
cause there is no pressure or flow at the hydrants !
The precious waters of the reservoirs preside over cities
with protecting influences, enhancing prosperity, comfort,
safety and health, and are not myths, as were the goddesses
in ancient mythology, presiding over harvests, flowers,
fruits, health and happiness.
586 SYSTEMS OF WATER SUPPLY.
Let the designer and builder of the public water system
feel that his work must be complete, durable, and unfail-
ing, and let this feeling guide his whole thought and
energy, then there is little danger of his going astray as to
system, whether it be called " gravitation," " reservoir/'
"stand-pipe," or "direct pressure," or of his being enam-
ored with lauded but suspicious mechanical pumping au-
tomatons, and uncertain valve and hydrant fixtures.
When the people have learned to depend, or must of
necessity depend, upon the public pipes for their indis-
pensable water, it must flow unceasingly as does the blood
in our veins. All elements of uncertainty must be over-
come, and the safest and most reliable structures and ma-
chines be provided.
Many times, in different cities, a neglect, apparently
slight, has cost, through failure, a fearful amount, when
sacrificed life and treasure and a broad smouldering swarth
across the city were the penalty. Having water- works is
not always having full protection, unless they are fully
adequate for the most trying hour.
553. Methods of Gathering and Delivering Water.
There is no mystery about "systems" of water supply,
as they have of late been often classified. The problem is
simply to search out the best method of gathering or secur-
ing an ample supply of wholesome water, and then to
devise the best method of delivering that supply to the
people.
Usually there is one source whose merits and demerits,
when intelligently examined, favorably outweighs the
merits and demerits of each and every other source, and
there is usually one method of delivery that is conspicu-
ously better than all others, when all the local exigencies
are seen and foreseen.
CHOICE OF WATER. 587
The usual methods of gathering the required supply are,
to impound and store the rainfall or flow of streams among
the hills ; draw from a natural lake ; draw from a running
river ; or draw from an artesian well.
The usual methods of delivering water are, by gravita-
tion from an elevated impounding basin ; elevation by
steam or water power to a reservoir and from thence a flow
by gravity ; elevation to low and high service reservoirs,
and from thence flow by gravity to respective districts ; and
by forcing with pressure direct into the distribution-pipes,
and cushioning the motion by a stand-pipe, or ample air-
vessel and relief valve.
554. Choice of Water. The pumped supplies are
usually drawn from lake, river, or subterranean sources.
The selection of a lake or river water for domestic use is
to be governed by considerations of wholesome purity ; and
cautiousness of financial expenditure must not in this direc-
tion exert too strong an influence in opposition to inflexible
sanitary laws.
This selection involves an intelligent examination of the
origin and character of the impregnations and suspended
impurities of the water, and the possibility of their thorough
clarification.
None of the waters of Nature are strictly pure. Some
of the impurities are really beneficial, while others, which
are often present, are not to be accepted or tolerated. A
mere suspicion that a water supply is foul or unwholesome,
even though not based on substantial fact, is often a serious
financial disadvantage ; therefore earnest effort to maintain
the purity of the water must extend also to the removal of
causes of suspicion.
Chemical science and microscopy are valuable aids in
this portion of the investigation of the qualities of waters ;
.588 SYSTEMS OF WATER SUPPLY.
but we have detailed in the first part of this treatise so
minutely the nature and source of the chief impurities, and
so -carefully pointed out those that are comparatively harm-
less and those that are deadly, that an intelligent opinion
can generally be readily formed of the comparative puri-
ties and values of different waters. We have also pointed
out how waters may be clarified and conducted in their best
condition to the point of delivery, and distributed in the
most efficient manner.
Predictions of any value as to quantity and quality of a
supply from a proposed artesian well, demand a knowledge
of the local geology and subterranean hydrology, which, is
rarely obtainable until the completion and test of the well ;
nevertheless we have shown the conditions under which a
good supply of water may be anticipated with reasonable
confidence.
555. Gravitation. When a good and abundant sup-
ply of water can be gathered at a sufficient elevation, and
within an accessible distance, the essential element of con-
tinuous full-pressure delivery can then most certainly be
secured, and in the matter of possible safety the gravitation
method will usually be superior to all others.
The quality of impounded water, when gathered in small
storage reservoirs and from relatively limited watersheds, is
subject to some of those unpleasant influences, heretofore
referred to, which are to be provided against ; and unless the
hydrology and substructure of the gathering basin is well
understood, the permanence of the supply may not fulfill
enthusiastic anticipations.
The value and importance of sufficient elevation of the
supplying reservoir, when the delivery is by gravity, to
meet the most pressing needs of the fire-service, ought not
to be overlooked, for an efficient fire-service is usually one
PUMPING WITH RESERVOIR RESERVE. 589
of the chief objects to be attained in a complete water
supply.
A water pressure of sixty to eighty pounds per square
inch in the hydrants in the vicinity of an incipient fire, ha&
a value which cannot be wholly replaced by a brigade of
fire-steamers in commission, for with light-hose carriages
and trained hosemen, connection will usually be made
with the hydrants, streams be put in motion, and the fire
overpowered before pressure is raised in the steamer's boil-
ers ; and the fire will not be suffered to assume unconquer-
able headway during the delay.
Constant liberal pressures in the hydrants is the first
element of prompt and effective attack upon a fire immedi-
ately after an alarm is given. Each moment lost before the
beginning of an energetic attack increases greatly the diffi-
culty of subduing the fire, and the probability of a vast
conflagration.
The element of distance of a gravitation supply, as re-
gards cost of delivery, is an exacting one, and the lengths
of conduit and large main are surprisingly short, while the
balance of economy of delivery remains with the side of the
gravitation scheme ; for conduits and mains are expensive
constructions, and soon absorb more capital and interest
than would pay for pumps and fuel for lifting a nearer
supply ; still an element of safety is not to be sacrificed for
a moderate difference in first cost.
556. Pumping with Reservoir Reserve. As re-
gards safety and reliability of operation, we place second the
method of delivery when the supply is elevated by hydrau-
lic power, and third when it is elevated by steam power to
a liberal-sized reservoir holding in store from six to ten
days reserve of water, from whence the supply flows by
gravity into the distribution-pipes. If in such case there
590 SYSTEMS OF WATER SUPPLY.
are duplicate first-class pumping-machines whose combined
capacity is equal to the delivery of the whole daily supply
in ten hours, or one-half equal to the delivery of the whole
daily supply in twenty hours, then this method is scarcely
inferior in safety to the gravitation method.
The elements of safety may Ibe equally secured in the
low and high service method, when the physical features of
the town or city make such division desirable. In a pre-
vious chapter we have shown how a union of the high and
low service may be made an especially valuable feature in
efficient fire service.
The records of nearly all the water departments of our
largest cities, having duplicate pumping machinery, show
how valuable and indispensable have been their reserve
stores of water, and refer to the risks that would have been
incurred had such reservoir storages been lacking.
557. Pumping with Direct Pressure. We place
fourth, as regards safety and reliability, the direct pressure
delivery by hydraulic power, and fifth, by steam power,
with either stand-pipe or air-vessel cushions and safety
relief-valves.
The mechanical arrangements that admit of this method
of delivery are simple, and several builders of pumping
machinery have adapted their manufactures to its special
requirements, but in point of continuous reliability the
method still remains inferior to gravity flow.
Even when the most substantial and most simple steam
pumping machinery is adopted, if not supplemented by an
elevated small reserve of water, this method of delivery is
accompanied with risks of hot bearings, sudden strains,
unexpected fracture of connection, shaft, cylinder, valve-
chest or pipe, and occasional necessary stoppages.
The best pumping combinations are so certainly liable
PUMPING WITH DIRECT PRESSURE. 591
to such contingencies that cities may judiciously hesitate to
rely entirely upon the infallibility of their boilers, engines,
and pumps, even when so fortunate as to secure attendants
upon whom they can place implicit confidence.
The direct pressure method, alone, necessitates unceas-
ing firing of the boiler and motion of the pumping-engine,
and consequently double or triple sets of hands, to whose
integrity and faithfulness, night and day and at all times,
the works are committed.
Hydraulic power and machinery are far more reliable
than steam machinery, for direct pressure uses, and hy-
draulic power presents the great advantage of being able
to respond almost instantaneously to the extreme demand
for both water and pressure, while a dull fire under the
boiler may require many minutes for revival so as to raise
the steam to the effective emergency pressure. An example
of pumping machinery of five million gallons capacity per
diem, driven by hydraulic power, is shown in Fig. 143.
This set of pumping machinery was constructed for the city
of Manchester, N. H., by the Geyelin department of Messrs.
K. B. Wood & Co., Philadelphia, from general designs by
the writer, and has operated very satisfactorily since its
completion in 1874. This machinery is adapted in all re-
spects to direct pressure service, and was so used during a
full season while the reservoir was in process of construction,
and it is equally well adapted to its ordinary work of pump-
ing water to the distributing reservoir.
The direct forcing method does not provide for the de-
position or removal of impurities after they have passed the
engine, but the sediments that reach the pumps are passed
forward to the consumers in all sections of the pipe distri-
bution.
In combination with a reservoir sufficient for all the
592 SYSTEMS OF WATER SUPPLY.
ordinary purposes, and equalizing the ordinary work and
the ordinary pressures at the taps, and also in combination
with a very small reservoir, the direct pressure facilities
may prove a most valuable auxiliary in times of emergency,
and they are then well worth the insignificant difference in
first cost of pumping machinery.
In the smaller works the entire machinery, and in larger
works one-half the machinery, may with advantage be
capable of and adapted for direct pressure action.
If, instead of substantial and simple machinery built
especially for long and reliable service, some one of the
intricate and fragile machines freely offered in the market
for direct pumping is substituted, and is not supplemented
by an ample reservoir reserve, then a risk is assumed which
no city can knowingly afford to suffer ; and if true prin-
ciples of economy of working are applied, it will generally
be found that no city can, upon well-established business
theories, afford to purchase and operate such machinery. '
Well designed and substantially constructed pumping-
machines, such as are now offered by several reliable build-
ers, when contrasted with several of the low-priced and low-
duty contrivances, are most economical in operation, most
economical in maintenance, and infinitely superior in reli-
ability for long-continuous work.
JONVAL TURBINE.
CONSTRUCTED BY R. D. WOOD & Co., PHILADELPHIA.
APPENDIX.
THE METRIC SYSTEM OF WEIGHTS AND MEASURES.
The use of the metric system of measure and weights
was legalized in the United States in 1866 by the National
Government, and is used in the coast survey by the engineer
corps, and to considerable extent in the arts and trades.
Several of the best treatises on theoretical hydraulics
give their lengths and volumes in metric measures, and we
give their equivalents in United States measures in the
following tables.
The metre, which is the unit of length, area, and volume,
equals 39.37079 inches or 3.280899 feet in length lineal, and
along each edge of its cube.
This unit is, for measures of length, multiplied decimally
into the decametre, hectometre, 'kilometre, and myriametre,
and is subdivided decimally into the decimetre, centimetre,
and millimetre.
The affixes are derived from the Greek for multiplication
by ten, and from the Latin for division by ten.
The measures for surface and volume are similarly
divided.
The gramme is the unit of weight, and it is equal to the
weight of a cubic centimetre of water, at its maximum
density, in vacuo. = .0022046 Ibs.
A cubic metre of water, at its maximum density, weighs
2204.6 Ibs. avoir.
38
694
APPENDIX.
TABLE OF FRENCH MEASURES AND UNITED STATES EQUIVALENTS.
Measures of Length.
No. of
Metres.
i Millimetre
.OOI
.0393708 inch .0032809 foot.
i Centimetre .
.OI
.393708 inch 032809 foot
i Decimetre
. i
^.0^708 inches ^280800 ft. .100^6^^ vd.
T J
= 39.3708 inches = 3.2808992 ft. .198842 rod
i Decametre .
(
IO
= .0006214 mile.
32 808902 ft i 08842 rods 0062138 mile
ICO
328.08992 ft. 19.88424 rods ,062138 mile.
i Kilometre ... .
IOOO
3280 8992 ft 198 8424 rods 621383 mile
i Myriametre
IOOOO
32808 992ft 1988.424 rods 6 21383 miles
Measures of Area.
No. of sq.
Metres.
J
= 10.7643 sq. ft. = 1.196033 sq. yds. = .039538
i Deciare
(
IO
sq. rod.
107 643 sq. ft. 39538 sq. rd. .002471 acre.
IOO
= 1076.43 sq. ft. 3.95383 sq. rds. = .02471 acre.
i Decare (not used)
i Hectare
IOOO
IOOOO
= 10764.3 sq.ft. = 39.5383 sq. rds. = .2471 acre.
107643 sq. ft. 395.383 sq. rds. 2.471 acres.
Measures of Volume.
No. of cu.
Metres.
I Millilitre .
OOOOOI
~ 0610279 cubic inch
i Centilitre
.00001
610279 cubic inch.
i Decilitre
.0001
6.10279 cu. ins. 'OO353 cu.
ft. .0264165 gal.
.OOI ]
= 61.0279 cu. ins. = .0353136
cu. ft. = .264165
.01 ]
gallon.
= 610.279 cu - ins - = 353 I 3 6
cu. ft. = .0130791
i Hectolitre
.1
cu. yard.
= 26.4165 gallons = 3-53I36 c
u. ft. = .130791 cu.
I
yard.
= 264.1651 gallons = 35.313
cu. ft. = 1.30791
cubic yards.
APPENDIX.
595
TABLE OF FRENCH MEASURES AND UNITED STATES EQUIVALENTS
(Continued).
Measures of Solidity.
No. of cu.
Metres.
I Millistere
.OOI
61.0279 cubic inches 3532 cubic foot
.OI
= 610.279 cu. ins. = .353166 cu. ft. = .013079 cu.
i Decistere
I
yard.
6102.79 cu. ins. = 3.53166 cu. ft. = .130791 cubic
i Stere
I
yard.
= 61027.9 cu. ins. = 35.3166 cu. ft. = 1.30791 cu.
I Decastere .
IO
yards.
353 *66 cu. ft. 13 0791 cu yards.
i Hectostere
IOO
3531 66 cu. ft. 130.791 cu. yards.
I Kilostere
IOOO
35316.6 cu. ft. 1307.91 cu. yards.
Measures of Weight.
No. of
Grammes.
.
i Milligramme ....
i Centigramme. . . .
I Decigramme
.001
.01
.1
I
= .015432 grain.
= .15432 grain.
= 1.5432 grains = .0035274 oz. Avoir.
15.432 grs. = .035274 oz. Av. = 002205 Ib- Av.
i Decagramme
I Hectogramme . . .
I Kilogramme
IO
IOO
IOOO
= 154.32 grs. = .35274 oz. Av. = .02205 Ib. Av.
= 1543.2 grs. = 3.5274 oz. Av. = .2205 Ib Av.
= 15432 grs. = 35.274 oz. Av. = 2.205 Ibs. Av.
2204.737 Ibs.
A cubic inch is equal to
.004329 gallon; or .0005787 cu. ft; or 16.38901 millilitres ; or 1.638901
centilitres ; or .1638901 decilitre ; or .016389 litre ; or .016389 millistere ; or
0016389 centistere.
A gallon is equal to
231 cubic inches, .13368 cubic foot; or .031746 liquid barrel; or 3785.513
millilitres ; or 378.551 centilitres ; or 37.8551 decilitres ; or 3.785513 litres ; or
.3785513 decalitre ; or .037855 hectolitre ; or .0037855 kilolitre.
A cubic foot is equal to
1728 cubic inches; or 7.48052 liquid gallons; or 6.2321 imperial gallons ;
or 3.21426 U. S. pecks ; or .803564 U. S. struck bushel ; or .23748 liquid bar-
696 APPENDIX.
rel of 31^ gallons ; or 2831.77 centilitres ; or 283.177 decilitres : or 28.3177
litres ; or 2.83177 decalitres ; or .283177 hectolitre ; or .0283177 kilolitre ; or
28.3177 millisteres; or 2.83177 centisteres ; or .283177 decistere ; or .0283177
stere.
The imperial gallon is equal to
.16046 cu. feet ; or 1.20032 U. S. liquid gallons.
A cubic yard is equal to
46656 cu. inches ; or 201.97404 liquid gallons ; or 27 cu. feet ; or 21.69623
struck bushels ; or 764.578 litres ; or 76.4578 decalitres ; or 7.64578 hectolitres ;
or .764578 kilolitre ; or 764.578 milisteres ; or 76.4578 centisteres ; or 7.64578
decisteres ; or .764578 stere ; or .0764578 decastere ; or .0076458 hectostere ;
or .00076458 kilostere.
TABLE OF UNITS OF HEADS AND PRESSURES OF WATER AND
EQUIVALENTS.
(RANKINE.)
One foot of water at 52. 3 Fah. = 62.4 Ibs. on the square foot-
" = .433 " inch.
" " " " = .0295 atmosphere.
" " " " = .8823 inch of mercury at 32.
One Ib, on the square foot = .016026 foot of water.
" " " inch = 2.308 feet of water.
One atmosphere ( 29.922 in. mercury) = 33.9 "
One inch of mercury, at 32 = 1.1334 "
One cubic foot of average sea-water = 1.026 cu. ft. of pure water in
weight.
One Fahrenheit degree = -55555 Centigrade degree.
One Centigrade degree = 1.8 Fahrenheit degrees.
Temperature of melting ice = 32 on Fahrenheit's scale,
" " = O " Centigrade scale.
APPENDIX.
597
TABLE OF AVERAGE WEIGHTS, STRENGTHS, AND ELASTICITIES OF
MATERIALS. (From Trautwine, Neville, and Rankine.)
MATERIALS.
Weight
per
cu. in.
Weight
per
cu. ft.
Specific
Grav.
Tenacity
per
sq. in.
Resist- v 3
ance per >,
sq. in.to 1
crush- ^u
ing force. NX\
JS
Woods (seasoned, and dry).
Ash
Lbs.
Lbs.
48.0
38
48
47
56.8
36.8
35
25
53
49
59-3
51-8
0-77
.61
77
75
59
56
.40
85
79
95
83
Lbs.
17000
16000
11400
12000
13500
13000
I6OOO
10250
i*. \^
9000 *A\
8500 N>
4900 A
5600 * Oj
10300 ^J
:::: x :
6400 oy ^
6500 \3
6000 X^>
" American white
Beech ,
Elm .. ..
Hemlock
Hickory
Oak, live
" white
red
34-3
45-0
25.0
38
<
162
525
524
533
529
538
549
560
153
441
440
485
474
717
713
846
644
49
456
437
Cu.yd.
2357
3375
2700
4050
1512
1339
55
.72
.40
.61
-
2.6
8.40
8.40
8-54
8.5
8.61
8.80
8.88
2-45
7.07
7.04
7-77
7.60
11.44
11.40
13-58
10.31
7.85
7-30
7.00
1.4
7800
12400
ISOOO
49000
36000
igOOO
30000
00000
9400
16700
13500
50000
48000
1800
3300
40900
120000
5300
7500
280
5400 /Jl
5500 1
7200 /
10300
33000
106000
108000
'Soo
" southern "
Walnut black
Metals.
.30972
Brass cast
" rolled
.03085
.03062
03113
" sheet
" wire drawn *...
-03241
.00885
.02552
Glass . . >.
" " hot blast
" " wrought sheet or plate
.02807
" " " large bars
.04152
" milled
Mercury (at 32 Fah., 849 Ibs.) (at 212, )
836 Ibs.), at 60 o )
.04896
0373
.02836
.02637
.02532
Cu. ft.
87.3
125
100
150
56
49.6
Silver ....
Steel
Tin cast
Zinc
Earth and Stones (dry).
Brick common hard
" best pressed . . . ....
Cement, American Rosendale, loose
APPENDIX.
TABLE OF AVERAGE WEIGHTS, STRENGTHS, ETC. (Continued}.
MATERIALS.
Weight
per
cu.ft.
Weight
per
cu. yd.
Specific
Grav.
Tenacity
per
sq. in.
Resist-
ance per
sq. in. to
crush-
ng force.
Lbs.
Lbs.
go
80
119
63
Ll>s.
2430
2l6o
3213
I7OI
....
Lbs.
280
1.9
....
556-
Coal bituminous .
84
50
2268
1350
i-35
....
" broken loose
75
95
no
168
96
168
IOO
187
107
IOO
120
130
168
53
165
165
154
138
125
144
no
125
IOO
140
no
103
25
IOO
no
125
150
86
1 80
170
58.7
2025
2565
2970
4536
2592
4 53 6
2700
5049
2889
2700
3240
3510
4536
1431
4455
4455
4158
3726
3375
3888
2970
3375
2700
3780
2970
2781
675
2700
2970
3375
4050
2322
4873
459
1585
" " moderately rammed .
" " as a mud . .
2.69
2.69
....
1 0000
" Quarried in loose piles
" ouarried in loose piles
Gravel
1.90
....
....
" " " moist . .
2.7
8335
Marble
2.64
5500
Masonry, dressed granite, or limestone. .
" well-scabbled mortar rubble of do.
" " " dry " " do.
" roughly " " " " do.
" dressed sandstone .
" dry rubble "
....
345
" " press'd bricks, close joints
Marl
1-75
1.65
50
....
1.76
....
....
5000
glate
2.89
2-73
0.94
42OO
12000
2OO
Miscellaneous Materials.
Ice
Oil, linseed
Petroleum
Powder, slightly shaken
58.68
54.81
62.3
12
50
62.334
324
1350
1693
.94
.878
I.O
Water .
I.O
....
APPENDIX.
599
FORMULAS FOR SHAFTS. (Francis.)
Wrought-iron prime movers, with gears :
d = V)/ 100P , and P =
Wrought-iron transmitting shaft :
d =
-, and P = .02Nd?.
Steel prime mover, with gears :
3/62.5P
Steel transmitting shaft :
3/31.25P
d =
N
and P = .OHUKP.
and P = .03&ZVS 8 .
In which ^ = diameter of shaft in inches.
-ZV = number of revolutions per minute.
P = horse powers.
TRIGONOMETRICAL EXPRESSIONS.
COTANGENT
Radius = AC.
Sine = Cd.
Cosine = Ce.
Tangent = Bf.
Cotangent = hg.
Secant = Af.
Cosecant = Ag.
Versine = Bd.
Coversine = he.
00
APPENDIX.
TRIGONOMETRICAL EQUIVALENTS, WHEN RADIUS = i.
Sine
=
1 -=- Cosec.
u
=
Cosin. -^ Cotan.
u
= '
l/(l - Cosin 2 .)
Cosine
=
1 -- Sec.
=.
Sin. -^- Tan.
=
Sin. x Cotan.
a
=
VT^^Sin 2 ?
Tangent
=s
1 -f- Cotan.
"
=
Sin. -^- Cosin.
Cotangent
=
1 + Tan.
"
Cosin. -^- Sin.
Secant
=
1 -j- Cosin.
"
=
VT+ Tan 2 .
Cosecant
=
1 -T- Sin.
Yersine
Coversine
+ Cotan 2 .
Rad. Cosin.
Rad. Sin.
Complement = 90 Angle.
Supplement = 180 Angle.
If radius of an arc of any angle is multiplied or divided
Tby any given number, then its several correspondent trigo-
nometrical functions are increased or diminished in like
ratio.
Diameter = Rad. x 2.
Circumference = Rad. x 6.2832.
" = Diam. x 3.1416.
Area of circle = Diam 2 . x .7854.
Surface of a sphere = Diam 2 . x 3.1416.
Volume of a sphere = Diam 3 . x .5236.
Length of one second of arc = Rad. x .0000048.
minute " " = Rad. x .0002909.
" degree " " = Rad. x .0174533.
" "
APPENDIX.
601
VALUES* OF SINES, TANGENTS, ETC., WHEN RADIUS = i.
Deg.
Sine.
Cover.
Cosec.
Tang't.
Cotan.
Secant.
Versine.
Cosine.
Deg.
o
.00
I.OOOOO
Infinite.
.0
Infinite.
I.OOOOO
o.
I.OOOOO
90
I
2
01745
.03480
.98254
.96510
57.2986
28.6537
.oi745
.03492
57.2899
28.6362
1.00015
I 00060
.0001
.0006
99984
99939
88
3
05234
.94766
19.1073
.05241 j 19.0811
1.00137
.0013
.99863
87
4
.06976
.93024
14-3355
.06993
14.3007
1.00244
.0024
99756
86
5
6
.08716
.10453
.91284
89547
9.5667
.08749
.10510
".4300
9-5144
I 00381
i 00550
.0038
.0054
.99619
.99452
85
84
7
.12187 .87813
8.2055
.12278
8.1443
1.00750
.0074
99255
83
8
13917
.86082
7.1852
14054
7-ii54
1.00982
.0097
.99027
82
9
15643
.34356
6.3924
15838
6-3137
1.01246
.0123
.98769
81
10
17365
.82035
5-7587
17633
5-6712
1.01542
.0151
.98481
80
ii
.19081
.80919
5-2408
.19438
5.1446
1.01871
.0183
98163
79
12
13
.20791 .79208
.22495 .77504
4.8097
4-4454
21255
.23087
4.7046
4-331?
1.02234
1.02630
.0218
.0256
978i5
97437
78
77
14
.24192 .75807
4-1335
24933
4.0108
1.03061
.0297
97030 i 76
11
.25882
.74118
.72436
3-8637
3-6^79
26795
.28674
3-7320
3-4874
1-03527
1.04029
.0340
.0387
96593
.96126
75
74
'7
.29237
.70762
3.4203
3573
3-2708
1.04569
.0436
95630
73
18
.30902
.69098
3-2360
32492
3-0777
1.05146
.0489
.95106
72
19
32557 1 -67443
3-07I5
34433
2.9042
1.05762
0544
.94552
71
20 .34202
21 .35337
.65797
.64163
2.9238
2.7904
36397
.38386
2-7475
2.6051
1.06417
1.07114
.0603
.0664
93969
93358
7
60
22
.37461
62539
2.6694
.40403
2.4751
1-07853
.0728
.92718
68
23
39 3 73
.60926
25593
42447
2.3558
1.08636
.0794
.92050
67
24
.40674
59326
24585
44523
2.2460
1.09463
.0864
91355
66
25
.42262
57738
.46631
2.1445
I - I0 337
.0936
.90630
65
26
43837
.56162
2.2811
.48773
2.0503
1.11260
.1012
.89879
64
27
45399
54600
2.2026
50952
1.9626
1.12232
.1089
6 3
28
46947
.53052
2.1300
.53171 1.8807
1-13257
.1170
.88295
62
29
.48481
51519
2.0626
55431
1.8040
1-14335
.1253
.87462
61
30
.50000
51504
.50000
.48496
2.0000
I.94I6
57735
.60086
as
1.15470
1.16663
.1339
.1428
.86603
60
32
.52992
.47008
1.88 7
.62487
1.6003
I-I7917
.1519
.84805
5
33
54464
45536
1.8360
.64941
1.5398
1.19236
1613
.83867
57
34
. 1:5919
.44080
1.7882
67451
1.4826
1.20621
1709
.82904
56
35
57358
.42642
1-7434
.70020
1.4281
1.22077 .1808 .81915
55
36
58778
41221
1.7013
.72654
1-3764
1.23606 .1909 .80902
54
37
.60181
.39818
i. 6616
75355
1.3270
1.25213 .2013
.79864
53
38
.61566
38433
1.6242
.78128
1.2799
1.26901 .2110
.78801
S 2
39
.62932
.37067
1.5890
.80978
1.2349
1.28675
.2228
77715
40
.64279
35721
1-5557
.83970 1.1918
1.30540
2339
.76604
50
41
.65606
34394
1.5242
.86929 i 1.1504
I.3250I
.2452
75471
49
42
66913
33086
1-4944
.90040
1.1106
1.34563
.2568
74314
48
43
.68200
.31800
1.4662
93251
1.0724
1-36732
.2686
47
44
.69465
30534 1-4395
.96569
i 355
I.390I6
.2808
71934
46
45
.70711
.29289 14142
i.
1-
I.4I42I
.2928
.70711
45
Cosine.
Versine.
Secant.
Cotan.
Tang't.
Cosec.
Cover.
Sine.
* When the angle exceeds 45, read upward ; the number of degrees will then be found in
the right-hand column, and the names of columns at the bottom.
602 APPENDIX.
IN RIGHT-ANGLED TRIANGLES.
Base = VRyp\ -- Perp*.
= '/(Hyp. + Perp.) x (Hyp. - Perp.)
Perpendicular = 4/Hyp. 2 Base 2 .
= '/(Hyp. + Base) x (Hyp. - Base.)
Hypothenuse = I/Base 2 + Perp 2 .
What constitutes a car load (20,000 Ibs. weight) :
70 bbls. lime ; 70 bbls. cement ; 90 bbls. flour ; 6 cords
of hard wood ; 7 cords of soft wood ; 18 to 20 head of cattle ;
9000 feet board measure of plank or joists; 17,000 feet
siding; 1 3, 000 feet of flooring ; 40,000 shingles ; 340 bushels
of wheat ; 360 bushels of corn ; 680 bushels of oats ; 360
bushels of Irish potatoes ; 121 cu. ft. of granite ; 133 cu. ft.
sandstone ; 6000 bricks ; 6 perch rubble stone ; 10 tons of
coal ; 10 tons of cast-iron pipes or special castings.
Lubricator, for slushing heavy gears:
10 gallons, or 3J pails of tallow ; 1 gallon, or \ pail of
Neat's foot-oil ; 1 quart of black-lead. Melt the tallow,
and as it cools, stir in the other ingredients.
For cleaning brass :
Use a mixture of one ounce of muriatic acid and one-
half pint of water. Clean with a brush ; dry with a piece
of linen ; and polish with fine wash leather and prepared
hartshorn.
Iron cement, for repairing cracks in castings :
Mix J Ib. of flour of sulphur and \ Ib. of powdered sal
ammoniac with 25 Ibs. of clean dry and fine iron-borings,
then moisten to a paste with water and mix thoroughly.
APPENDIX.
603
Calk the cement into the joint from both sides until the
crack is entirely filled. In heavy castings to be subjected
to a great pressure of water, a groove may be cut along a
transverse crack, on the side next the pressure, about one-
quarter inch deep, with a chisel ^%-inch wide, to facilitate
the calking in of the cement.
Alloys. The chemical equivalents of copper, tin, zinc,
and lead bear to each other the following proportions, ac-
cording to Rarikine :
Copper.
31-5
Tin.
59-
Zinc.
32-5
Lead.
When these metals are united in alloys their atomic pro-
portions should be maintained in multiples of their respec-
tive proportional numbers ; otherwise the mixture will lack
uniformity and appear mottled in the fracture, and its
irregular masses will differ in expansibility and elasticity,
ajid tend to disintegration under the influence of heat and
motion.
MATERIALS.
COMPOSITION.
By Equivalents.
By Weight.
Very hard bronze
Copper.
12
14
16
* 18
20
Copper.
4
2
3
4
Tin.
Znc.
2
3
Copper.
6.401
6.966
8.542
9.610
10.678
Copper.
3-877
1.938
1-454
1.292
Tin.
Zinc.
I
Hard bronze for machinery bearings
Bronze or gun-metal, contracts -j-^ in cooling
Bronze somewhat softer ... .
Soft bronze for toothed wheels
Malleable brass
Ordinary brass, contracts ^ in cooling
Yellow metal for sheathing ships
Spelter solder, for brazing copper and iron. .
Babbitt's metal consists of 50 parts of tin, i of copper, and 5 of antimony.
604 APPENDIX.
Aluminum bronze, containing 95 to 90 parts of copper
and 5 to 10 parts of aluminum, is an alloy much stronger
than common bronze, and has a tenacity of about 22.6
tons per square inch, while the tenacity of common bronze,
or gun-metal, is but about 16 tons.
Manganese bronze is made by incorporating a small
proportion of manganese with common bronze. This alloy
can be cast, and also can be forged at a red-heat.
A specimen cast at the Royal Gun Factory, Woolwich,
in 1876, showed an ultimate strength of 24.3 tons per square
inch, an elastic limit of 14 tons, and an elongation of 8.75
per cent. The same quality forged had an ultimate resist-
ance of 29 tons per square inch, an elastic limit of 12 tons,
and an elongation of 31.8 per cent. A still harder forged
specimen had an ultimate strength of 30.3 tons per square
inch, elastic limit of 12 tons, and elongation of 20.75 per
cent.
The tough alloy, introduced by Mr. M. P. Parsons, will
prove a desirable substitute for the common bronze in hy-
draulic apparatus, where its superior strength and greater
reliability will be especially valuable.
APPROXIMATE BOTTOM VELOCITIES OF FLOW IN CHANNELS AT
WHICH THE FOLLOWING MATERIALS BEGIN TO MOVE.
> ,2,5 feet per second, microscopic sand and clay.
.50 " " " fine sand,
i.oo " " " coarse sand.
1.75 " " " pea gravel.
3 " " " smooth nut gravel.
4 " " " 4-inch pebbles.
5 " " " 2-inch square brick-bats.
APPENDIX.
606
TENSILE STRENGTH OF CEMENTS AND CEMENT MORTARS, WHEN
7 DAYS OLD, 6 OF WHICH THE CEMENTS WERE IN WATER.
(Compiled from Gilmore.*)
BY WEIGHT.
BY VOLUME,
LOOSELY MEASUR'D
BY VOLUME,
WELL SHAKEN.
s ..
/I
U
m
e/5 3
^s
^.S'S
en
^'l
Sj
a o a
How MIXED.
,0
1
U-
jL fl
1
(iAro
Jjj
a
"wl^
S'l 1 "
o-'
.j
i
I
TiT'
jy
V
s j
C
g
L
o
^
^^
1
O
t*
c
s
3*1
Is
1
ll
1g
O
a
a
1
~
jls
SB 8
O 4 O
1
O 4)
1
73
I
1
1
g
3-g-
0,0
K
c/!
duO
(^0
OH
&
w
H
Lbs.
Lbs.
Like beton agglome're'.
25
X
.21
.25
377
" common mortar. .
2 5
44
_
44
__
289
_^
'' beton agglomere'.
5
I
.42
5
320
'' common mortar. .
__
.5
44
44
44
222
1 beton agglome're'.
' common mortar. .
i
i
I
14
'?
V
244
197
4 be*ton agglome're'.
1-33
I
X * X 3
x -3
179
' common mortar. .
1.33
* fc
i^
44
**
129
1 beton agglome're'.
2
I
1.7
1.9
138
2804.4
41 common mortar..
1 beton agglome're".
2
6
I
__
if
5
5 u 9
109
66
1038.0
259-5
41 common mortar..
__
6
44
M
14
__
35
' beton agglome're'.
8
I
6.8
I
7.8
39
259-5
44 common mortar..
4 beton agglome're'.
8
8
44
1
xx.6
^~
i4
24
96
104.7
14 common mortar..
8
44
kt
__
4
44 beton agglome're.
2
I
2.0
129
11 common mortar. .
1 be"ton agglomere'.
2
i
44
51
~
44 U 11
I
2
I
1.2
I
1.4
40
310.7
44 44 44
I
3
I
1.8
I
2
33
116.4
44 44 14
!
4
I
2.4
I
2.8
22
156.0
44 44 11
-
. I
6
I
3-6
I
*J
Less than
10 Ibs.
52.4
11 44 14
I
8
46.5
44 14 41
i
400
846.7
44 common mortar..
44 beton agglomere".
J
I
z
72
579-2
14 common mortar..
~
I
~
~
~
~
~
~
~
104.7
* Vide Treatise on Coignet Be"ton, p. 28, et seq. New York, 1871.
606
APPENDIX.
STANDARD DIMENSIONS OF BOLTS, WITH HEXAGONAL HEADS
AND NUTS.
Diameter
of bolt
in inches.
No. of
V threads
per in. of
length.
Breadth
of head,
in inches.
Thickn'ss
of head
in inches.
Breadth
of nut
in inches.
Thickness
of nut
in inches.
Weight
of round rod
per foot
in pounds.
Weight of
head and nut
in pounds.
t
2O
t
i
1
A
.1653
.017
T S *T
18
\
T7T
^
1
2583
033
i
16
1
t
1
TV
.3720
.057
-T6
14
s
nr
i
.5063
.087
13
i
i
I
rk
.6613
.128
A
12
i
T 9 ^
i
1
.8370
.190
1
II
i
1
I
H
r -33
.267
*
IO
4
f
4
H
1.488
43
7
?
9
if
1
4
H
2.025
73
I
8
4
I
4
irV
2.645
I. 10
li
7
if
4
i|
iA
3.348
i .60
I*
7
4
4
4
ITT
4.133
2.14
If
6
2i
4
2 i
ITT
5.001
2-95
l|
6
2i
4
2 i
iA
5-952
3.78
4
si
4
T l
2^
ixi
6.985
4.70
ij
5
2 I
J i
2 f
iii
8.101
5.60
l|
5
2|
4
2-J
IT!
9.300
7 .00
2
4!
3
2
3
2yV
10.58
8.75
2 i
4i
3f
2 i
3*
2T%
13-39
12.40
2\
4
3f
2 i
3i
2TT
i6.53
17.00
2 !
4
4i
2j
4j
2Tf
20.01
22.30
3
3i
4i
3
41
3rV
23.81
28.80
APPENDIX.
607
WEIGHTS OF LEAD AND TIN LINED SERVICE-PIPES.
Calibre.
AAA.
Weight
per ft.
AA
Weight
per ft.
A.
Weight
per ft.
B.
Weight
per ft.
C.
Weight
per ft.
Weight
per ft.
D. Light.
Weight
per ft.
E .
Weight
per ft.
E. Light.
Weight
per ft.
Inches.
Lbs.
Lbs.
Lbs.
Lbs.
Lbs.
Lbs.
Lbs.
Lbs.
Lbs,
I
1.5
1.3
1. 12
I
1. 06
0.62
0-5
*
3
2
1-75
1.25
I
0.81
0.7
0.56
I
3-5
2-75
2-5
2
i-75
1.5
1.25
I
0-75
t
4-5
3.5
3
2.25
2
1-75
i-5
1.25
I
I
6
4.75
4 3-25
2-5
2
1-5
I*
6 75
5-75
4-75
3-75
3
2-5
2
4
9
8
6.25
5
4-25
3-5
3-25
2
10.75
9
7
6
5-25
4 .
A manufacturer' s circular states that the following quanti-
ties of water will be delivered through 500 feet of their pipes,
of the respective sizes named, when the fall is ten feet :
Calibre .
jr inch
i inch
f inch
f inch
i inch
j i inch
Gallons per minute. . .
.348
.798
1.416
2.222
4.600
6-944
Gallons per 24 hours. .
576
1150
2040
3200
6624
IOOOO
A f-inch clean service-pipe connected to a J-inch tap
under a hundred feet head, will deliver at the sink, through
a common compression bib, ordinarily about three pails of
water, or say 8.25 gallons, or 1.1 cu. ft. of water per minute.
Lead is more generally used for service-pipes than any
other material, but wrought-iron pipe, lined and coated
with cement, or with a vulcanized rubber composition or
sundry coal-tar compositions and enamels, have been used
to a nearly equal extent within a few years past. Block-
tin pipe, tin-lined pipe, and galvanized iron pipe, have been
used also to a limited extent.
608
APPENDIX.
Lead pipes of weights as in class A are used ordinarily
when the head of water on them does not exceed 75 feet ;
class AA when the head is from 75 to 150 feet ; and class
AAA when the head, or strain from water-ram, is great.
The strain from water-ram, in service-pipes, is very
much dependent on the character of the plumbing with
which the services connect.
METERS AND METER RATES, 1875.
CITY.
No. of
Meters
used.
Rate per
100 CU. ft.
Cents.
Kind of Meters.
Furnished by*
Boston Mass
Q74
22l
W
Baltimore Md
^2O
2O
w.
Bridgeport, Conn . . .
Charlestown, Mass. .
Chicago 111
I
1 80
1050
26^ to 40
22 i
141
W.
W. B. & F.
W
Water-works.
Water-works.
Cleveland, O
18
iql tO 2li
W B & F
Columbus O
1^8
26!
B & F E Nav
Fitchburg, Mass
Fall River, "
Hartford Conn .
25
4
6
ni to 37 i
22 i
1C to 22 1
B. &F.
B. & F.
B & F D
Consumer.
Consumer.
Jersey City, N. J
Louisville Ky
208
IIQ
26!
20
W.
W
Water-works.
W^ater- works
Meriden, Conn
Q
26^ to 40
B & F
\Vater-works
Manchester, N.H....
New York, N.Y
New London, Conn..
New Haven, " . .
New Bedford, Mass. .
Providence, R. I
Portland Me
1 6O
2OO
20
3
3
1358
15 to 30
12
261
22}
22 i
22i tO 37i
B. & F. N.
W.
N.
N.
B. &F.
B. & F. W.
B. & F W.
Water-works.
Consumer.,
Water-works.
Consumer.
Water-works.
Consumer.
Consumer
Springfield, Mass. . .
St Paul Minn
8
4O
22|-
4.O to 64.4
W. & B. & F.
B & F N
Water-works.
\Vater-works
San Francisco, Cal. .
Waterbury, Conn. . . .
Worcester, Mass
800
8
800
641 to 133
26! to 40
n to i8|
W.
W. B. & F.
B. &F.
Water- works.
Water-works.
Water- works.
The initials refer to kinds of meters, as follows :
W. Worthington.
B. & F. Ball & Fitts.
N. National Meter Co. (Gem.)
-Hagl
Nav. Navarro.
D. Desper.
* A common practice is, for the water- works to furnish the meter and main-
tain and control it, and to charge the consumer from ten to fifteen per cent, on
its original cost, annually, to cover the expense, in addition to the regular meter
rate for water consumed.
APPENDIX. 609
RESUSCITATION FROM DEATH BY DROWNING.
Persons may be restored from apparent death by drown-
ing, if proper means are employed, sometimes when they
have been under water, and are apparently dead, for fifteen
or even thirty minutes. To this end
1. Treat the patent INSTANTLY, on the spot, in the open
air, freely exposing the face, neck, and chest to the breeze,
except in severe weather.
2. Send with all speed for medical aid, and for articles
of clothing, blankets, etc.
I. To CLEAR THE THEOAT.
3. 'Place the patient gently on the face, with one wrist
under the forehead.
(All fluids, and the tongue itself, then fall forwards, and
leave the entrance into the windpipe free.
II. To EXCITE RESPIEATION.
4. Turn the patient slightly on his side, and
(I.) Apply snuff, or other irritant, to the nostrils ; and
(II.) Dash cold water on the face, previously rubbed
briskly until it is warm.
If there be no success, lose no time, but
III. To IMITATE RESPIEATION.
5. Replace the patient on the face.
6. Turn the body gently but completely on the side, and
a little beyond, and then on the face alternately, repeating
these measures DELIBEEATELY, EFFICIENTLY, and PEESE-
VEEINGLY, fifteen times in the minute only.
(When the patient reposes on the chest, this cavity is
39
610 APPENDIX.
compressed by the weight of the body, and EXPIRATION
takes place ; when it is tnrned on the side, this pressure is
removed, and INSPIRATION occurs.)
7. When the prone position is resumed, make equable
but efficient pressure along the spine, removing it immedi-
ately before rotation on the side.
(The first measure augments the EXPIRATION, and the
second commences INSPIRATION.)
IV. To INDUCE CIRCULATION AND WAEMTH, CONTINUE
THESE MEASURES.
8. Rub the limbs upwards, with FIRM PRESSURE and
ENERGY, using handkerchiefs, etc.
9. Replace the patient's wet covering by such other cov-
ering as can be instantly procured, each bystander supply-
ing a coat or a waistcoat. Meantime, and from time to time,
Y. AGAIN, TO EXCITE INSPIRATION,.
10. Let the surface of the body be slapped briskly with
the hand ; or
11. Let cold water be dashed briskly on the surface,
previously rubbed dry and warm.
Avoid all rough usage. Never hold up the body by the
feet. Do not roll the body on casks. Do not rub the body
with salts or spirits. Do not inject smoke or infusion of
tobacco, though clysters of spirits and water may be used.
The means employed should be persisted in for several
hours, till there are signs of death.
INDEX.
The figures refer to the pages.
Acceleration of motion, 185.
Adjustable effluent pipe, 36^.
Advantages of water supplies, 29.
Air, resistance of, to a jet, 190.
44 valves, 523.
41 vessel, 564, 565.
Ajutage, an, 213.
inward projecting, 218.
u vacuum, 214.
Algae, fresh water, 129. _
Analyses of lake, spring, and well waters, icjf.
44 u mineral waters, 143.
44 potable waters, table, 117.
44 " river and brook waters, 118, 120.
Analysis of impure ice, 136.
Angular force graphically represented. 175.
Aquatic life, purifying office of, 132.
44 organisms, 131.
Arago's prediction at Grenelle, 106.
Areas of sluice valves, 360.
Artesian wells, 105, 106, 108.
44 temperature of, table, 127.
Artificial clarification of water, 159.
" gathering areas, ioo.
u pollution of water, 152.
storage " . 84, 93, 95, 98, 99.
Aspnaltum bath for pipes, 475, 487, 490.
Atlantic coast/rainfall, 53.
Atomic theory, 162.
Attraction, capillary, 296.
Atmospheric impurities of water, 122.
pressure, 182.
Average consumption of water, 44.
Basins, clear-water, 550.
infiltration, 537.
44 settling, 50.
Bends and branches, 272, 275, 478, 485.
44 coefficients for, table of, 274.
Blow-off valves, 513.
Boilers, 577, 578, 580.
Bolts in flanges, table of, 462.
Bolt-holes, templet for, 460.
Boyden's hook-gauge, 297.
Branches and bends, 272, 478, 484.
" composite pipe, 484.
formula for flow through, 275.
Bucket-plunger pump, 557, 567.
Bursting pressure, 232.
C.
Caloric, influence of, 163.
Canal banks, 370.
in side hill, 370.
' miner's, 375.
44 open, 370.
Canal revetments and pavings, 371.
slopes, 371.
44 stop-gates, 373.
Canals and rivers, observed flows in, table of^
307.
Canals and overs, coefficients for flow in, 308.
Capacity for filter-beds, 552.
Capillary attraction, 296.
Cast-iron pipes, 451.
" weights of, 465, 468, 469.
Cast socket on wrought pipe, 483.
Casting of pipes, 452.
Cement joints of pipes, 482.
u lined pipes, 479.
44 lining ot pipes with, 481.
11 mortar, for lining and covering pipes,
487.
Census statistics, 31.
Central rain system, 49.
Chamber, effluent, 358.
" influent, 366.
" walls, 369.
Chandler's, Prof., remarks on wells, 140.
Channels, coefficients for, 308.
44 depths and relative volumes and
velocities, 328.
44 flow in. experimental data, 306.
44 flow in open, 299.
formulas for flow, table, 310.
44 inclination in, 304.
44 influences controlling flow in, 316.
44 ratios of surface to mean veloc., 315.
44 surface velocities, 313.
44 velocity of flow in, 303, 304.
44 velocities of given films, 311.
44 water supply, protection of, 431.
Characteristics of pipe metals, 470.
Charcoal clarification of water, 535, 537.
44 filters, 536.
Check-valve, 367, 525.
Chemical clarification, 532.
Choice of water, 587.
Cities, families in various, 32.
persons per family in various, 32.
population of various, 32.
44 water supplied to, 35, 36, 37. .
Clarification of water, artificial, 159, 532.
charcoal, 535, 537.
chemical, 532.
natural, 149, 530, 532.
Cleaning of filter-beds, 553.
Clear water basin, 550.
Climate effects, rainfall, 47.
Coal required for pumping, 581.
Coating (asphaltum) pipes. 475, 487, 490.
Cochituate basin, rain upon, 72.
Coefficients, compound tubes, 219, 220.
convergent tubes, 217.
J, table of, 271.
experimental, 198.
table of, 237.
612
INDEX.
Coefficients for channels, Kutter's, 305.
" circular orifices, 203.
u " flow in conduits, 444.
" " hydrometers, 325.
* u " pipes, table of, 242.
" " rectangular orifices, 205, 206.
u " service-pipes, 528.
" u weir formulas, 287, 288.
" wide-crested weirs, 294.
u from Castel, 200.
u u Eytelwein and D'Aubuis-
son, 256.
" General Ellis, 201.
" " L'Abbe Bossut, 199.
u " Lespinasse, 201.
Michelotti, 198.
" Prony, 255.
w u Rennie, 199.
w increase of, in short tubes, 213.
w m, 234, 247.
" mean, for smooth and foul pipes,
248, 249, 267.
of efflux, factors of, 197, 208.
" " table of, 227.
u " entrance of jet, 267.
u flow for channels, 305, 308.
" *' friction of earth-work, 345.
" " table of, 495.
" issue from short tubes, 218.
' " masonry frictions, 396.
w " velocity and contraction for
orifice jets, 208.
practical application of, 197.
range of, 222.
resistance in bends, 274.
u variable values of, 210.
Coffer-dams, 430.
Combined reservoir and direct systems, 525.
Commercial use of water, 34.
Compensation flow, 86.
to riparian owners, 94.
Composite branches, pipe, 484.
Composition of water, the, 112.
Compound tubes, 218, 220.
" coefficients for, 220.
Compressibility and elasticity of water, 167.
Concrete conduit, a 438.
" foundations, 368.
" foundations for pipes, 487.
" paving, 355.
" proportions of, 368.
" revetments, 429.
Conduit arch, thrust of, 437.
1 data, 445.
masonry to be self-sustaining, 437.
' of concrete, 438.
1 of wood, 439, 441.
shells, 434.
Conduits and pipes, 223.
" backing of, 438.
coefficients for, 444.
u examples of, 431,438, 439.
" exposure to frost, 437.
" formulas for flow in, 442, 443.
* foundations for, 433.
" locked bricks for, 435.
u masonry, 431.
" mean radii of, 441, 442.
" protection from frost, 436.
" stop-gates in, 436.
" transmission of pressure in, 436.
" under pressure, 435, 439.
u ventilation of, 434.
Confervae, 129.
Construction of embankments, 348.
of filter-beds, 548.
Consumption of water, 34, 43, 503.
Core of an embankment, 348.
Cornish pump, 557, 563.
Costs of pumping water, 574, 575.
Crib-work foundations, 385.
" weir, 384.
Croton basin, rainfall upon, 72.
Curbs, stop-valve, 515.
Curved-face wall, 421.
Cut-off wall, embankment, 348.
Cycle, low, rainfalls, 69, 77, 78.
Cylindrical penstock, 440.
tubes, 222.
D;
Dams, thickness of, 387.
Darcy-Pitot tube gauge, 322.
Data from existing conduits, 445.
Debris, floating, 530.
Decimal parts of an inch and foot, 457.
Decomposing organic impurities, 127.
Densities and volumes of water, relative, 164.
Desmids, in fresh ponds, 129.
Details of stop- valves, 513.
Depths of pipes, 501, 502.
Diagonal force, 175.
Diagrams of pumping, 42.
" of rainfall, 55, 57, 59.
Diameter of sub-mains, 507.
" of supply-main, 506.
Dimensions of existing canals, 373.
*' '' filter-beds, 554.
" " retaining walls, 420.
Direct pressure system, 590.
Discharges of pipes, 498, 500.
' over waste-weirs, 378, 381.
Domestic draught of water, 34, 508.
Draught, variations in, 41.
Duplicate pumping machinery, 590.
Duplication in pipe systems, 510.
Duty of pumping-engines, 574, 576, 580, 583^
Dwellings in various cities, 32.
Dykes, canal and river, 371.
E.
Earth and rock, porosity of, 102.
embankments, 333, 347, 348, 353, 370;
" evaporation from, 89, 90.
" pressures against walls, 408.
Eastern coast rain system, 50.
Economy of high duty of pumping-enginesj
579 581-
" " skillful workmanship, 369.
Eddies, in weir channels, 292.
Effect, mechanical, of the efflux, 225.
Effluent chambers, 358.
" ice-thrust upon, 358.
Efflux, equation of, 211.
" factors of the coefficient, 197.
" from pipes, coefficients of, 196, 227.
" mechanical effect of, 225.
" peculiarities of jet, 207.
' volume from short tubes, 194, 210, 214.
Elasticity and compressibility of water, 167.
Electric moulinet, Henry's, 326.
Elementary dimensions of pipes, 504.
Elements, the vapory, 45.
Embankment, a light, 353.
core materials. 339, 342, 348, 354.
cut-off walls, 336, 338, 348.
example of, 347.
failures, 334.
fine sand in, 353.
foundations, 335.
frost covering, 350.
gate chambers, 357, 358.
masonry-faced, 354.
materials, coefs. of friction, 345.
" frictional angle of^.
345-
INDEX.
613
Embankment materials, proportions of, 340,
349-
weights of, 341.
pressures in, 343.
u puddle wall, 351.
puddled slopes, 356.
44 sheet-piling under, 339.
44 site, reconnaissance tor, 347.
slope-paving, 350.
44 Slopes, 344, 345, 350.
sluices, 355, 356, 358.
44 soils beneath, 337.
44 springs under foundation, 337.
substructure, 336.
ciphon waste-pipe, 358.
" test borings at site, 336.
treacherous strata under, 338.
Embankments, canal, 370.
Indian, 334.
reservoir, 333.
Energy of jet, 276.
England, supply per capita, 37.
Equation of motion, 186.
u " resistance to flow, 233.
Equilibrium destroyed, 170, 300.
Errors in application of formulae, 252, 257.
" " weir measurements, 296.
Estimates of flow of streams, 78, 94.
European infiltration, 544.
Evaporation, effect upon storage, 93.
examples of, 90.
from earth, 89, no.
" reservoirs, 94.
water, 88, 89.
phenomena. 87.
44 ratios of, table, 92.
Evaporative power of boilers, 578, 580.
Examples of conduits, 431, 438, 439.
Experimental channel data, 306.
coefficients forny drometers, 325.
Experiments with weirs, 234.
Eytelwein's coefficients, 222,
F.
Faced revetments, 429.
Failures of embankments, 334.
44 " walls, 427.
Falling bodies, 190.
Families in various cities, 32.
Fascine revetments, 371.
Filter-beds, 547.
44 capacity of, 552.
" cleaning of, 55?.
construction of, 548, 557.
ice upon, 556.
protection of, 548, 555.
44 temperature of, 555.
" vegetal growth in, 555.
Filters, Atkin's, 536.
Fire draught of water, 34, 506, 508.
' extinguishment, reserve for, 44.
' 4 hydrants, 516, 519, 521.
' losses, effect of water upon, 26.
4 service, 493, 588, 589, 591.
head desirable for, 493.
1 supplies, diameters of pipes for, 510.
Fish screens, 365.
Flanges, diameters of valve, 462.
" of cast-iron pipes, 462.
Flash-boards, 378.
Flashy and steady streams, 71.
Flexible pipe-joints, 463.
Floats, double, gauge, 326.
maximum velocity, 328.
44 mid-depth, 326.
Flood flow, 65, 98.
44 volumes, 65, 67^ 381.
Floods, ratios of, to rainfalls, 62.
Floods, seasons of, 68.
Flow, available, for consumption, 94.
coefficients of, 230.
compensation, 86.
equivalent to given depths of rain, 81.
from Croton and Cochituate basins, 73.
" different surfaces, 77.
gauged volumes of, 277.
gravity the cause of, 299.
in seasons of minimum rain, 69.
increase and decrease of, 86.
influence of absorption and evaporation
upon, 68.
minimum, mean, and flood, 75.
of streams and channels, 65, 299.
44 water, 184.
over a weir, 280.
periodic available, 69.
resistance to, in channels, 232, 300.
sub-surface equalizers of, 70.
summaries of monthly statistics of, 71.
through orifices, 194.
pipes, 223, 508, 560.
short tubes, 213.
44 sluices, pipes, and channels, z6x.
Fluctuations of streams, 319.
Flush hydrant, 519, 521.
Foot and inch, equivalent decimal parts of, 457.
Force, loss of, in pipes, 224.
44 percussive, of particles, 221.
Forces, angular, 176.
44 equivalent, 172.
44 graphically represented, 175.
Formula, efflux from an orifice, 196, 209, 211.
4k ' 4 short pipes, 215.
44 for capacity of air-vessel, 566.
44 coal for pumping, 581.
44 curved-face walls, 421.
44 depth upon a weir, 286.
44 duty of pumping-engines, 576.
* 4 earth pressures upon walls, 410,
inclination in channels, 304.
power to produce flow in pipes,
561.
412, 413, 415, 416.
icli
)\V
56
44 pressure in pipes, 447.
44 pressure on submerged walls, 393,
44 resistance in channels, 301, 303.
4k surcharged pressure walls, 414,
416, 423.
44 triangular notch weir, 294.
44 velocity in channels. 303, 304.
44 volume at given temp., 165.
41 weights of cast pipes, 465, 467.
44 of M. Chezy, pipes, 252.
" Weisbach, * 257.
Formulas, coefficients for weir, 287.
44 for diameters of pipes, 251, 266, 269,
270, 49 8.
flood volumes, streams, 320.
14 flow in conduits, 442, 443..
44 44 44 pipes, 254, 257.
origin of, 229.
" 44 through bends, 272.
44 44 u " branches, 275.
" " " " channels, 310.
41 gauging streams, 320.
44 head, pipes, 250, 266, 268, 270, 494.
44 lengths of pipes, 269, 270.
4k pipes, various compared, 254.
44 * 4 resistance to flow, 230, 234, 250.
44 thickness of pipes, table, 466.
44 " " " cast pipes, 453, 454,
466.
44 wrought pipes, 448,
450, 486.
" 44 velocity, pipes, 249, 266, 267, 268,
270, 498.
614
INDEX.
Formulas for volume, pipes, 250, 254, 266, 498.
44 weir volumes, 282, 283, 284, 286.
" " wide-crested weirs, 293.
44 many incomplete, 252.
44 misapplication of, 316.
44 stability of masonry, 395, 397, 398.
44 velocities and times offalling bodies,
186.
Foundation, concrete, 386.
embankment, 335.
for pipes, 4 8 7 .
of gate chambers, 367.
of conduits, 433.
4 ' walls, 395, 406, 407.
under water, 430.
Fountain use of water, 34.
Francis, Jas. B., experiments with weirs, 284.
" tubes, 517.
Frankland's definition of polluted water, 137.
Friction, coefficient of masonry, 396.
in pipes, 230, 234, 250, 508.
of ice on canals, 372.
" pumping machinery, 578.
Frictional head, formula for, 494.
44 in pipes, 493. 494, 527.
stability of masonry, 395.
Frost curtain, 367.
44 disintegrates mortar, 436.
44 protection of conduits from, 436.
Fuel, expense for pumping, 581.
*' required " 44 575.
Fungi, microscopic, 129.
a.
Galleries, infiltration, 539, 540.
Gate chambers, 357, 367.
44 hydrants, 522.
Gates, stop, canals, 374.
Gauge, Darcy-Pitot tube, 322.
" Darcy's double tube, 322.
44 double float, 326.
44 formulas, 319.
* 4 hook, Boyden's t 296, 297.
14 maximum velocity float, 328.
44 mid-depth float, 326.
44 Pitot tube, 320.
41 rain, 63.
4 ' rule, for wens, 298.
44 tube, 317.
tube and scale, weirs, 298.
44 Woltman's, 322.
Gauges and weights of plate iron, 487, 488.
Gauging, hydrometer, 316,
" of mountain streams, 296.
44 rainfall, 62.
44 4 ' rivers, 318, 319.
Gears for sluice-gates, 359.
General rainfall, 46.
Geological science, application, 106.
Granular stability of masonry, 402.
Graphical representation offeree, 175.
Gravitation system, 588.
Gravity, 185, 230, 299.
centre of, 177.
Great rain-storms, 61.
Grouped rainfall statistics, 52.
Grouting, 353, 369.
H.
Hardening impurities, 125.
Hardness of water, 125.
Head, desirable for fire service, 493.
44 effective in pipe system, 493.
how to economize, 276.
44 loss by friction, 493.
subdivisions of, 225.
44 value of, 493.
Heat, units of, utilized, 578.
Heights of waves, 388.
Heisch's sugar test of water, 159.
Helpful influence of water supplies, 27.
Hook gauge, Boyden's, 296.
Hook gauge, use to detect fluctuations, 319,
Horse-power, to produce flow, 561.
Hose streams, 510, 520.
4k use of water, 34.
Hudson valley, rainfall in, 53.
Hydrants, 516, 517, 519, 522.
' 4 high pressures, 522.
44 streams, 520.
Hydraulic mean depth. 235.
44 radius, 236.
44 power pumping, 589, 591.
44 proof of pipes, 477.
Hydrometers, Castellis' and others, 326.
coefficients for, 325.
44 gauging with, 316.
Ice covering of canals, 372.
44 impure, in drinking water, 135.
44 thrust, 358, 386.
Impounders, flow to, 86.
Impounding of water, 144.
Impregnation of water, 141, 152.
Impurities of water, 112.
44 agricultural, 134.
44 atmospheric, 122.
44 manufacturing, 134.
44 mineral, 115, 133.
organic, 116, 127, 130.
44 sewage, 134.
44 sub-surface, 123.
44 " deep wells, 125.
Inch and foot, decimal parts of, 457.
Incidental advantages of water supplies, 29.
Inclination in channels, 235, 304, 371.
Increase in use of water, 39.
Indian embankments, 334.
Indicator, stop-valve, 361.
Infiltration, 537, 540, 543, 544.
Influent chamber, 366.
Infusoria, 130.
Inhabitant, supply per, 40.
Intercepting well, 546.
Interchangeable pipe-joints, 469.
Introduction of filters, 551.
Insurance schedule, 29.
Investment, value of water supplies as an, 29..
Iron, gauges and weights, 488.
44 sluice valves, 360.
44 -work, varnishes for, 474, 476, 489.
Irrigation canals, 370, 373.
Isolated weirs, 383.
Jets, 211, 267.
Joint mortar for pipes, 487.
Joints of cast pipes, 457, 461, 463, 469.
K.
Kutter's coefficients for channels, 305.
Lake waters, 142.
Lakes, 150.
Laying of wrought-pipes, 482.
Lead, joint, 468.
Lengths of waste- weirs, 381.
Level, use of, in gauging, 319.
Leverage of water pressure, 397.
44 resistance of walls, 402.
44 stability of masonry, 397.
Life of dams, 388.
Lining of pipes, cement, 481.
Logarithms of ratios, 121.
INDEX.
615
Loss by evaporation, 87.
tk from reservoirs, 84.
" of head by friction, 276, 493.
M.
Mains and distribution pipes, 446.
" power to produce flow in, 561.
Masonry conduits^.431, 437.
coverings of waste-pipes, 357.
examples of pressure in, 403.
faced embankment, 354.
frictional stability of, 397.
granular stability of, 402.
limiting pressures in, 404.
weight leverage of, 398.
Materials, embankment, 339, 341.
Maximum velocities of flow, 508.
Metals, pipe, 470, 472.
" tenacities of wrought, 451, 486, 491.
Microscopical examination of metals, 471.
Mineral impurities, 115, 530.
springs, 142, 143.
Miners' canals, 375.
Misapplication of fc
"ormulae, 316.
Mississippi valley, rainfall in, 54.
Molecular theories, 162, 296.
Molecules, 185.
Moment of earth leverage, 412.
Monads, 130.
Monthly and hourly variations in the draught,
41.
fluctuations m rainfall. 56.
Mortar for lining and covering pipes, 487.
Motion, acceleration of, 185.
equations of, 186.
of a piston, 562.
of water, 184, 194.
u parabolic of a jet, 187.
Moulding of pipes, 451.
Moulinets, 323, 326.
Municipal control of water supplies, 28.
N.
Natural clarification, 149, 532.
" laws, uniform effects of, 61.
Necessity of water supplies, 25.
Noctos, 129.
O.
Ohio river valley, rainfall in, 54.
Open canals, 370.
Ordinary flow of streams, 80.
Organic impurities, 80, 113, 116, 531, 532.
Organisms, 129, 131, 133.
Orifices, classes of, 194.
** convergent, 212.
path toward, 194.
cylindrical and divergent, 212.
" flow of water through, 194, 210.
Orifice-jet, form of submerged, 195.
peculiarities, 207.
ratio of minimum section, 195.
variations, 204.
velocity, 196, 208, 209.
P.
Pacific coast rainfall, 54.
Parabolic path of jet, 187,
" segment, appli
umes, 282.
Partitions and retaining walls, 390.
Paving, concrete, 355.
" embankment slope, 350.
Peculiar watersheds. 71.
Penstock, cylindrical, wood, 439, 441
Percolation from reservoirs, 85, 94.
ition to weir vol-
Percolation of rain, 104, in.
under retaining walls, 406.
Permanence of water supply essential, 585.
Persons per family, 32.
Physiological effects of the impurities of water,
Pipe
office of water, 25.
, adjustable effluent, 364.
and conduit, 223.
branches, composite, 484.
joints, cast, 457 . 4 6i, 463, 469, 483.
' hub on wrought, 483.
dimensions of, 459, 451, 462.
u flexible, 463.
" interchangeable, 469.
metals, 470, 472.
kl wrought, strength of, 451, 486,
491.
resistance at entrance to, 226.
shells, wrought, thickness of, 448, 485,
486.
systems, duplication in, 510.
" illustrations, 493, 510.
walls, resistances of, 227, 228.
and sluices, embankment, 355.
cast-iron, 451.
thickness of, 453, 454, 455, 466.
weights of, 465, 468, 469.
' cement joints, 482.
*' lined, 479, 481.
" coefficients of friction, 242, 495.
' concrete foundations for, 487.
" depths of, 501, 502.
" sockets, 459. 461.
' diameters for fire supplies, 510.
" elementary dimensions of, 504.
" flanges, table of, 462.
formulas for thickness of cast, 453, 466.
velocity, head, volume,
and diameter, 224, 266,
268, 270, 498.
" " weights of cast, 465.
u frictions in, 224, 495, 508.
hydraulic proof of, 477.
lead in joints, 468.
' mains and distribution, 446.
'* preservation of surfaces, 473, 480, 489,
49 1 -
" relative capacities of, 498, 500.
1 short, 223.
" square roots of fifth powers of diameters,
400 500.
" static pressure in. 446.
' sub-coefficients of flow (cO, 271.
; temperatures of water in, 502.
" thicknesses of wrought, 447, 450, 486,
488.
u volumes of flow from, 223, 225, 495.
water-ram in, 448, 449.
wood, 491.
" wrought-iron, 479.
" plates for, 490.
Piping and water supplied, 38.
" rati9 to population, 35.
Piston motion, 562.
" pump, 557, 558.
Pitot tube gauge, 320.
Plant and insect agencies, 147.
" growth in reservoirs, 145.
Plates for wrought pipes, 490.
Plunger pump, 557, 563.
Pluviometer, 63.
Polluted water, definition of, 137.
Polluting liquids, inadmissible, 154.
Pollution question, 156.
u of water, artificial, 152.
Population, and relation of supply per capita,
40.
of various cities, 32.
616
INDEX.
Portland cement for joint mortar, 487.
Porosity ot earths and rocks, 102.
Post hydrants, 517.
Power consumed by variable flow in a main,
" required to open a valve, 361, 364.
Practical construction of water-works, 333.
Precautions for triangular weirs, 295.
Precipitation, influence of elevation upon , 50.
Preservation of pipe surfaces, 473, 480, 489, 491.
Pressure, a line a measure of, 174.
" conduits under, 435, 439, 440
u conversion into mechanical effect,
230.
of velocity into, 227.
" direction of maximum effect, 176.
" leverage of watei, 307.
" of earth against walls, 408, 410, 413,
415, 416.
" water, 168.
" " in a conduit, 437.
" proportional to depth, 169.
" sustaining upon floating oodies, 179.
" transmission of, 183.
upon a unit of surface, 171.
" surfaces, 391, 393.
weight a. measure of, 173.
Pressures, artificial, 171.
at given depths, table, 172.
atmospheric, 182.
centres of, 177.
convertible into motion, 184.
from inclined columns of water, 170.
great in hydrants, 522.
horizontal and vertical effects, 177.
in embankments, 343.
limiting in masonry, 404.
static in pipes, 446, 448.
total of water, 176.
" upon circular areas, 179.
" curved surfaces, 178.
" upward upon submerged Iintels,i8i.
Prism of weir volumes, 282.
Processes for preserving iron, 474, 476, 489.
Profile across the United States, 48.
" of retaining walls, 407.
Properties of water, 113.
u of embankment materials, 342.
Proportions 349.
Protection of filter beds, 548, 555.
" "water supply channels, 431.
Prony's analysis of experiments, 255.
Proving press, hydraulic, 477.
Puddled canal bank, 370.
Puddle- wall, 351.
" slope, 352.
Pump, bucket-plunger, 557, 567.
u Cornish, 557, 563.
piston, 557, 558.
plunger, 557, 563.
rotary, 558.
Pumping of water, 557.
" diagram of, 42.
engines, 557, 567, 573, 577-
^ adaptability of, 584.
" cost of supplies, 575, 582.
" attendance, 575, 582.
duties, 574, 579, 580, 581, 583.
" fuel expenses, 581.
principal divisions, 577.
" special trial duties, 580.
" values compared, 583.
machinery, 591, 592.
duplicate, 590.
for direct pressure, 590,
591.
" "' Manchester, 585.
system, 589, 590.
*' water, cost of, 574, 575.
Pumps, types of, 557.
" variable flow through, 550.
Purity of water, chief requisites for, 144.
Purity of water, preservation of, 148.
Purihcation of water, natural, 134, 157, 158.
Q.
Quality of water, sugar test of, 159.
R.
Radii, mean of conduits, 441, 442.
Rainfall, along river courses, 51.
diagrams of, 55, 57, 59.
gauging, 62.
general, 46.
in the United States, 53.
influences affecting, 60.
u low cycle, 69, 77, 78.
monthly fluctuations in, 56.
" ratio of floods to, 62.
secular fluctuations in, 60.
" sections of maximum, 47.
" statistics, review of, 46.
" volumes of given, 62.
Rain-gauge, 63.
Rains, river-basin, 50.
Rates of fire supplies, 506.
Ratios of evaporation, 91.
u monthly consumption, 43.
" monthly flow in streams, 76.
qualification of deduced, 99.
rainfall, flow, etc., table, 100, 101.
" standard gallons, 120.
" surface to mean velocities in chan-
nels, 315.
variable delivery of water, 564.
Reaction and gravity, opposition of, 230.
Recounoissance for embankment site, 346.
of a water-shed, 78.
Rectangular and trapezoidal walls, moments
of, 399.
weirs, 277.
Reducer, pipe, 478.
Relation of supply per capita to total popula-
tion, 40.
Relative values of h, h', and h"^ 253.
discharging capacities of pipes, 498,
500. i
" rates of domestic and fire draughts,
508.
Repulsion, molecular, 296.
Reserve for fire service, 44.
Reservoir coverings, 556.
" distributing, 353.
' embankments, 333.
" plant growth in, 145.
" storage, surveys for, 347,
" strata conditions in, 146.
' system, 598.
Reservoirs, subterranean, 105.
Resistance of the air to a jet, 190.
at entrance to a pipe, 226.
of masonry revetments. 417.
to flow, measure of, 230, 231.
Resistances to flow within a pipe, 227.
" in channels, 300.
Resultant effect of rain and evaporation, 92.
Retaining walls, 390.
effect of traffic on, 425.
for earth, table, 420.
front batters, 424.
percolation under, 406.
sections of, 407.
top breadihs, 424.
Revetted conduits, 431.
Revetments, faced and concrete, 429,
" final resultants, 418.
I NDEX.
617
Revetments, resistance of, 417.
trapezoidal, table of, 420.
Riparian rights, 85.
Rip-rap, slope, 371.
River waters, 151.
Rivers and canals, table of flows, 307.
" basin rains, 50.
41 basins of Maine, 84.
" courses, rainfall along, 51.
" pollution committee, 154.
Roof for filter beds and reservoirs, 548, 555.
Rotary pump, 558,
Rubble, grouted, 353.
" masonry, 252.
" priming wall, 352.
S.
Sand in embankments, 353.
Sanitary discussions, 152.
" improvements, 26.
" office of water, 26.
" views, precautionary, 154.
Schussler's process of coating pipes, 489.
Screens, fish, 365.
Seasons of floods, 68.
Sections of maximum rainfall, 47.
Secular fluctuations in rainfall, 60.
Sediments, 530, ^31.
Service pipes, frictions in, table, 528.
Services, high and low, 524.
Settling basins, ^50.
Sewage impurities, 134.
dilution of, 153, 155.
Shells of conduits, 434.
Sheet-iron, gauges and weights, 488.
Sheet-piles, 371.
" u under embankment, 339.
Short-tubes, 215, 216.
Showers, source of, 45.
Sleeves, pipe, 479, 482.
Slope, earthwork, 344, 345.
paving exposed to frost, 355.
" puddled, 352.
" embankment, 356.
Slopes, velocities for given, 258.
Sluice areas, 360.
Sluice and pipes, embankment, 355.
" gate areas, 359.
4 temporary stop-gate, 359.
44 tunneled, embankment, 356, 358.
u valves, iron, 360.
Sines of slopes, table, 259.
Siphon, 182, 184.
Site for embankment, reconnoissance for, 346.
Smith's (A. F.) adjustable pipe, 364.
Soils beneath embankments, 337.
" evaporation from, no.
Solutions, organic, 532.
u in water, 112.
Source of showers, 45.
Springs, mineral, 141.
44 under embankments, 337.
u and wells, 102.
" supplying capacity of, no.
" waters, 141.
Stable use of water, 34.
Statistics, census, 31, 32.
rainfall, 46, 52.
Stability of masonry, 395, 397.
u u pumping machinery, 578.
Stand pipes, 526, 564.
Static pressures in pipes, 446.
Storage, additional required, 98.
basins, substratas of, 85.
44 percolation from, 85.
Storage of water, 84.
44 influence upon a continuous
supply, 99.
Storage of water, effect of evaporation on, 93.
44 required, 95.
Storage reservoir, 338.
embankment, 353.
supply to and draught from,
table, 96.
Strata conditions, 146.
Streams, available annual flow, 94.
" estimates of flow, 65, 78.
44 flashy and steady, 71.
gauging, 296.
minimum, mean, and flood flow, 75.
44 ordinary flow cf, 80.
u ratio of monthly flow, 76.
Strengths of wrought pipe metals, 451, 486, 491.
Stop-gates in conduits, 436.
Stop-valve curbs, 515.
Ludlow's, 514.
44 Coffin's, 493.
" Flowers', 493.
Eddy's, 511.
system, 511.
Storms, great rain. 61.
Sub-heads compared, 253.
Sub-mains, diameters of", 507.
Subterranean reservoirs, 105.
waters. 102.
watershed, 109.
waters, temperature of, 126.
uncertainties of search
for, 106.
Substrata of a storage basin, 85.
Supply main, diameter of, 506.
44 to, and draught from a reservoir, table,
96, 97.
Supplying capacity of watersheds, 94.
Surcharged pressure, earth, 414, 416, 423.
Surfaces, pressure of water upon, 391, 393.
Surveys for storage reservoir, 347.
Sources of water supplies, 587.
Symbols, definitions of, 235.
44 combined reservoir and direct, 525.
Systems of water supply, 585, 586.
44 " distribution, 493.
u 4t rainfall, 47,49, 50.
T.
Temperatures, artesian well, 127.
of deep sub-surface waters, 126.
u filter beds, 555.
44 water in pipes, 502.
Templets, for flange bolt-holes, 460.
Tenacities of wrought-pipe metals, 451, 486,
491.
Tests of pipe metals, 472.
Testing of hydrometers, 325.
Theory of flow over a weir, 278. 280.
Thickness of a curved-face wall, 422.
" dams, table, 387.
' 4 pipes, formulas, 466.
' walls for water-pressure, 399.
" " wrought-pipe shells, 447, 486,
488.
Thompson's molecular estimate, 162.
Thrusts of a conduit arch, 437.
Timber weirs, 384.
Transit, use in gauging, 313, 318, 319.
Transmission of pressures, 183.
Traffic, effect upon retaining walls, 425.
Trapezoidal revetments, table, 420.
Treacherous strata beneath embankments, 338.
Trial shafts, at embankment sites, 336.
Tube gauge, 317.
Tubes, short, 213.
Tubercles, in pipes, 247.
Turbine water-wheels. 559, 579.
Turned pipe-joints, 458.
Type curves of rainfall, 55, 57, 59.
618
INDEX.
U.
Uniform effect of natural laws, 61.
Union of high and low services, 524.
Units of heat utilized, 578.
Use of water increasing, 39.
V.
Vacuum ajutage, 214.
imperfect, short tubes, 215.
" rise of water into, 182.
" tendency to in compound tubes, 221.
" under a weir crest, 292.
Values of ^, 271.
" " h and h', table, 264.
44 " pumping engines compared, 583.
44 " water supplies as an investment, 29.
Vanne conduit, 438.
Vapory elements, the, 45.
Valves, air, 523.
blow-off, 513.
Cornish, 569, 570.
check, 525.
" curbs, 515.
44 disk, 571.
44 double beat, 560, 570.
" flap, 568.
44 iron sluice, 360.
piston, 569.
power required to open, 361, 364.
44 stop, 493, 511, 513, 514.
k indicator, 361.
41 " system, 511.
1 waste, 513.
Variable flow through pumps, 559.
,555-
, 128.
Varnishes for iron, 474, 476, 489.
Vegetal growth in filter beds,
Vegetable organic impurities
Velocity, conversion into pressure, 227.
" equation, modification ot, 270.
44 formula for, 249, 250.
Velocities in canals, 371.
44 theoretical table, 190.
of falling bodies, table, 190.
" for given slopes, table, 259.
44 ratios of surface to mean, 315.
relative, due to different depths in
channels, 328.
44 of given films, in channels, 311.
41 surface in channels, 313.
Vermin in canal banks, 371.
Vertical shifting of water, 365.
Virginia City, wrought-iron pipe, 489.
Voids of earths and rocks, 103.
Volume delivered by pipes, table, 495.
of efflux from an orifice, 194, 209.
44 u " formula for, 196.
41 flood inversely as the area of the
basin, 65.
Volumes, formulas for flood, 65.
flood, from watersheds, 381.
44 relative, due to different depths in
channels, 328.
of given rainfalls, 62.
for given depth upon weirs, 290.
from waste weirs, table, 380.
W.
Walls, back batters of, 422.
44 chamber, 369.
counterforted, 427.
curved face, table, 422.
earth pressure against, 408, 410, 412, 413,
415, 416.
elements of failure, 427.
end supports of, 429.
44 front batters of, 424.
Walls, formula of thickness for water pressure,
399-
44 foundations of, 395, 406, 407.
44 leverage resistance of, 402.
44 profiles of, 407.
44 retaining, 390.
44 to retain water, table, 406.
44 to sustain traffic, 425.
" top breadths, 424.
44 wharf, 426.
Waste pipes, embankment, 357.
44 sluice, 356.
44 weir formulas, 379.
44 u volumes, table, 380.
44 " aprons, 383.
44 ballast, 385.
44 weirs, 377.
discharges over, 378.
44 " forms of, 382.
44 " thickness, table, 387.
44 valves, 513.
Water, analyses of potable, 117.
characteristics of, 113, 159,161.
44 crystalline forms of, 165.
41 choice of, 587.
44 clarification of, 530.
44 compressibility and elasticity of, 167.
44 commercial use of, 34.
44 consumption of, 34, 503.
44 the composition of, 112.
44 domestic use, 34.
44 engine, 569.
evaporation from, 88, 89.
44 flow of, 184, 194.
44 force of falling, 388.
44 hose, use of, 34.
44 impregnations, 112, 141.
44 impurities, 112, 141.
44 molecular actions, 168, 169.
44 pressure upon surfaces, 168, 176, 391, 393.
44 pressure leverage of, 397.
44 physiological office of, 25.
effect of the impurities of,'
114.
44 pipes, organisms in, 129, 133.
plant and insect agencies in, 147.
44 pumping of, 557.
44 rarity of clear, 530.
44 ratios of variable flow, 564.
" river, 151.
44 sanitary office of, 26.
44 storage of, 84.
44 spring, 141.
44 solvent powers of, 113.
44 subterranean, 102.
44 sugar test of quality, 159.
44 supplies, gathering and delivering, 586.
44 " incidental advantages of7 29.
44 necessity of, 25.
44 supplied, 31, 35, 36, 37, 38. 40.
supply, permanence of, 585.
44 " systems of, 585, 586.
44 volumes and weights, table, 161, 164,
166.
44 vertical changes in, 365.
44 waste, 34.
44 weight of constituents, 164.
44 " pressure and motion of, 161.
44 well, 139.
44 wheels, 559, 579.
works, construction of, 333.
Watersheds, 71, 100.
supplying capacity of, 94.
Water-ram in pipes, 449.
Wave formula, 388.
Waves, heights of, 388.
Weir apron, 279.
Weir benches, 384.
44 caps, breadths, 386.
INDEX.
619
Weir coefficients, 288, 289, 291.
" crests, 278, 292, 293.
gauging, 77.
overfalls, 377.
Weirs, crest contractions, 280.
" dimensions of, 278, 279.
" discharges over, table, 289, 290.
experiments with large, 284.
" forms of, 277.
" formula for wide-crested, 293
" " depth upon, 28 '
formulas, 282, 283, 284, 286.
gratings in front of, 292.
u hook-guage for, 297.
" initial velocity of approach to, 285, 292.
" measuring, 277, 295.
rule gauge for, 298.
stability of, 279.
tail-water of, 292.
triangular notch, 294, 295.
" tube and scale-gauge for, 208.
" timber, 384.
varying lengths, 279.
" volumes, formulas for, 282, 283, 284,
286, 287, 293.
waste, 337, 383.
wide-crested, 293.
Weight, a line a measure of, 173.
Is, 341.
Weight, a measure of pressure, 173.
and volume of water, table, 166.
leverage of masonry, 398.
" of pond water, 167.
Weights of cast pipes, 465, 468, 4<
" " embankment materia
" " molecules, 168.
Well, intercepting, 546.
" water, 139.
' waters, analyses of, 121.
Wells and springs, 102, no.
" condition of overflowing, 107.
" fouling of old, 140.
" influence upon each other, 107.
" impurities of deep, 125.
locations for, 139.
" watersheds of, 108.
Western rain system, 47.
Wharf cap-log, 426.
" fender and belay piles, 427.
" walls, 426.
Wood pipes, 491.
Woltmann's tachometer, 322.
Wrought-iron pipes, 479.
" pipe-joint, cast, 483.
1 plates, gauges, and weights, 488.
WyckofTs wood-pipe, 491.
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25
26 MILITARY BOOKS PUBLISHED BY
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D. VAN NO STRAND. 27
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D. VAN NO STRAND. 29
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D. VAN NOSTRAND. 31
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D. VAN NOSTEAND. 37
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38 MILITARY BOOKS PUBLISHED BY
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/>, VAN NOSTliANl). 41
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19C6
OCT 10 193|6
22 1937
LD 21-100m-8,'34
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