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T P o fl C b ti Sl o SI o T SI T \M d ai b ri rt IT This Item is filmed at the reductio i ratio checked below/ Ce document est filmd au taux de reduction indiqud ci-dessous. 10X 14X 18X 22X 26X 30X J 12X 16X 20X 24X 28X 32X The copy filmed here Itas been reproduced thanks to the generosity of: McLennan Library McGIII University Montreal L'exemplaire fllmA fut reproduit grftce A la g^nirositi de: McLennan Library McGill University Montreal The images appearing here are the best quality possible considering the condition and legibility of the original copy and in keeping with the filming contract specifications. Lee images suivantes ont iti reproduites avec le plus grand soin, compte tenu de la condition at de la nettet* de l'exemplaire filmi, et en conformivA avec las conditions du contrat de filmage. 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Un dee symboles suivants apparaitra sur la derniire image de cheque microfiche, selon le cas: le symbols —»> signifie "A SUIVRE ". le symbols y signifie "FIN". Maps, plates, charts, etc., may be filmed at different reduction ratios. Those too large to be entirely included in ore exposure are filmed beginning in the upper left hand corner, left tc right and top to bottom, as many framee as required. The following diagrams illustrate the method: Lea cartes, planches, tableaux, etc.. peuvent dtre filmte A dee taux de rMuction diffirents. Lorsque le document est trop grand pour Atre reproduit en un seul clichA, il est filmA d partir da Tangle supArieur gauche, de gauche A droite. et do haut en bas. en prenant ie nombre d'images nicessaire. Lee diagrammes suivants illustrent la mithode. 1 2 3 1 2 3 4 5 6 A PAPER ON THE LATEEAL PEESSURE OF EUMING WATER, R&AD BEFORE Ck ♦ !♦ mxxwk m%mi\\m FOR THE ADV iNCEMENT OF SCIENCE, At the Meeting of that body in Montreal in the year 1857, BT THOS. GUERIN, Civil Engineer. k Montreal : PRINTED BY J. STARKE & OO. 1858. \ a T U n Let a horizontal pipe A B be fitted to a reservoir wh,oh.skept full of water, let X be a cock who^S equals the section of the pipe, let C N, D 0, B p"^ tubes inserted in the pipe, and let us sum,e fo^ » moment that the« is no contmction at A, bT^Ie wlr running through the pipe. ^ "***" When the cock is closed, the wbnlo«f*i.„ • ■, faceof the pipe will e.,.rL^ :l^..^lZXZ must nse m the tubes to the same level as the « but when X IS opened, the water rushing out afl^ h a velocity due to the head A M will Lmedial a^^ qmre the direction A B, and by its impulse wU rut along the p.pe without being turned into Lj otCdi^ tion, the water in the tubes coming m contoctet^' moment with that in the pipe will !e borrat " ^ level in the tubes mnst soon fall and be redu^;! to nothing hence while the section at A and B 1 the same^he horizontal pipe can experience no Tjitl 8 If the cock be only partiiilly opened, the phenomcici must chancre ; the water will pass through the orifice with a velocity due to the hcoiX A M, but the head due to the velocity at C or D must be less, for the reason that the sections there are greater ; let V be the velocity at or D, and 7, will bo the head employed to produce it, {g denoting the force of gravity or 32.18 ft.) and whereas it still acts in the direction A B, it can pro- duce no lateral pressure. The quantity S is less than A M, it is that portion of A M which produces the velocity V along the pipe A B, but as the water in the pipe ex- periences the force of the whole head A M the re- maining portion A U=^V, would appear to be the head indicating the pressure on the pipe, and undw these circumstances, if there had been no friction, the water rise in the tubes to that height, or if we take M E equal to !g, A E will represent the height to which the fluid will rise in the tubes. Now it is well known that friction in pipes destroys a great portion of the head, and it is also well known, that this friction is directly proportional to the length, that is, it increases from nothing at A to its greatest limit at B ; let us call F the friction at B and make v'' a" equal to F and join E a", the friction at C & D will then be represented by v a kv' a', hence we conclude that the column C N which measures the pressure when in a state of rest, will, when motion begins, first fall the quantity N v 9 (-■«)and secondly V a; this last part of the head being deEtroyed by the friction of the pipe from 4 to The pressure at C will then>fo« be represented by aC and will bo equal to A M-^-friction at 0. This last teiTO otjnction ai C, will be equfl to .00071 \f wher« L IS the length, Q the discharge, and D the diameter of the pipe, but m the present instance, these quantities are to be estimated at C. If the pipe instead of being horizontal is inclined our course of reasoning will be similar to the fore- going-when the orifice is closed, the water will rise in the tubes to the same level as in the reservoir, but when motion begins the level in the tubes will undergo the same d,n.,u„tion3 as in the case of horizontal pipes, and their summit will only attain the line E a * If the pipe is bent and not a shuightline, the ex- pressm for pressure must be the same, recollecting that Lw the real length along Ae sinuosities of the pipe, lience we conclude in general terms, that if H represent the height of the reservoir above any point of a pipe whether curved or straight, that the pressure on ais point will be H--_.00071 \f where V denotes the velocity at that point, and .00071 \fis the height representing the loss frem friction at the sa^e po£ then as H-.00071 \f is the efficient head, we havj the pressure a,lways equal to the efficient head (not the ordinary head) minus the height due to the velocity Having treated of the lateral pressure of water in \l 10 pipes, I come now to the pressure of water running in a bed, the subject which this paper principally aims at. I will suppose A B C D to be a section of ^he bed of a River, the depth of water there being H B, and I will suppose that at the depth x n, (=ll n') an opening is made ; it is required from thence to deter- ■ mine the quantity of water that will flow out at n, through the small canal n S into the basin Z. The velocity of the River being given. Suppose* that the motion of the water in the bed of the stream is aiTested for a moment, then it is evident that the flow through n would be that due to the head X w, but as soon as motion commences this phenomena no longer holds, a portion of the head on n, will be destroyed by so much as causes the velocity in the bed ; let us denote this by H m, that is, let the head H m be that which is due to the velocity in the bed or I? where V denotes the velocity, and g the force of gravity (32.18 ft.), then it is evident th? fc x n will be dimin- ished by H m. Now besides the force which H m exerts, there is another force acting in the direction of n moment. In all steams, however LJ! 7 a uniWty of motion, k^rTZL^r^^ZZ^ t.on. even m canals of the sm^thest and m st „^£: bottoms, where one would suppose the friction woulZ exceedingly small, hence it follows, that the forZsS mvariably destroyed in all streams by somellltt sistance, such as friction, &c. "^^ Now if V denote the velocity in the bed of the stream . would be the head, which would be sufficirntl' generate thjs velocity if there had been no such thL^ •t fncnon but as ./ S also assists in its generatiln aMough be„,s destroyed by friction, we ha^ S^' :*city V^ ;:;'" ■--■-P'oy-l togenen^te : velocity V. 1 lus force is employed in the direction nf ished by this quantity, in order to determine the head which forces the water through this of^ning The S on the opomng will therefore be H n-7-y "enead 12 ■ From this it follows, that at least the portion of H % Which IS equal to g + gr S will be employed in the direc- tion of the current, it will cause no pressure on the banks, aad It will therefore denote the point below the surface of a stream at which the lateral pressure commences. To apply this theorem to the St. Lawrence at Mon- acal, the reader will perceive that owing to St. Helen's Island and Isle Ronde, which are opposite to this city, the bed of the River is divided into two parts, by far the greater portion flows between the Islands referred to and the city, and is called the current St. Mary, a name which I will adopt in this paper. The length of the current St. Maiy is about 5,000 feet, Its width is about 3000 feet, its Hydraulic depth in Summer is 35 feet (estimated), and the difference of level in Summer between the head and foot of the current St. Mary or rather between those portions of the River St Lawrence, above and below those Islands referred to, is 2i feet. From these data we can easily ascertain the ^lue of the expression V, + g S, it will be 2.36 feet Hence we conclude, that a stream or sewer can be dis- charged m Summer into the current St. Mary, at a depth of 2 feet 4 inches, below the surface of the River with- out meeting any impediment. In Winter the St. Lawrence rises so high as to cause a hydraulic mean depth in the cmTent St Mary of about 52 feet ; there will be a difl-erence of level between the head and foot of the current in Winter generally of 8 feet. 13 ^*- This is the LihZrVi + « «'= "-10 of this depth that the ,:i;'l^' '^^ t«-ination an opening «« ^^, in fte h T''/°"""^°'=''«- ^ l-rtion of this depth no Z^'o^:;}^' f «'- ."^^ any tf a stream or sewer diseharS in "!'"«'' "'' ""^ Mary at any portion of this IZl . ', '"^'«"' S'- no impediment from the water of Lp'''"'''' '"^*^'* Having thus far deveW i^ ^?''- pressure of running water Iw. u P'"""" "^ ^^f^ral oluding this paperf tTat V ^ ^ '"«Sest, befoi^ con- iead than g's i'd sdyTf *** ^™^ l-e said by theory at pwlt • f'""' ''" ^'^^ "an destroyed for the reason haH *'' "*'^'' ^ » is ^^ velocity of the ste^m ''^^ ;^. "^ "f"""- « greater portion than g S we n,,^/ T "^"''^^^ * Must be diminished by a JIT ''°°''"'^'' ^'''Hn and consequently theiirarXT7 J'^" '' + ^ « nre commences must be still f.f ? * '*'*'^' P^^s- of the stream than J + g g ^'*"'^«'- ^^°^ t^e surface --/Set:tiLtt:rt\"-«'^^-e- Paper has not at pST * '^' '"'''' »f this but it is to be hoz^riVt '^Tf ^""-""Pli^ting give the subject aftought °' '^'^ '°^^ -'" ^'^t THOMAS GITERIN. OJ IE be 8: thi no sta its bac ha^ the alei rive sew the aboi Mar Ti wate appei at th in ti COROLLARY. r -to a„J other pit ontt ritef'^' ""'•''*/'«''' *- 8 feet higher i„ the winteTa^dTtstoeut""^" ""'"" the shore being retarded hi ft I ^ ^'^•''"*°* ^ nothin,. ; h.„ce^he water it"^ tt "''' '' "'™" 3tandator„earthele?of th If"" T' ^°"''» A co,,r.« r 1. .^^ ^^ t^e water m the river A sewer discharging into the current St IVl" Its foot, will have th- advnnfon. T! ^- ^^^^' ^^ar backpressure ofLtSlJ^'^^f''^^ '^'^ have already shewn and II^ . '«'' ™*^''' *» I the harbour't wnUe "L ^jT^"^/'* ^ «-er at alent f„ the difference of t™i f f "'' ^''''"^^ ^1°'^- river in the harTu^^^d t ,'^^0 T T' °^ *« sewer, which difference 1 t „ "'^'"^ "^ t^"* the current, will ZlTfTl " °''I ^'^ '°°' ^^ about 17 feet of ad aZrin£or !?!*'" ^'" "^^ Mary in this case ** """«»' St. waSiatrss;^™r- ?'^^*^-^^- appearfrom the fact twT. f f ""''^JagaBay.&c., will « the sewer .iK^afhitr:! ^.'^^^^^^ -*«' 16 Now if we suppose that the water of the river at the locality of the proposed sewer at the current St. Mary is two feet higher than at Hochelaga Bay, &c., it would appear from what I have already shewn that the level of the water in a sewer at the current St. Mary will stand almost nine feet lower than in a sewer at Hochelaga Bay, &c. Hence there will be about nine feet in favor of the current St. Mary, when it is high water in the St. Lawrence, this being the stage of the river for which these calculations have been made, because at any other stage there can be no difficulty or impediment to the discharge of a sewer in any locality. Other important advantages which can be urged in favor of the current St. Mary when compared to Hoch- elaga Bay, are the increased length and increased de^jth of excavation which the latter locality requires. From levels which I had occasion to take in that vi- cinity some time ago, it appears that there is a regular ascending grade from the Victoria Road onwards to Hochelaga. This will appear evident, even to a casual observer, from the fact that the stream which crosses the Victoria Road near the Queen's Square comes from the direction of Hochelaga, so that there can be no doubt of the increased depth of excavation in that direc- tion. Hence, I conclude that a main sewer from the City, entering the river near the foot of the current, will be much more efficient and much less expensive than one entering Hochelaga Bay, or any point below it.