,M-NRLF c z aba sn GIFT OF AN INVESTIGATION OP THE HYDRAULIC JET PUMP A thesis submitted in partial satisfaction of the requirements for the degree of MASTER OP SCIENCE at the University of California HOWARD HAMILTON BLISS Berkeley, California, April, 1913 ff a Y K Object - Description of Pump *!'*'***' * It was the purpose of the work herein described to study the operation of the hydraulic jet pump in the laboratory of the University of California. The investigation included finding the loss coefficients in each part of the pump, testing various ar- rangements of the parts for efficiency, and studying the rate at which tha parallel jets of water unite to acquire a common velocity. An attempt was made to test experimentally the accuracy of a theore- tical expression for the impact losses, which are very large in this kind of apparatus. Finally, certain relations were analytically de- veloped for the operation of the device, and tests and calculations made to check them practically. This jet pump has two concentric cylindrical cham- bers, the inner one for the high pressure working water and the other for the low pressure water to be lifted. The liquid emerges from these compartments through concentric nozzles, the low pressure water coming through the annular orifice surrounding the other. Because of the difference in head, the jet in the center has a higher velocity, and the operation of the pump depends upon the communication of this to the surrounding water. The streams mingle in the mixing chamber and then enter the diffuser, where the kinetic energy is largely converted into pressure. The pump tested has .a number of mixing chambers of different lengths, any one of which can be set between the nozzles and the diffuser. They are all cylindrical, the diameter at every point being five-eighths inch, which is also the diameter of the ou- ter nozzle and of the throat of the diffuser. o 4 rr Kf\ 4 :" ! o , ' " - So . i* Nomenclature - Efficiency tests In making the tests described below, the low pres- sure water was taken from a storage tank by a centrifugal pump which delivered it to a stand pipe, whence it flowed through piping and valves to the jet pump. The rest came from the tank through a Quimby screw pump and a water meter. The delivery water was usually weighed and sent into the storage tank. For some of the tests, however, it was allowed to issue into the open air and was diverted downward into the weir box on which the jet pump was located. The other apparatus used consisted of two pressure gauges, a mercery manometer, a water manometer, a watch, and a Pitot tube built especially for this pump. It will be necessary in this report to express by formulas the relations of various quantities measured and computed. After trying in vain to make satisfactory use of a system of nomen- clature with numerical subscripts, I have developed a system using the letters B, e, r, j_, m, t_, d, and f as subscripts. A glance at sketch No. 1 vill make clear their use. Thus Q s signifies the cubic feet of suction water per second, v s its velocity, and h g its pressure head (measured in feet of -ater above an absolute vacuum), Subscript _e indicates the high pressure water entering the pump, r signifies the annular nozzle stream, j_ the inner jet, m the mixing chamber, the throat of the diffuser, d the diffuser, and f_ the final condition as the water leaves the apparatus. The letter a indicates area of cross section in square feet, and "| is the loss coefficient. EFFICIENCY TESTS On account of the high speed at which the water passes through the mixing chamber, it was expected that a considerable loss of energy would occur, due to friction there. Hence a variation :jSV ni sr a of testing efficiency in the length of the chamber would change the efficiency, as this loss would increase with increasing length. However, since the entire operation of the pump depends upon the imparting of the kinetic ener- gy of the working water to the surrounding stream, too short a chamber would also destroy the efficiency. These assumptions were abundantly justified by two series of tests with varying lengths. In the first series the working water was always admitted to the pump at 70 Ibs. per D" above atmos- phere and the suction \vater entered at atmospheric pressure. In the second series the pressures were 39.4#/D" and atmospheric. With each mixing chamber twelve or more runs were made with different delivery pressures. For each run the data taken consisted of the delivery pressure, the weight of vater delivered, the cubic feet of high pres- sure water used, and the duration of the run. All pressures were kept constant and verified several times during each test. The gauges were calibrated practically every day and four tests of the water meter at different times showed that its readings were reliable within the limit of errors of observation. The efficiency, n , is computed as foot Ibs. of work done on the water lifted + foot Ibs. of energy lost by the working fluid. Letting t represent the seconds, n = + S 8 fh f Ih R 1 V w V^_ \^o "~ 11^ / (t Of - tQ )pf tt Q np" - "p ) ***re P_ indicates gauge pressures, p g being 0. On curve sheets Nos. 6 to 10 inclusive will be found plotted the results of these tests upon chambers varying in length from to 6 inches. Under otherwise constant conditions the efficiency varies with varying delivery pressure, reaching a maxi- mum when this is about 34 % of the high pressure (by gauge). The !to *i Results of efficiency tests ^ greatest efficiency with zero mixing chamber is 22,7 $>. Each succeeding longer chamber s 1 owg better operation until the length becomes 13/8 inches. For this and those of lengths 2", 2 1/2" and 3" the maxima are almost equal within the limit of probable error at about 31 $>. Beyond three inches the efficiency falls gradually until it reaches 25 % for the six inch chamber. This is shown graphically on curve sheet No. 10 , which is plotted from the previous curves. r Tabulated below will be found the data of these runs. In most cases more runs were made than recorded here, but the more inefficient ones v/ere omitted. It will be noticed that the time is recorded, though not use* in computing efficiency. It was measured necessarily while making the runs - as most of the time I had no assistant and had to read the water meter a definite number of seconds after attending to the weighing - and is inserted here with the idea that it may be useful for later study from this data. The series on the two inch chamber was run last and most carefully, the time being extended more than ordinarily to decrease the effect of errors in reading the meter. Mixing chamber 0" long. IPe =, 39. 4# /D' p e = 70.07f/n P f t Q Q t Q 3 H t p f t Q e t Q s >v t 17.5 7.2 0.8 2.9 131 17.3 9.9 6.1 20.2 126 15.7 6.7 1.3 12.9 120 19.2 9.0 5.4 22.7 116 14.1 6.3 1.7 15.0 111 21.2 7.8 3.4 13.9 100 12.4 5.7 2.3 18.6 99 53.3 6.0 2.0 1617 78 10.8 7.0 4.2 21.8 120 25.4 8.9 2.3 14.7 118 8.9 5.5 4.1 21.8 89 28.3 6.8 1.2 12.0 92 .'> r no yl.l :cs nuwsfr. ai ; . >rf: rfoni xia &: ^otvsaq etf* ffloa? 6e**of,i t.Jt ietrTw , 01. o^ oa eesj0o .te 6TOT- s&xo tfrtoioi on Efficiency testa taoulated Mixing chamber 1" long. = 39.4 #/r = 70. 0# /D' Pf t t n t Pf 19.7 23.4 25.2 27.1 28.9 31.1 t 7. 7. 5. 9. 9. 9, fc 6 6 2 7 3 4.1 8 3.6 2.4 3.6 3.1 1.9 22.6 23.8 24.2 24.7 23.5 16.4 Mixing chamber 13/8 " long 18.8 10.5 2. 3 20.0 190 21.3 7. 4.2 26.2 17.5 6. 1 1. 9 24.9 108 23.3 12. 1 7.2 29.7 15.8 5* c . 4 23; 7 98 35.4 7. 4 3.8 29.2 13.5 7. 9 4. 9 32.4 138 27.5 5. 3 2.7 33.0 11.6 6. 7 4. 5 28.0 112 29.5 11. 5 4.5 28.5 10.0 5. 7 3. 9 23.2 90 31.5 8. 4 2.8 27.3 Mixing chamber 2 " long 9.3 9. 8 7. 8 24.7 174 32.8 18. 3 2.5 12.0 . 9. 7 6. 3 29.1 178 30.4 15. 4.2 21.5 15.0 id). 65 5. 35 30.9 203 27.1 11. 1 4.9 27.9 17,5 13 .9 3. 7 21.3 268 24.9 13. 7 7.1 28.6 19.1 13 .2 1. 4 8.2 318 22.6 11. 9 7.3 29.3 20.1 9. 4 6.6 28.3 17.7 9. 7 6.3 22.0 Mixing chamber 2 1/2 long 8.9 6. 2 5. 23.5 101 32.5 6. 3 1.7 23.4 11.0 5. 4 4. 2 30.0 89 30.6 5. 9 2.1 27.6 13.5 4. 9 3. 1 29.4 81 28.5 6. 7 2.9 29.7 14.6 5. 3 2. 7 30.0 90 2 5.. 5 6. 3 3.3 30.0 15.9 10. 1 4. 3 28.8 174 23.5 7. 1 4.1 29.2 17.5 17. 9 6. 1 27.2 316 21.3 5. 3.0 26,3 Mixing chamber 3" long 18.4 6. 8 1. 2 15.4 119 32.4 6. 3 1.7 23.3 16.8 5. 8 2. 2 23.2 102 30.6 5. 9 2.1 37.6 14,9 5. 3 2. 8 32.8 89 23.7 5. 7 2.3 28.0 13.3 4. 9 3. 1 33.2 79 26.5 6. 3 3.3 31.9 11/7 5. 5 4. 1 31.5 90 24.4 7. 3 3.9 28.6 10.8 4. 7 3. 3 26.5 75 21.6 7. 4 3.8 23.0 J.:ixing chamber 4" long 10.6 4. 8 3. 2 22.7 77 32.3 6. 2 1.8 24.8 12.4 5. 7 3. 9 30.9 93 30.0 5. 7 2.3 30.2 14.1 5. 3 2. 7 28.3 85 27.6 5. 4 2.6 31.4 15.8 5. 7 2, 3 27.2 96 25.4 5. 3 2.7 29.0 17.4 6. 2 1. 8 23.0 106 23.2 6. 6 3.0 22.5 18,4 5. 4 1. 16.2 103 20.5 6. 4 3.2 20.7 95 155 97 73 153 114 273 223 163 197 170 134 134 86 77 88 82 91 64 76 80 75 82 92 92 84 76 72 67 80 80 " . Traverses of mingling Mixing streams chamber 5" long 6 Pe = = 39.4 #/[ p fi = 70.0 #/ d" P f 20.2 6.4 6 t Q a 0.0 0.0 t 105 P f 2176 t Q e 6.3 t Qs 3.3 23.4 t 81 18.3 4.0 0.8 17.3 74 24.2 7.4 3.8 27.1 94 1616 5.9 2.1 25.9 102 26.4 5.5 2.5 27.6 71 14.7 8.5 4.3 30.1 146 28.6 6.9 2.7 29.1 92 12.9 4.9 S.I 30.8 84 30.5 6.0 2.0 25.8 82 10.7 5.8 3.8 24.4 93 31.7 7.7 1.9 20.4 105 Mixing chamber 6" long. / 9.6 6.0 3.5 18.8 107 21.5 5.4 2.6 21.3 72 11.7 5.1 2.9 24.0 93 24.4 5.5 2.5 23.6 76 13.7 S.7 2.3 21.5 99 28.2 5.8 2.2 25.6 82 15.7 5.8 2.2 25.1 107 31.1 6.4 1.6 20.0 90 17.7 7.8 1.7 17.8 142 34.0 7.5 0.5 6.3 104 19.6 7.3 0.7 9.5 140 TRAVERSES OF MINGLING STREAMS In order to study the manner in which the inner and outer jets combine, I made a series of traverses with a pitot tube at different distances from the nozzles. The first was very close, within about 1/32 of an inch of the tips. For the other traverses I attached mixing chambers of lengths varying from one to six inches and tested the spped at the open end. In every case the water spurted into the open air and was defledted downward into the weir box. Pressures behind the nozzles were kept constant at 50#/D" and 9.0 #/D" for all of these tests. The Pitot tube was moved across in steps averaging ,o2" each (less where the speed was varying), and the pressure witlin it read on a gauge at each step. Taking the constant of the tube as .99, a value determined by Professor LeConte, the velocity at any point is .99 V^g h , where h is the head in feet of water corresponding to p , gauge reading. Hence v = .99 ^64.4 x p x 144/62.4 = 12.07J p The velocities are plotted on curve sheets Nos. 1 to 3 inc. aea-rov p t lo lia Results of mingling stream traverses 'It will be seen by reference to the curves that the streams act upon each other to a considerable extent within one inch of the nozzles, the inner part of the annular jet gaining speed lost by the outer part of the other. Friction against the mixing tube is seen to decrease the peripheral speed of the annular stream. With each increase in length these effects become more marked, except that the higher speed is gradually communica- ted clear to the periphery of the outer jet and counteracts the friction on the walls. The rubbing velocity, which commenced at 25 ft. per second, drops to about 21 within the first 1 3/8 " and then rises gradually until it reaches 45 ft. per second at the end of six inches. Probably the deceleration of friction at the begin- ning would be considerably greater but for the fact that the outer jet contracts very much as it leaves the nozzle and so hardly touches the walls for a certain distance from that point. This can not be shown by the Pitot tube because of its imperfect action near the periphery. See also page 10. Meanwhile the effect of the drag of the outer wa- ter is propagated toward the center of the driving stream. The ra- pid portion of this grows more and more slender to two inches from the nozzles. Here the center continues to keep the velocity with which it left its nozzle, 86 ft. per second. From this point onward the slower water decelerates it until the central speed becomes 65 ft. per second at six inches. There is an irregularity to be noticed in all the later curves - that the speed is greater above the axis than at cor- responding points below it. Possibly this is due to some small ob- struction lodfred in the lower nart of the annular riozzla after one 30 xiiiti't: ; I beeqa arrlai^ ts; .0*3 ,-. ;- r; 3 ifj tB saeioeb ot nses aqf .* aesit rrerlt n r*^ f* f^ ! e;i J \cf swarfs ecf io:i o 608 .Ysarf.-V.J:-*:; tfstriw Loss coefficients begun - Inner nozzle or two of the traverses had "been made. I did not notice it at the time and after the curves were drawn did not have an opportunity of making any of the runs again. LOSSES IN PARTS OF JET PUMP A considerable part of the work consisted in testing the inner and outer nozzles, mixing chambers, and diffuser to find their loss coefficients. In general this coefficient, , is defined by: v^/feg = lost head(in feet of water) in the part considered. It is assumed that ^ is a constant for any piece of apparatus under varying conditions of velocity. I found in all cases that experi- oz r ferine f mental results for each part, when plotted against v gave no sig- nificant trend either way, which shows that the exponent 2 in the expression J v^/2g is correct within the limits of my work. I supposed that there was no contraction of the inner jet and made a series of the ordinary tests to determine its coefficient, using' various pressures behind the nozzle. The water issuing at each pressure was weighed for a measured time . The diameter of the nozzle is 3/8", giving an area = .000768 sq. ft. The velocity, v^ , is computed as Q/a. he t Lbs. CuPt CuPt (L v 1 vjf 1 + i J Wt. Meter J Bg 185.7 180 1400 22.4 22.5 .0711 92.6 133.1 1.395 .395 161.5 242 1400 22.4 22.6 .0662 86.2 115.2 1.403 .403 90.7 317 1400 22.4 22.6 .0506 65.9 67.5 1.345 .345 35.0 459 1500 24.0 24.1 .0314 40.9 26.0 1.345 .345 The impossible magnitude of the thus obtained proves that the jet must contract. I made two other tests using the Pitot tube to determine the velocity of the water in every part of the stream, measuring the Pitot pressure once with a mercury ffl ianoo tfrow &&t Jo JTJ e 9iJ* rtl ( / et -i, lo 9 cat ( T^s tsriJ' sseso IIj5 rf'r on ovs v t8niB3B I>e nl S tneriO'-fxs ecltf- Jjsrf . ^i TO s * cjn.t lo oj- ata erf J ! i>rr.s t(; te-t- , ^i'te tr rfose Jr. ^.rii/aa o^t erft l-.t i v , t ' Inner nozzle - Analysis for nozzle coefficient column and the other time with a pressure gauge. As shown on page 6 the velocity v = 12.07 ^ . Similarly v = .99 J2gx 13.6 h m A2 = 84.55f 1 , where h indicates the inches of me-rcury - of course 9 corrected for water column. In the appended fi- gure let v be the component of the x or h. T Y$ velocity of the stream parallel to the axis of the nozzle at a point distant R feet from it. Let dR re- present the thickness of a differential hollow cylinder of water of radius R and length v. The weight of the water = 2-rrR dR v y* , where y* is the number of pounds per cubic foot. The integral of this from R = to R = the outer radius of the jet would be the weight of water leaving the nozzle in one second. The kinetic energy of the differential cylinder = . weight v 2 /3g = ~ T Mf R dR v 5 . The total energy of the water lea- O " ving the nozzle in one second is the integral of this from center to circumference. If we measure the variable radius in inches ( =r), the expression becomes j| Now let x = r2; thgn dx = r-dr-2. Substituting: Ft. Lbs. per second of jet = TT The integral can be evaluated by plotting v 5 against x (= r 2 ). The curves will be found on curve sheet No. 4 and a tabu- lation of most of the data and computation is on page 10. \ ca i* . 6 * - ; ia For the first of the runs the mercury column was used. Pressure p Q = 23.0 #/D" } Q Q = .0399; Q 8 Aj = 52.0 ft. per sec. For velocity head, a Q = .0104 Oft. (l 1/4 " pipe at pressure gauge). Hence v e = 3.84 and velocity head = .23 ft. Pressure head = 53.1 ft. " ** C r R ^JL ,, - leJ'WW -iO'-l ijy;?' erf* o -^afifio-iiaoo e.". f ^ 90* v t&i OTW^ ' T " 8 t : i j" tO l S 1 1 CO j r3 '. test "io -istBW lo Tefcai\'o. v?o r lorf trfiev? rfT .-/ rf^nel .tool oMi/c 7q ebmroii lo T&C ow *&!; orfJ 1 lo etfbjsi teforo rft H o^ H MO-I .Ixiooes Gfto nt s^^ib srU lo \sTnd oiJeniat iiT Jel rlt &i i>flooe efft | x i alsad t j* SV Ji .8-ifc- . ( vx 01^.3 eti* lo t o.ss - 10 Pitot tube traverses of inner nozzle The energy behind the nozzle, then, = .0599 62.4 53.3 = 132.6 foot Ibs. per second. For the second run'. h_ = 91. 4j Q_ = .0523; V Q = V V? C- 5.03 and velocity head = .39; energy behind nozzle = 300.0 ft. Ibs /sec. First run Second run r x or r 2 * V v^ r x or ? v v^ r 2 *P .190 .0361 15. B 33.5 37 , 500 .190 .0361 21.6 56.0 176,000 .185 .0342 33.5 48.9 117,000 .185 .0342 34.9 71.2 361,000 .180 .0324 43.9 56.0 176,000 .180 .0324 38.2 74.5 415,000 .170 .0289 47.0 57.9 194,000 .170 .0289 38.5 75.0 420,000 .150 .0225 47.2 58.0 196,000 .160 .0256 39.5 75.9 435,000 .120 .0144 47.4 58.2 197,000 .120 .0144 39.5 75.9 435,000 .070 .0049 47.6 58.3 198,000 .020 .0004 39.5 75.9 435,000 .020 .0004 47.2 58.0 196,000 .080 .0064 39.5 75.9 435,000 .030 .0009 47.1 58.0 195,000 .180 .0324 39.1 75.5 430,000 .060 .0056 46.8 57.8 192,000 .185 .0342 35.4 71.7 370,000 .080 .0064 46.8 57.8 192 , 000 .190 .0361 24.4 59.5 211,000 .130 .0169 46.9 57.9 194,000 .160 .0256 46.5 57.6 191,000 .180 .0324 46.1 57.4 190,000 Second run: area = 151.4 .185 .0342 45.1 56.7 182,000 D cm = 15,140 units; average .190 .0361 24.9 42.1 75,000 ordinate = mean v^ = 430,000 First run: area = 67.28 D cm = 6,728 units; average ordinate = mean v 3 = 191,100. Inserttng the area of the curves in the expression for kinetic energy on page 9 gives 142.3 and 320.0 ft. Ibs per sec respectively, values in excess of the total energy behind the nozzle. This is, of course, absurd. The trouble is due to the fact that the jet really contracts but the Pitot tube erroneously indicates a con- siderable velocity up to and beyond the point where its center is op- posite the edge of the nozzle (r = 3A6 " = .1875) as shown in the tables above. This is because the water received when the tube is partly in the air makes a pressure within the apparatus. To avoid the difficulty I have taken v. = the J .A ~- A .* J ' a- 1 * t* * * I 0.00?; = alsson L J 10 X T a . is o . - O.V 0. 0?I. 0. 031, 00 7 noiaaeiqxa erfd" rri a e.ft tad* rs - OX t I9I = v dl : = QJ ao qo Bt cr>; Y 7 ir> oi ov e,i.' erft eft . _ Contracted jet from inner nozzle cube root of the average ordinate of the curve, considering it the "effective velocity" in analogy to the use of the word effective in electrical calculations. This value is subject to some error in that the curve area, taken for the full radius of the nozzle, is wider ':>. '? . Tfce C3i '.-?. :t tta fcouMfe?1s of the outet or. : .1 s a;- than it should be, and the diminishing velocity near the periphery is too large. The result is that the area of the curve is considerably too large, accounting for the tobsurd result on page 10, but the ab- It wa.8 n. jv.lt to Ust^rr^l n-o uniform speed across the jet as is usually given with nozzles it is unnecessary to take the trouble to find the effective velocity. The values of v^ as found were 57.6 and 75.5 feet J per second respectively for the two runs, giving 51.5 and 38.5 feet as the velocity heads. Dividing into 53.3 and 91.8 ( the total - pres- sure and velocity - heads behind the nozzle) , gives 1.035 and 1.037 as 1 + ^ in each case. Another run, not recorded above and not worked throu& with the v^/r2 plot, gave ^ = .045. Giving greater weight to the first two, I take the average value of J j = .037 ^ ' Let a . = the contracted area of the jet, defined "by QJ Aj . The ratio a o j / a j = ^j * the coefficient of contraction, where a^ ^ B the nozz i e area . with this nozzle the three runs give .000693, .000693, and .000692 = a O i . Hence CX^= 693/768 = .90S. el tvtcug ff* lo -cfs edf *wo' t OI e^ecj no ^ e - t-.i j at - elf?' 1 - . G.I Friction and contraction coefficients, outer nozzle To determine the coefficients of the annular nozzle I made one traverse with the Pitot tube, measuring quantity and pres- spres as before, except that instead of weighing the water I sent it into a measuring tank. The v-^/r 2 curve will be found on curve sheet No. 5 . The positions of the boundaries of the outer nozzle are shown there, and it may be seen that the stream is very much contrac- v ?,o -vTJ vJrical " l v ~- r * n '/ definite length A- ted and converges into the space supposed to be occupied by the cen- tral jet. It was difficult to determine the width to use in getting the area and mean ordinate, but by several applications of the cut \a ittp:U' change the value of j r thus derived to .018 or .035 , the result is not very reliable. It is unimportant, however, for as will be shown later (page 18 ) the loss in this nozzle is almost zero compared with ;,..;> >^ci to tha emois of th* d if fax the other losses in the jet pump. .. j 4 T- ? f i - ft, a *> * Htf> ' i > * . - ^ . . . \> G - * i Q a in this test was .04461. Baking v r =43.2 we find a or = .04461/43.2 = .001033 Dft. The nozzle area, a r , = .00136; hence CX r = 1033 A3SO = ,76 . This is much more accurate than the value, for it does not depend at all upon the pressure measurement. Of course, a or indicates the area of the contracted stream leaving :- u ;.<*b!3< of > t* o* the annular nozzle = Q s /v r . erit/o no bauclt cf XI r* Isson iPtifo erftf lo s ; L t V1-. V FiX I.'.. Sr 1 . \cf Jbeiqjjfooo ecf o^ i)ea at e*f ot ifj-fjiv.- eift e fi o ijevrreeeiq Jon is ed" II . & 8X0. j'r.eVewoil t . a . I Lcdt&tf. l* of Jtoo.1 en'T s fen^ 8Vii/r I fc e.T;l) .730.1 lo -* I 0, -j. = Method of getting mixing chamber coefficient Since a number of mixing chambers of different lengths are used with this jet pump, a more convenient form for the friction coefficient is X instead of . The symbol is defined by: lost head (in feet of water) = Xl/d v 2 /2g , where 1/d is the ra- tio of the length considered to the diameter - of course ajbplying only to cylindrical bore. For any definite length = Xl/d. For a uniform flow of water between the points 1 and, 3 of a cylindrical ?h ave lat^n'; results, tha ralu^fs fc ;o,- \ tube, the speed of the water being constant throughout the area ex- cept as impeded at the periphery by skin friction, h 1 + v 2 /feg = h g + v2/feg + Xl/d v 2 /feg ; hence Xl/d = (h x - h s ) + v 2 /2g . The method of testing was to connect several of the mixing chambers in series between the nozzles and dlffuser and send \vater through from both orifices at once under equal pressures. To escape the complications at the contracted jet and to allow the water to achieve a uniform speed across the cross section, the measurements were always made at least six or eight inches from the nozzle plane. j 1 Water and mercury manometers were used to measure the drop in head across all possible different combinations of mixing chambers, and the water was weighed and the time measured for each run. One side of the manometer was always connected to the throat of the diffuser and the other side connected to the ends of the different chambers, a small brass tube being inserted in orifices in ithe flanges which communicated with the interior. Because the aperture in the throat was located about 3/8 " from the end of the last chamber it was ne- cessary to add this length (which is that of the cylindrical portion of the diffuser) to the length of mixing tube measured, a^ =.OOS13G '. Following is a table of a few of the tefcts: io ISTO;! Jneinevnoc. etoi &ftj-leJb ei locfsrta erfT . erf* ,i>\lX erf? lo Itnee i>jb TOBirll rb : :^ eelsson OT . 86- ti/t.810[ tre.ti-w feiU 7?oXljs ot Lrr>5 t&t i'&^o drr&raeiuaBr. ^;atlYs o* lo wo II to i.eeq *>? babeqrui BJS J \,< -f ,^S ni eiedafiao rt 20 lo liiO'i i* erfj o* i.'f'W 88">.alB r "l rT* e 'i J" i - ^ . Mixing chamber and diffuser coefficients 14 Water Lbs. 1100 t sees. 700 1500 483 1500 366 Length (hj-ho ) Al/d X inches Ft. Water 8.75 .708 .326 .0233 17.25 1.383 .637 .0231 2.75 1.033 .122 .0277 4.75 1.475 .174 .0230 2.75 1.575 .107 .0243 4.75 2.520 .171 .0225 8,75 4.100 .278 .0199 17.35 7.830 .535 .0193 Omitting tests with very short lengths (under two inches), which gave inconsistent results, the values found for \ are shown in the following table. The table on the right gives values of ^ for all the different mixing chambers, computed from the mean X = .0243 by per inch length = X + 5/8 = .0389. .--".. ' < >- -v .*. . fi4t~ "* ' ' iL "" * "" tw< ' ' * "* ' i7 . : L . a v* v IM Length velocities Mean inches used X 3.75 23 - 31 .0260 4 36 13 - 20 - 26 .0234 I!75 12 - 23 - 31 .0236 6.25 13-20 .0262 8.75 12 - 31 - 35 .0240 17.25 12 - 31 - 35 .0226 Final Average .0343 Mixing Chamber 1 in. 13/8 2 2 1/2 3 4 5 6 ^ depended upon the speed Cylindrical length .5 in. 1.5 1.875 2.5 3.0 3.5 4.5 5.5 6.6 ,020 ,058 073 097 ,117 136 175 ,214 253 In order to find whether of the water I plotted all the values against v, and found the curve, r .-*- >* * ' f though exceedingly irregular, roughly parallel to the axis cf v. To find the coefficient of the diffuser, water was run through it at measured rates and the difference in pressure be- tween the two ends read on a mercury column. The water came through both nozzles at the same pressure and several mixing chambers were inserted to give it time to get over the effects of contraction and impact. The loss in head is refferred to the higher velocity, v t , and = b d v|/2g = v|/3g - v|/3g - (h f - h t ). Following is a table , . f..L sol bnwcl ;i i.! rfrrrfi?:' t (8rfo*tl . 'x f-rlj" I IB to 1 ^ lo Toq[ Si 30. ielco >.:!& ,v s r ^ w sr, it r V J . V ti * Analysis of friction in mixing chamber showing the values obtained in eight different runs: v t 13.0 30.3 21.8 26.0 39.7 30.7 30.7 33.7 3 d ..138 .120 .135 .113 .111 .110 .110 .116 The average of all these values is l d = .119 or .12 Two other runs under similar conditions gave answers so widely dif- feront as to show error in measurement or irregular action and their results were thrown out. ANALYSIS OF FRICTION IN MIXING CHAMBER It is customary to express the head lost due to friction in the mixing chamber as v/feg * m , where v t is the aver- age value of the speed of the water at the throat of the diffuser, ''i , t ir. the tn.t.viri^, that of Qf /a t . This is considerably in excess of the true loss of head, for the rubbing velocity is variable through the tube, never becoming so great as v^ and approaching it only near the end. It is theoreti- cally v r at the plane of the nozzles, assuming no contraction. Hence a ,nearer approach to exactness would be to substitute for v^ in the expression above an average velocity = (v r -fv^)/2 . This gives head lost = ~ ffi - (v r + v t )^/feg . It should be noted in this connection that any measurement of ]> such as recorded on pages 13 and 14 must be made with constant rubbing velocity. The term 'rubbing velocity' as used here refers not to the actual speed of the water particles in contact with the wall of the tube, but to the velocity of the ma- jor part of the water near it - a value corresponding to the velocity obtained in the tests mentioned by dividing Q by a^ . Following is the derivation of an expression for the loss of head here, which is perhaps more accurate, at least theo- retically, than those mentioned above. No account is taken of the 11. >? i pressure it would have had if there were no friction. Hence the ener- gy at that point is less than the no-friction value by the quantity: Qf ^ ' im/ 6 & * ( v r + v r v t + v t ) which is the loss of energy per second through the tube. To compare the result thus obtained with the other formulas mentioned previously, I have computed the loss in each of the three ways in each of five runs made with the six inch mixing chamber. The data and computation follow: Run Q f v r v t Qf v^/2g Q f (v r +vt) 2 /8g Last Way 1 .111 35.0 52.1 73.8 51.5 52.3 2 .1052 31.2 49.4 63.6 41.9 42.6 .0976 25.9 45.8 50.2 30.7 31.6 4 .0889 17.2 42.2 39.2 19.2 20.4 5 .0769 4.6 36.1 24.5 7.8 9.3 It is seen that the losses "last way" and using the average velocity are in close agreement and much lower than the value obtained in the usual wav. i)r- '"' >-'.. If , erf* jfo*srf5 t ib srfj to ^A ( T v~^v).,vS + If) v r i erf* ei ecfut erf* ni *sol iu;erf X*oi eiiT b\/< TO l I iiftB =1 aeew^e'd eeol eonts ^xecfiajsrio j/iixiai e/ftf ni *eoX i lo btxJo'oT t^oarft erft BerfojyeT Te .noiJoiTl ei n'cJt cf */toiaB ed lo saol too ore *o aefri/qmco ev&rf I t x-t8irorv9i(i LenofJr.-j . twoXXol .e o. . A v IT Professor Hesse's expression for impact loss IMPACT LOSSES All the friction losses in the jet pump are not enough to account for its low efficiency. (She additional loss is considered to be due to impact and eddying in the mixing chamber, and in the analysis as developed by Professor Hesse it has been expressed by the same formula as that used for the loss due to sudden enlargement in pipe section. Both the suction water and that entering through the central nozzle are considered to suffer loss of energy in this way, making the total diminution of energy = Q e )f (v.j- v t ) s /2g+ Q s v>(v t - v r ) 2 /3g , as for sudden enlargement. In order to test the reliability of this expres- sion and at the same time secure as thorough a check as possible on all the work described in this thesis, I have computed the entire losses for the series of five runs made with the six inch chamber with 70#/D " pressure on the inner nozzle. The data will be found on page 6. Below are the work and results . It will be seen that the sum of the computed losses of friction, impact ancl eddying is almost exactly equal to the difference between output and input. Velocity heads are allowed for for both the delivery water and that entering the central nozzle, and the work has been checked over to insure accuracy in the mathematics. See the following page for the tabulation: ion et qpu/qr Jet atitt at eessol r si asol l&ttotttbbs etfU .Yoneioi^l wol a grtijcisj orf* ni arrJh(fc~ ^^ *r-x:;pai I1A so! tni/oooje o* owi: ecf o^ hsi neeof ajsrf tt eeaeK ToseeloTl ot 8wL aeol erft 10^ Jboejj tjarf eisol telli/a oj LeTetiferioo sus e = Yg-rsn-e "Jo fro f f urrimirl) XBJ-OJ .^newbr.tjtslrte nebluya 10! a^ t -eaiqaBB BlrfJ lo \'i'lIid'ireT &rf* erfj bfe^qproc eVBxI I t siaerfit rforti xie erf* ri^lw >Brn uri 6vi JB^ eifT .f!5aori isnn JI ;&^ lo ni moe ^ ^ 6; - I ecf* riajj:.'X.'tt anlTce^ne * W eirfu ni Y^ene to t .I rf* ni tecfixoeel* XTOV/ 8:?^ Il no lo aeJ:tj:s ert* tol eeesol aTi^ae wolea 8 e&sq no I>i/i oo erf- lo aa/8 cwlt J-, .d'uqnJ; ttfue Juqtfiro nov.-j-&cf eonete'ilii eriJ ot I^urpe ^Itojsxe J8o r :il*5 al jBrf* Lns -ss-tflw x"it*vilb erf t fftocf tol io"i i.ewoX3 et etfie.i \ f txcoIeT t eli ' ' 'j '- erld TO! r. -.->. 'j'ol sa'j Input, output, Run Time tQ and losses A 3 O computed. Energy balance. tQ 8 Qs Q s /*or sees. ^ v i)" V |/2g (v r ) 1 73 5.4 .0750 108. 3 31.4 2.6 .0361 35.0 3 76 5.5+ .0730 105. s 39.0 3.5- .0322 31.2 3 82 5.8 .0707 102. 26.3 2.2 .0263 25.9 4 90 6.4 .0711 102. 6 36.8 1.6 .0178 17.2 5 104 7.5 .0722 104. 1 28.0 0.5 .0048 4.6 Rttn tQ f & Q f Q f /a t I Q v S d v3 + v r v t+v 2 %fA( (v t ) V \fe 8 1 8. .1110 52.1 35. 5, 763 2 8. .1052 49.4 29. 3 4, 954 i 3 8. .0976 45.8 23. 8 3, 956 j 4 8. .0889 42.2 18. 4 2, 803 < 5 8. .0769 36.1 11. 7 1, 483 1.3 .9 .5 .2 .003 53.3 42.4 31.6 20.4 9.3 Run 1 3 3 4 5 228 213 217 252 334 Run 1 3 3 4 5 Output 10.2 21.5 50.1 112.3 113.3 10.3 24.4 56.8 114.1 105.5 10.3 38.2 65.4 109,5 96.9 10.8 31.1 72.1 80.1 90.3 4.6 34.0 78.7 23.6 83,6 Input - Output Sum computed losses 413 358 366 525 317 309 320 329 353 378 Input 526 480 427 400 377 * l V, 5.X Q.33 0. - e. s. 3. , 0* * ' ^*? 0. *.8 JT . ^01 3 ,^ Y -^^P i^ ( t v ) O ' * v x.sd Jin. o.s - 8.1 8. 0. i 8.9 **I r - & v " ' d ( ) S> K { jtt S8B80I ie*x|BSoo au;3 .tuq^rjO - Juqnl nafl 865 SIJ^ I as* eos S5 c 19 Conclusion CONCLUSION The results of the investigation have been: With constant applied pressure from thirty-nine to seventy pounds per square inch above atmosphere, the efficiency of this jet pump reaches a maximum when the delivery pressure is about thirty-four par-cent of that applied, the suction pressure being atmospheric . Comparing mixing chambers shows that under these conditions the greatest efficiency - about thirty-two per-cent, is secured by using the three inch chamber. However, any length from one and three-eights inches to four gives almost as good operation. All lengths outside of these show much lower efficiency. The Pitot tube traverses show that, with fifty and nine pounds respectively behind the inner and outer nozzles the jets mingle in a distance of six inches so that the highest velocity in the center is less than three- halves that of the slowest water. Up to this point the outer jet is continually accelerated and the inner one re- tarded. The loss coefficients of the parts of the pump are: Inner nozzle, .037; outer nozzle, .03; mixing chamber, .0389 per inch length; diffuser .12. The coefficient of contraction of the in- ner nozzle =.902 and of the outer nozzle .76 The expression derived by integration for the fric- tion loss in the mixing chamber has been checked numerically on a reasonable approximation. Professor Hesse's expression for the less due to impact has been tested by substituting values from five efficiency runs and shown to a^ree very closely with the loss not accounted for by friction. Incidentally a rough check was secured on all the meed evari nc . tebrus rJ-JSrftf aworfs eiecte-aAC! ^ao-iaq ovt-^^itAt tucds - \"0fl . l>oos BJB teoailB eev .V '. '''v'f ': eelsson retix) LHB if- ^^- c -t^v *88rf2.irf e.i* i'jB.'i* cU .le^c'w tra-v:ol& 9 ild" lo ;o e^isq erf* lo a*nioj:j , T . t lJoBTc.tnoo lo tneioitleoo 9V. elsaon j ; l TO! floJ^ : ' noo eeerf* l-etwoea ai >ajs erto II A , "i i. : rti eac- . : . ;K 1 E ~ - H t _> M E E H.i, N M N 33 . n c i - i ' < z NON-CIRCULATING BOOK U.C. BERKELEY LIBRARIES 245594 UNIVERSITY OF CALIFORNIA LIBRARY \