ENGINEERING RESEARCH INSTITUTE THE UNIVERSITY OF MICHIGAN ANN ARBOR Final Report A MODEL STUDY OF CITY OF DETROIT BOOSTER PUMPING STATION V. L. Streeter F. M. Henderson Project 2564 CITY OF DETROIT DEPARTMENT OF WATER SUPPLY DETROIT, MICHIGAN April 1957

The University of Michigan ~ Engineering Research Institute TABLE OF CONTENTS Page SUMMARY ii OBJECTIVE iv 1 0 THE MODEL 1 1 1 MODEL CONSTRUCTION! 102 MODEL MEASUREMENTS 2 1.3 MODEL THEORY: APPLICABILITY OF MODEL RESULTS 2~0 MODEL PERFORMANCE AND DESIGN MODIFICATION 7 2.1 HEAD LOSSES 7 202 PUMP INTAKES 13 2.3 BEHAVIOR OF DESIGN AT PARTIAL FLOW 19 APPENDIX I 22 ii

The University of Michigan ~ Engineering Research Institute SUMMARY This report describes the setting up and operation of a model of the City of Detroit's raw water booster pumping station. As a result of this model study, it is recommended: 1) That a system of 8-21-in.-radius turning vanes be installed at the downturn where the vertical line to the suction pit joins the main 14-ft line. 2) That a twin system of 9-21-in.-radius turning vanes be installed at the junction of the vertical line and the suction pit. 3) That two baffles in the form of 24-in. square grids, 5 ft long, be installed in the suction pit upstream of Pumps Nos. 3 and 4. 4) That a false floor, 4 ft above the existing floor, be installed in the pit under the intakes of Nos. 1 and 2, and that vertical turning vanes be installed between Pumps Nos. 1 and 3, and between Nos. 2 and 4. 5) That a vertical partition wall, 8 to 12 ino thick, and 5 ft wide, be installed at the end of each limb of the suction pit, as shown in Fig. 3. 6) That a system of six radial equally spaced vanes be placed in each pump intake, Although the intake itself forms part of the pump structure and is strictly speaking beyond the scope of this study, the vane system mentioned was tested for the sake of completeness: it improved the intake flow so materially that mention is made of it here as an addendum to the main results of the study. The proposals above are shown in detail in Fig. 3. The proposed alterations would improve the performance of the station in two ways: (1) by reducing the head loss through the station from 3.38 times the velocity head in the main line to 1.40 times this velocity head; (2) by substantially improving the flow conditions at the pump intakes, although some irregularities still remain. The primary purpose of the model study was the reduction of the head loss; however, the fact of the model's availability for testing prompted a further study aimed at improving pump intake conditions, with the results noted above iii

The University of Michigan * Engineering Research Institute OBJECTIVE The objective of this study was to reduce the head loss through the pumping station and to improve the intake conditions of the pumps. iv

The University of Michigan ~ Engineering Research Institute 1.0 THE MODEL This section contains a description of the model-construction, material, etco., and of the detailed measurements that were taken on each run. There is also a discussion of the theoretical considerations affecting model operation, and of the reliability of predictions made about prototype performance. It is hoped that this discussion will serve not only as an assessment of the merits of this particular model, but as a guide in the consideration of making model studies of other schemes in the future. lo 1 MODEL CONSTRUCTION The modelwssmade to a l:21 scale from Lucite, a clear plastic. The walls of the pipes and pit were 1/4 in. thick, and flanges for connections were either 1/4 in. or 1 in. thick. Flanges were fixed to the body of the model with plastic cement, and bolted together. In some cases tightening of the bolts led to cracking of the cement, but the cracks were easily repaired and in general it was found that the flanges could be bolted firmly with a screw driver and an 8-in. wrench without putting excessive strain on the cemented joints. The main 14-ft-diameter pipe was represented by an extruded 8-in. plastic pipe, available ready made. Other pipe sections were fabricated from 1/4-in. sheet, two half cylinders, or half-cones, being placed together and cemented along the longitudinal joints. These joints gave a little trouble with leakage, but were easily repaired with plastic cement. The flanged joints were sealed with thin rubber gaskets and, at first jointing compound. When the model was first tried out with water as the working fluid, these joints, particularly those on the suction pit, gave a great deal of trouble, and it was necessary to place bolts at 3-in. centers to make the joints tight. The strength of Lucite is not very high and although the pipe sections had a high enough thickness/diameter ratio to make them hold pressure satisfactorily, the suction pit, being of a rectangular 11 in. by 9 in. section, was rather weak structurally. In fact, one wall of the pit developed a bad crack when the model was first filled with water under a head of about 8 ft 13ecause of this fact and of the difficulties in sealing the joints, it was decided to run the model with air as the working fluid. Pressures inthis case would be well below bursting pressure, and the joints could be easily made good with masking tape on the outside of the flange. The model was therefore con1

The University of Michigan * Engineering Research Institute nected to a centrifugal blower capable of delivering 4000 cfm of air and the full series of tests was run in this way. The reliability of tests performed with air instead of water is discussed in Section 1.3. The decision to use air instead of water greatly simplified the running of the tests, and serious consideration should be given to using air in any future tests, particularly where: a) there are any large box-type sections which are inherently weak structurally. b) it is likely that many alterations will have to be made to the interior of the model, necessitating the continual breaking and remaking of joints. When air is used, no jointing compound is necessary and it is a clean, simple job to make and remake the joints. Figure 1 is a general arrangement drawing of the model showing some of the leading dimensions, and the location of the pressure tappings. A detail of a typical tapping is also shown. there were 41 in all, connected through a manifold to a water manometer grIaduated at intervals of.01 in. Als shown are the location of the sections, on the discharge lines of Pumps Nos. 2 and 4, where pitot tube traverses were made to measure the discharge in these lines. The total discharge through the system was also measured by a pitot tube traverse in the 12-in, supply line; so that it was possible to compare the discharges in lines 2 and 4, and also to compare their sum with the total discharge. Plates 1 and 2 are photographs of the model as set up with its air supply. The elbow in the 8-in, supply line is a sharper bend than the corresponding bend in the prototype, but tests showed that straightening vanes down stream of the elbow did not improve the flow characteristics, so it was assumed that the elbow did not materially affect the flow through the model. The sheet-metal diffuser downstream of the model reduced the outlet velocity substantially. This made the model less of a nuisance in the laboratory, and reduced the mean pressures in the model to values which could conveniently be measured with manometers having a high sensitivity but a small pressure rangeo Thus, the range of pressures in the model was about 5 inches of water; the presence of the diffuser meant that the pressures varied, not from 0 to + 5 in., but from -3 in. to + 2 in., making possible the use of a 0-3 in. inclined tube manometer with a sensitivity greater than that of a 0-5 in. manometer. 1.2 MODEL MEASUREMENTS The pitot tube traverse in the 12-in. supply line was made with a standard differential pitot tube giving velocity head directly in inches of

The University of Michigan ~ Engineering Research Institute water. In the pump supply lines, which were around 5-6 in. in diameter at the measuring sections, a standard tube would have been rather large compared with the pipe area, so it was decided to use a total-head tube consisting of a 1/4-in. diameter copper tube with a sealed end and a small hole in the wall of the tube very close to the end. This tube was laid along a diameter of the pipe, enabling a traverse across the diameter to be made. There was little interference with the flow, and velocity readings very close to the wall could be made. Static pressure was obtained by linear interpolation between the readings obtained from the manometer tappings, e.g., in line No. 2, interpolation was made between the pressure at No. 22 and the mean of the pressures at No. 23 and No. 240 At all measuring sections traverses were made across two perpendicular diameters, at points which divided the pipe into equal areas. Hence the mean velocity head was simply the arithmetic mean of all the pitot-tube readings. Inclined tube watermanometers were used for all readings, as follows: Pitot tube traverse, 12-ino supply lineo range 0-1 in. graduations.01 in. Pitot tube traverse, pump lines: range 0-3 in. graduations o01 in Static pressure readings: range 0.-3 ino graduations.01 in These gave sufficient accuracyo Flow conditions in the pit were investigated by means of a set of woolen tufts, I in, long, attached to light rods mounted across the pit, in the right-hand limb of the pit, looking downstream. They are shown in Fig. 1, and in Plates 3, 4, and 5, and indicate clearly the presence of any irregularities in the flow. Conditions in the pump intakes were explored with another rod with a tuft attached to its end. This rod could be inserted through a hole in the side of each of pump intakes Nos, 1 and 3, and the end moved round to cover most of the cross sectiono Another method of examining the flow was to feed confetti through the system. Although the inertia of the confetti made it a poor flow indicator at abrupt changes in direction, it gave a satisfactory, if shortlived, picture of such features as stationary vorvices, 1.3 MOIDEL THEORY: APPLICABILTY OF MODEL RESULTS In a closed conduit system such as the pumping station considered herel the general nature of the flow depends on the form of the solid boundaries, and a parameter called the Reynolds number, defined thus. NR = vL (L) where v is a characteristic velocity of the system (in this case, the mean velocity in the main line) L is a characteristic length (the diameter of the 5

The University of Michigan * Engineering Research Institute main line) and v is the kinematic viscosity of the flowing fluid. NR is a dimensionless number, hence its value will be independent of the particular system of units chosen. The term "general nature of the flow" is more specific than it appears to be. It includes, for instance, such numerical coefficients as the head-loss coefficient; the ratio of the head-loss coefficient in any part of the system to the velocity head. We haveo V2 head loss, hL = CL 2g (2) where CL is the loss coefficient. The remarks above imply that for a piping system of given shape, CL is a function of NR alone and is not influenced by any other characteristic of the flow or the fluid. The Reynolds number also determines the more general qualities of the flow, such as the turbulence. For a specified Reynolds number the size, shape, and location of the eddies will be fixed, as will be the ratio of eddy velocity to mean forward velocity. It follows that to make sure that events in the model faithfully reflect those in the prototype, it is necessary only to make the model NR equal to the prototype NRB,hether or not the same fluid is used in model and prototype. When this requirement is met, a state of "dynamical similarity" is said to exist between model and prototype. The practical difficulty in realizing this condition is that model velocities would have to be much higher than prototype velocities. The way out of the difficulty lies in examining more closely the nature of the Reynolds number. It is essentially an inverse measure of the effect of viscosity on the flow-at very high values of NR the mechanism of turbulence and of energy dissipation is determined largely by the inertia of the fluid, with comparatively little restraint from viscosity. This is particularly true when pipe lengths are short and there are many abrupt changes in direction. On the other hand, viscolus effects tend to become important in long, straight, smooth reaches of pipe where wall shear influences the flow strongly, and the wall shear is itself dependent on viscosity. On the other hands if the pipe is rough, inertia effects tend to become more important. The points made above are exemplified in the standard f-NR curves for circular pipe (e.g., in Vennard Elementary Fluid Mechanics Fig. 86, p. 195); "f"' is the Darcy coefficient, a loss coefficient similar to CL as defined above. It is seen that for rough pipe the curves flatten out at high values of NRi~e., inertia effects have taken over and the flow pattern remains substantially fixed, independent of NR. This argument suggests that dynamical similarity can be achieved simply by making the model NR high enough, even if it does not approach the 4

The University of Michigan * Engineering Research Institute prototype NR. Checking this question numerically, we have in the prototype: Main line velocity 10 ft/sec diameter 14 ft v(water) 1.2 x 10-5 ft2/sec Hence (NR)p 1 x 10-5 1 17x 107 (3) 1.2 x 1x0' ( In the model: max. possible velocity 200 ft/sec diameter 2/3 ft v(air) 1.58 x l0-4 Hence max. (R)m = 200x8 /- 8.45 x o105 (4) (NORm 1. 58 x 107-4 This value is about one-fourteenth of the prototype NR, but is high enough to make it likely that model and prototype flow will be similar. Using as a guide the f-NR curves referred to above, it will be found that for a rough pipe the curve has flattened out well before NR reaches the value of Equation (4)~ To clear up the question, a series of runs was made at different velocities and Reynolds' numbers and the loss coefficients in various parts of the model were measured, and plotted against NR (Fig. 2). The highest value of NR at which a curve flattened out was around 355 x 105, corresponding to a velocity in the main line of 83 ft/sec, so it was decided to use a velocity of about 110 ft/sec in all tests, giving an NR of 4.65 x 105. The above considerations, and the evidence of Fig. 2, make it possible to be quite confident that model events faithfully reflect prototype events even though a different fluid is being used. However, it must still be realized that the model time scale is very different from the prototype time scale, simply because the velocity and length scales are different. If the suffix "r" indicates the ratio of prototype quantity to corresponding model quantity, we can write T = (5) and this statement is generally true, whether or not the model and prototype are dynamically similaro Since Lr = 21, and vr = 1/10, then Tr,_ o 200 (6)

The University of Michigan * Engineering Research Institute This means that events in the prototype will take 200 times as long to happen as corresponding events in the model, e.g., if a fluid particle takes 1/10 second to get through the model station, then a fluid particle in the prototype will take 20 seconds, or 200 times as long, to get through the station. Similarly the oscillations induced by eddies will be 200 times slowe in the prototype than in the model. This point will be discussed further in Section 2.2. The only question remaining is whether the compressibility of the air might not produce effects in the model which will not occur in the prototype. The effects of compressibility depend on the Mach number M, the ratio of flow velocity to sonic velocity, and make proportional changes that depend on the square of the Mach number. For instance, the relationship between stagnation pressure ps and static pressure po is, for incompressible flow. 1 2 Ps = Po + pv (7) and for compressible flow: ps o= po+1 pvo2 (1+ M2 + (8) 2 4 In our case M = 110/1100 = 1/10, so that compressibility effects will make changes in the flow parameters of the order of one-quarter of one percent. These changes are negligibly small. 6

The University of Michigan * Engineering Research Institute 2.0 MODEL PERFORMANCE AND DESIGN MODIFICATION This question is discussed under three headings. The first is that of head loss in flow through the station, and the second the flow conditions in the suction pit and pump intakes insofar as they seem likely to affect pump performance. Discussion of both topics is concerned mainly with full flow through the station (all pumps running); a third section is added in which partial flow is considered both from the viewpoint of head loss and that of pump performance. 2.1 HEAD LOSSES As implied in Section 1.3, a general measure of head loss is provided by the loss coefficient CL, defined in Equation (2), and if the model NR is high enough (as it is in this case) the CL in any region of the model should be the same as the CL in the corresponding region of the prototype. The losses in various parts of the system will be considered in the following discussion. The coefficient CL will be defined in two ways. The "nominal" CL is the head loss divided by the velocity head in the main 14-ft line. The "true" CL is the head loss divided by the velocity head at the particular section concerned. The significance of each coefficient will be discussed below. The Original Design The original design was given a test run, and pressure measured at the points indicated in Fig. 1. Measurementsonpump lines were made on Pumps Nos. 2 and 4 only. Nominal and true values of CL are tabulated below. The following system is used to define the terms used. Velocities:- Subscript "o" - velocity in main line "p" - velocity at entry to pit from vertical line. "t" - velocity at throat of pump intake. "e" - velocity at elbow, in pump discharge line. "d" - velocity at downstream end, horizontal pump discharge line, The nominal CL's indicate whether the losses in individual parts are a significant fraction of the losses through the station as a whole, and the true CLs are in sufficiently general form to be compared with text book values; if they are sufficiently far above standard values, then there is some hope of 7

The University of Michigan ~ Engineering Research Institute TABLE I SUMMARY OF LOSS COEFFICIENTS, ORIGINAL DESIGN Locality Nominal CL Basis for True CL True CL Downturn from main 1.81 vo2/2g 1.81 Vertical into pit 0.71 (vo - v )2/2g 8.25 Pit entry 0.40 vp2/P2g 0.80 No. 2 No. 4 No. 2 No. 4 Pit to pump intake -0.19 0 vt2/2g -0. 083 0 Vertical pump line 0.26 0.06 (vt - ve)2/2g 0.893 0.318 Elbow, pump line 0.27 0.24 Ve2/2g 0.287 0.400 Horizontal pump line 0.13 0.07 (ve - vd)2/2g 0.553 O. 625 Manifold entry 0 0. 106 (Vd - Vo)2/2g 0 0.239 Total 3.38 reducing them by the installation of turning vanes, etco The immediate conclusion from the above results is that over 80% of the loss occurs in the flow from the main into the pit. Losses in the flow from the pit back to the main, although high in terms of the true CL, are not a significant part of the total head loss. Study of these parts was therefore mainly deferred until work was done on the flow conditions at the pump intakes (Section 3.2). The various parts of the station are now considered one by one. Downturn from Main The installation of vanes in a right angle bend should normally reduce the loss coefficient to around 0.2 - 0.3, so vanes would seem to be the obvious remedy. But because of the possibility that these vanes would interfere with the straight-through gravity flow when the station was not pumping, alternative remedies were tried, e.g., the installation of vertical splitters and baffles to reduce the vorticity, and the moving of the main butterfly valve upstream so that when closed it formed a flat surface lying across the junction of the main line and the vertical line. None of these proposed remedies made any appreciable improvement, so they will not be described in detail in this report. Finally it was decided to try vanes, and to reexamine the question of what interference they would cause in the gravity flow and whether the consequent increase in pumping costs might not be offset by the savings made by the vanes when the station was pumping. To this end tests were made with various vane installations, the decrease in pumped-flow CL and the increase in gravity-flow CL were measured, and a complete economic analysis made based 8

The University of Michigan * Engineering Research Institute on the present annual operating cycle. The result of this analysis is summarized in Tables II and ITIo Table II shows the detailed breakdown of costsboth the savings during that part of the year when pumping is necessary, and the extra costs during the part of the year when only gravity flow is needed. Duringr gravity flow the water is flowing through the main line as well as through the pumping station, which is on a bypass off the main lineo Hence increased resistance to flow through the station is not serious, and the extra costs referred to above are smallo Thus for all vane arrangements there is a substantial net saving which is a maximum for arrangement "L"-.- 8/21-in. radius vanes on a line at 45~ to the pipe center lines. Detailed calculations leading to Tables II and III are given in Appendix I. For arrangement "L," the loss coefficient at the downturn is 0,49. However, when further modifications were made in the vertical line, pit entry, etc., it was found that the downturn CL was further reduced from 0.49 to 0.32. Since this approaches the lowest value that can be hoped for in a vane installation at a right-angle elbow, arrangement "L" is taken as the final design recommendation. The last line in Table III gives the corresponding figures in money, and the series is described as series LI. The net saving is approximately $5700 poa. This reduction in pumping flow CL, from 0.49 to 0.32, is brought about by features down in the pit structure, below the main line. These features cannot, of course, affect the gravity flows hence the CL for gravity flow remains at 2.95, unaffected by the further change in pumping-flow CL. Vertical Line to Pit, and Pit Entry Table I shows that these two sections have, in the original design, a total nominal CL of loll The true CL for the vertical line is extremely high, and the true CL for the pit entry approximates to the figure for discharge of a pipe into a reservoir. This suggests that guide vanes might substantially lower the CL in both cases. Various kinds of straightening guide vanes were tried in the vertical line, without any success, but there was an improvement when diffusing vanes were installed at the pit entry, and a hump was placed in the floor of the pit directly under the vertical lineo A sketch of the system is shown En Fig. 4, described as "Old vanes at pit entry." This system reduced the total CL for the whole system to around 1.. 5, with slight variations from this figure depending on particular installations in the pit. A further system of vanes, described as "New vanes at pit entry" in Fig. 4, was also tried and gave a further slight decrease in CL. This system is incorporated in the final recommended design not only because of head loss considerations, but also because it gave slightly better flow conditions in the pit and at the pump i;ntakes The installations described gave a total nominal CL from the station entry to the pit of about 0.81; the remaining 0.6 (approximately) occurred in the pit, pump lines, and exit manifold. 9

TABLE II -I E i-ONOMtC STJDY OF VABE I1NS3TALLATION AT DOWNTURN Sample Calculation - Series F Length of 2 Reduction in CL Hlead Money, Period Period Avgo Flow Luring Period vo (same for partial Saved Saveda (days),% of maax, mgd cfs 2g as for full flow) (ft) $ per year 1 13605 91 891 15378 1245 3 38 - 2 58 0, 8 1,00 oo00 2 13605 76055 75) 1160 0.882- 0.8 0.705 772 Pumping 3 36.j 67 2 658 1018 0 68 0.8 0 544 523 4 360. 62,2 610 943 0.584 0o8 0o467 416 5 3605 60.25 590 91i2 0.54 0o8 0,436 376 Total 3387 Head Money _. Increase in Ko Lost Lost 6 36. 5 58 85 576 891 1 553 - 1 39 = 0.163 0 130 109 7 36 5 57.9 56 7 7 0.163 0.125 104 Gravity 8 36. 5 564 552 855 0 163 0119 96 9 36.5 53135 522 808 0o.163 0o.1065 81 10 36. 5 47.9 469 725 0o163 0.0857 59 Total 449 Net Saving $2940 p.a. F'

TABE III E:'ONOM!0-l STTJi)DY OF VAIME ITNTALIATION AT DOWNTURN Summary of Results r P med Flow Gravity Flow I Description r DCecrease ~JIncrease i -ncrease Ke LoJ Netg r Series nt*aving ~ Kr K I Increase Loss Sa-ving DescriptiCn eea~T ai rnJL from in K, Originai pKv I in=Ko per yr $ per yr o Original Design 3 38 0 0 0.54 0 0 4 75 1 39 0 0 0 D 5 5 45~ 3~38 0 0 0.88 0o 34 0.22 4.97 1o429 0.039 108 -108 E 5 10-1/2w" 45~ 2.83 0.5, 2326 1.55 1o01 0o653 5.40 1.486 0~096 264 2060 m F 5 16" 450 2.58 0~80 3387 2.22 1.68 1.087 5,84 1.553 o.163 449 2940 G 5 21" 45~ 2.52 0.86 3640 2.95 2,41 1.56 6.31 1.614 0.224 617 3020 M 8 16" 45~ 2034 l.o4 4400 2.54 2.00 1.294 6.o4 1,580 0.190 523 3880 L 8 219' 45~ 2.06 1.32 5590 2.95 2.41 1.56 6 31 1,614 0.224 617 4970 m N 9 16" 45~ 2.25 1. 13 4780 270 216 140 1.590 0.200 4230 | K 5 o101/2" 6o0~ 2.82 0.56 2370 1.47 0.93 0.602 5.35 1.483 0O093 256 2110 0 J 5 16"' 60O 2.6'7 0.71 3010 2.26 1 72 1 112 5 86 1 553 0 163 449 2560 L1 8 21" 45~ 1.88 1.49 6310 2.95 2.41 1.56.631 1.614 0,224 617 5700' n vanes,;s radiumsi r

The University of Michigan ~ Engineering Research Institute Pit, hPump Lines, and Exit Manifold In discussing these parts of the system it is impossible to isolate the head-loss question for separate consideration, as most of the modifications made were aimed not at reducing head loss but at improving flow conditions through the pumpsO The turning vanes described above had reduced the overall nominal CT to about 1.5, and in testing modifications to the pit and pump lines it was decided simply to keep track of variations in this overall CL to insure that improvements in pump-line flow conditions were not purchased at the expense of overall head losso No detailed consideration was given to the distribution of losses to the various parts, because, as exemplified above in the case of the downturn vanes, the CL for one part may vary depending on what changes are made in other parts of the system. However, there is some point in breaking down the head-loss figure for the final recommended design and checking whether the head loss in any one section is excessive. This is done in Table DV which is in similar form to Table I. TABLE -TV SUMMARY OF LOSS COEFFICIENTS, FINAL DESIGN Locality Nominal CL Basis for True CL True'L Downturn from main 0o32 Vo2/2g 0.32 VerticaL into pit 0,08 (vo Vp)2/2g 0.93 Pit entry 0o41 vp2/pg 0.82 No. 2 Noo 4 No. 2 No. 4 Pit to puimp intake -0,04 0 vt2a/~g -0.02 0 Vertical piznp line 0.28 0.20 (vt ~ Ve)2/2g 0.96 1,06 El'bow r p' p 0i25e 0 28 o 25 e/2g Oo 302 0 413 Ror-izo.r:ta p',M-p line 0.07 Oo.O (ve vd )_/g 0301 0.104 Maarnifolid entry 0 O.13 (vd vo)2/2g 0 0o.9 Total 1.40 It will be seen from Table _7V that most of the saving effected by the pit-entry vanes is in the vertical line rather than the pit entry itself. Some of this effect may be more apparent than real due to local variations in pressure, but in ary case a substantial saving has been made. Flaow into the pump intake again takes place with negligible loss; the apparent negative value is probably due to some impact pressure effect at the pump in.take. The true loss coefficients in the pump discharge lines are all rather higher than they should be, bat these losses form such a small part of the total loss that it would not be worth trying to reduce them furthers In any case, the fittings that will form part of the pump installation may materially alter the situation. 12

The University of Michigan ~ Engineering Research Institute Flow into the manifold takes place with negligible loss; some runs were made with a vertical splitter installed in the main line at the outlet but the losses at full flow were not reduced thereby, and at partial flow the splitter produced severe interference which substantially increased the losses. It remains to make a final assessment of the savings made by the model study~ The overall loss coefficient has been reduced from 3.38 to 1.40; in the prototype, where the velocity head is l15 ft, this represents a saving of 3.0 ft head. It has already been pointed out that the reduction in the downturn losses yields a net saving of $5700 p.ao Savings elsewhere in the system are not reduced by any extra resistance to gravity flow, so the position can'be summed up thus: Annual Ar i'ual Net Original inal Reduction aving Loss Anal _C-L CL in CL (Pump Flow) (Gravity) Saving Downturn 1.81 032 1l49 $6310 $617 $5700 Remainder of system lo57 lo08 0o49 $2070 $2070 Total 3-38 1.40 1 98 $7800 Hence the net annual saving in pumping costs is $7800, representing a capital value of $125,000. 2o2 PJiMP -Z\IAKES This part of the project was aimed at improving the flow conditions in the pit and into the pump intakes to insure the best possible operating conditions for the pumps. The main difficulty lay in setting up standards defining good and poor flow conditions, and devising means of measurement by which those standards could be applied to a particulfar installation. The obvious approach in the first instance is to examine the flow visually by introducing some kind of indicator, such as smoke or confetti, into the flow; this was tried at the beginning, and later a system of woolen tufts, mounted on rods, was placed in the pit. Further significant indices are the flow distribution between different pumps, and the flow distribution within each pump line. The first step is to examine the flow in the model, from the viewpoint of the asbove remarks o Flow Distribution zn the original design, and with practically all other designs tested, the flow divided almost equal y between the two sides of the station, ioe~, Piumps Nos~ 2 and 4 between them shared 30% of the flowo However, the flow in No. 2 was about 27% greater than the flow in No= 4, and the flow distribution 13

The University of Michigan * Engineering Research Institute within the horizontal delivery line of Pump No. 2 was very uneven, the ratio of maximum/minimum velocity being about 2.3. The distribution in No. 4 was much more even, the maximum/minimum velocity ratio being about 1.6. Some of the modifications made in the downturn and pit entry altered the ratio Q2/Q4 substantially, but the vane system finally adopted yielded a value of 1.25, very little different from the original figure. Modifications in the pit, aimed at improving flow conditions, brought about some variation in this discharge ratio, but as can be seen from the results in Table V, it kept mainly within the range of 1.20-1o30. Although no complete analysis was made of the point, it was concluded from the evidence and from the current knowledge of flow in manifolds that the system is such as to favor flow in Line No. 2 at the expense of Line No. 4o However, this does not mean that there will be the same difference in flow between Noo 2 and No. 4 when the pumps are running in the prototype, because each pump works against a total head of which the head loss through the pump line is only a small part. If we assume that the pumps will equalize the flow we can estimate the difference in the pump heads in this way: Noo 2 No. 4 If the flow divides in the ratio, 1.25 1.00 then the loss in each line (Table IV) is: 0o60 (vo2/2g) 0o,60 (vo2/2g) o If the flow now divides in the ratio 1.125 1.125 then the loss in each line becomes Co060(1l125 2 vo2 60 252 1.25 2g.0o 2g JioQe O g) 07486 () 76 (v2/2g) or, in terms of prototype heads~ 0,73 ft 1o14 ft o But each pump must produce a net head rise across its line of approximately 50 ft 50 ft nhence p'nmp heads are 5073 51o 14 a difference of 0o8%. This should produce a difference of only one or two percent in the pump discharges. Since the pump discharges Q2 and Q4 are unequal in the model but about eqg-ual in the prototype, the character of the flow in the pit, where it divides between the two pump intakes, will be rather different in the model and the prototype. Tests indicated, however, that the difference was not significantg it was found that gradual closure of the delivery valve in Line No. 2, to reduce Q2/Q4 to unity and below, did not aiter the form or intensity of the turbulence in the pit and the pump intakes. The value of Q2/Q4 was recorded as a significant parameter in each te,, inotbecause it wzas hoped to obtain Q2 = Q4, but because it was still thought desirable to keep Q2/Q4 as low as reasonably possible, even though it was in most cases somewhat greater than unityo The ratio of maximum/minimum velocity within each pump line was 14

The University of Michigan ~ Engineering Research Institute definitely thought to be a significant parameter, which should be as close as possible to unity for satisfactory intake conditionso It is thought to be a definite merit in the final recommended design that in Line No. 2 this ratio is as low as 1.4 (in many cases it was as high as 3 or 4) and in Line No. 4 it is only 1.21. In the pitot-tube traverses of these lines, the velocity readings nearest the wall (1/32 of a pipe diameter from the wall) were not considered in picking the minimum velocity as the velocities so close to the wall would be expected to be low in any case. Turbulence and Vorticity in the Pit In the original design a very strong vortex formed under the intake of each of Pumps Nos. 1 and 2, with its axis approximately coincident with the pump center lineo Much of the remedial work was aimed at cutting and breaking up this vortex in the pit where velocities are still low, rather than relying on straightening vanes in the pump intake bell mouth, where velocities are high. This vortex could originate either locally or further upstream, being carried down with the flow to the end of the pit. While much vorticity could originate in. secondary flows in the downturn and the pit entry, such secondary flows should be broken up considerably by the vane installations placed at these points. However, with the vanes installed the vortices at the end of the pit appeared as distinctly as ever, although with somewhat less intensity. It seems more profitable, therefore, to explore these possible causes of the vorti.city e 1) The pit is curved in plan and there will be separation from the inner wall, concentrating the flow on the outer side, When this flow hits the curved end of the pit it naturally tends to sweep round in a circle before going into the intake. The observed sense of rotation of the vortex confirms this view. 2) The pump intakes are in series and there will be marked retardation (and separation) of the flow just downstream of the upstream intakes (3 and 4). This will make the flow more unstable and more susceptible to the development of vorticeso 3) The inherent instability in flow to a small intake from a large mass of fluido this would apply even if the intake were inserted into a lake of still water. All attempted remedies, therefore, were designed to overcome the problems set by (1) and (2) above. The best direct way of observing the vorticity was by means of confetti introduced into the air supply. This gave a clear, although short lived, picture of any vortices. A steadier, though less direct, means of obo 15

The University of Michigan * Engineering Research Institute servation was provided by the woolen tufts described in Section 1.2, The single woolen tuft placed in each pump intake gave a clear picture of a further development~ the existence of a limited zone of sometimes very strong turbulence, evidenced by a strong high-frequency flutter of the tuft. Reducing the size of this zone and the intensity of the flutter became an object of concern, and in the final recommended design the zone in each pump intake is small, and the intensity not very strong-the tuft23 max.imum displacement from the vertica was no more than 15~o Some light was thrown on the origin of this small region of turbulence when its frequency was measured with a Strobotac. The speed given by the Strobotac in rpm was found to be very close to the speed in rpm of the fan supplying the model. This was found to be true at several different speedso If the fan is responsible, then it might be thoughnt that this turbulence would be removed by sucking air, rather than blowing it, through the model. This is rather doubtful~ there is no reason why disturbances should not be propagated upstream from the fan as well as downstream. Even if this oscillation is a property of the design and not of the model supply blower, the time scale effect mentioned in Section 1.3 will greatly reduce the period of the corresponding prototype oscillation. Maximum model frequency is 30 cps so that the prototype frequency will be around 1/6 cps. This will be much less significant in the operation of the pumps than is indicated by the high frequency in the model. Design Modifications in the Pit This section contains a brief summary of the rmodifications tried, their significance, and concludes by describing the recommended design. All modifications tried are sketched in Fig. 4, and all of them were placed in each arm of the pit i.eo, any remarks made about Pumps Nos, 2 and 4 apply also to uamps Nos. i and 3. Results of all tests are summarized in Table V. End'iast.. L is recomended'y some manufacturers for this kind of pump intake. Tt was successful in cutting the large vortex under No. 2 intake,' dreaking It into two vor-.es more or less in the vertical plane, but gave rise to a very uneven flow distribution within Line Noo 2 (see Modo No. 5, Table V)O However, this feature was succesesfully used with other modifications such as baffles, etco Baffles.-These were the most generally successful modificationo The'idea was to CuEt down large-scale vorticity and turbulence ins the pit, even at the expense of some energy losso Since the pit velocity head is only, at most, one-fourteenth of the maTn-line velocity head, this energy loss is small anyway. The baffles could not actively remedy the flow separation from the inner wall of the pit, but coul;d at least hold the flow in position without further separation. Three forms of baffles were used and are shown in Fig. 4. It was 16

The University of Michigan * Engineering Research Institute found that the type described as "paper" gave slightly better results than the other two, and the type of prototype baffle recommended (24-ino square openings, 6 ft long) is a compromise between the "pipe" and "ttpaper" types. In general the model has shown that with this design baffling is essential; no other modification is so successful in keeping separation, turbulence, and vorticity under control. Reducing clearance under bell mouths. -A standard recommendation in the design of propellor pump intakes is to bring the bell mouth down until it is separated from the floor by one-half the bell mouth diameter. This was tried (Mods. Y and Y!, Table V) but without success. The effect was to starve Pump No. 2, even when both the intakes were lowered, to increase the overall CL by about 0.7 ($50,000 in capitalized pumping costs) and to produce very uneven flow distribution within the pump lines. Further, the vortex under No. 2 was as strong as ever. When a false floor was brought up under the intake of No. 2, the CL was still on the high side and the flow distribution was still uneven (Modso W and W1, Table V)o Accelerating flow at end of pio.-Attempts were made to reduce the vortex under No. 2 by constricting and accelerating the flow as it approaches the end of the pit. The first attempt consisted of the false wall sketched in Fig. 4 (Modso Q-u, Table V)o All these arrangements performed quite well except that the flow distribution within Noo 2 was poor but for Modo 50 This latter was worth serious consideration but is not quite as good as, and is probably more expensive than, the final recomrmnended designo The poor flow distribution was probably due to the "piping" of the flow into the intake, producing the asymmetrical flow distribution typical of flow round a bend. Further runs (11, 12, 12a) were made with the original false walls and paper bafflesq results were fairly good except for rather poor flow distribution, some unsteadiness in the manometer readings, and the small regions of intense turbulence in the pump intake.o When the false walls were extended right back to the upstream intake, and the flow was raised slightly to make the pit crosssection area half the full area, the throat turbulence in Noo 2 became very violent o One run (No. 16) was made with a false floor underneath No. 2 up to half the height of the pit. The overall CL went up to 2.19, and the No. 2 intake was deprived of most of its supply (Q2/Q4 = 0.36). This was too extreme, and it was decided to try a false floor going up to 1/4 of the height of the pit. This will be discussed in the next section. Prevention of separation from the inner wall_.-IJn open channel flow there has been some success in making flow round a bend more uniform, and inhibiting separation, by setting up an artificial secondary flow opposing the natural secondary flowo In this case, the concept could be applied by using small vanes which direct the flow outward along the floor and the top of the pito This should set up a secondary flow which would bring the flow inward 18

The University of Michigan ~ Engineering Research Institute along the horizontal plane halfway up the pit. A scheme of this sort was tried (Mod. 8, Table V), but with no successo The flow which was directed outwardre turned inward not across the median horizontal plane, but round the end of the pit, accentuating the vortex under Noo 2 intake. Turning the vanes inward (Modo 9) was no better. It seemed that the most satisfactory way of preventing separation was simply to force all the flow inward by means of vertical turning vanes running the full depth of the pit. These were tried in various positions (Modso 17-19) but operated best when placed between the pump intakes and associated with a false floor rising to 1/4 of the depth of the pit (Mod. 17)o The CL was only 1,40 and the maximum/minimum velocity ratio for No. 2 was only 1,40 (for No. 4 it was 1.21). This was the best velocity distribution obtained to dates further, the flow in the pump intakes was straight. The zones of turbulence were small, and the turbulence itself was the least violent encountered in the whole study (displacement of tuft ~ 15~ from vertical). Vertical vortices were still present in the pit and the woolen tufts disclosed some backflow along the inner wall under Noo 4 and along both walls under No. 2 (Plates 3-5). However, the backflow was not serious enough to affect conditions in the intakes themselves. Final Recommended Design The recommended design is therefore that described as Modification Noo 17 in Table V, and shown in Fig. 3. The operation might be further improved by altering the angle of the vanes, but the present recommended angle should give satisfactory operation. The vanes mentioned in recommendation (6) of the summary —6 radial vanes in each pump intake-were observed to make a further substantial reduction in the intensity of the localized turbulent zones in the throat of each in take. When in addition to this the effect of a butterfly valve and a reduction from 72 ino to 60 ino diameter is taken into consideration it seems that most disturbances will have been damped out by the time the flow reaches the pump impeller o 2,3 BMEAVIOR OF DESIGN AT PARTIAL FLOW The report so far has dealt with full flow, i.oeo all pump lines open. It remains to check the performance of the design when some of the pump lines are closedo Four combinations were tried in all —two with two pumps running, and two with three pumps runningo Table VI summarizes the performance with regard to flow distribution, loss coefficient, and behavior at the pump intakes. 19

The University of Michigan * Engineering Research Institute TABLE VI BEHAVIOR OF RECOMMENDED DESIGN WITH PARTIAL FLOWS Run |-Pump Line Disharges (Q in Lines Overall Behavior at No. 1 No. 2 No. 3 No, 4 CL Pump Intakes Large vortex No. 1 closed 0 0.378 0.331 0.291 1.51 1.66 1.82 under No. 1 small turbulnt spot in No. 3 Spot of weak turbulence in No. 3 closed 0.314 0.377 0 0.309 1.58 1.75 1.84 No. lregular No. l; regular flow in pit Vertical vortex under Nos. 1 and 2 No. 3; moderat closed 0 0 0.509 0.491 - 1.45 2.91 turbulence in No. 3 Spot of weak Nos. 3 and 4 turbulence in closed O, 508 0o492 0 0 1.88 - 2.94 No. 1; regular flow in pit The question of head loss is straightforward: there is little to choose between alternative arrangements for a given number of pumps, and the values of CL are approximately those that would be expected with the higher velocities through the pump lines. The value of 1.40 for full flow can be split into two parts~ 0.8 - applying to flow before it splits and goes to the pumps 0.6 applying to flow after it splits and goes to the pUmps The first part should remain approximately the same at partial flow; the second part will be increased in proportion to the squares of the velocities in the pump lines. Hence we can say, approximately: For 1 pump closed, CL = 0.8 + 0.6 (4/3)2 1= 87: cf measured 1.82, 1.84 For 2 pumps closed, CL = 0.8 + 0.6 (4/2)2 = 3.2: cf measured 2.91, 2.94 Considering the crudeness of the approximation, the agreement is quite good. The behavior at the pump intakes was substantially sound, although the flow distribution within each pump line was rather uneven. This unevenness, although undesirable, does not weigh very heavily against the fact that the 20

The University of Michigan * Engineering Research Institute flow in the intake throats appeared regular and parallel except in the nsmall zones of turbulence. Even in these zones the turbulence was no stronger than in the case of full flow. There is not a great deal to choose between alternative arrangements for a given number of pumps, but the observations suggest slightly better performance when the upstream pump or pumps is closed —i.e., for 3 pumps running, close No. 3 or No. 4; for 2 pumps running, close No. 3 and No. 4. 21

The University of Michigan ~ Engineering Research Institute APPENDIX I The annual operating cycle can be approximated by breaking the year into ten equal periods of 36.5 days each. The average flow in each period is shown in Column 2 of Table II. The upper part of the table is concerned with the high-flow portion of the year during which pumping is necessary. In this part of the table the columns after No. 2 lead in logical order to figures for the head saved. This is converted into money by using the conversion 1 million gallons raised 1 foot = 4 cents. We finally arrive at a figure for dollars saved per year. Table II relates to the particular case F (5 —16-in. radius vanes at 45~) and the gross saving is $3387 per annum. In considering the gravity-flow part of the year, we allow for the fact that the pumping station is in one of two parallel branches, the other one of which (the main line) has a constant loss coefficient. We introduce loss coefficients K defined by the equation hL = KQ2 where Q is the discharge in thousands of cfs. e K" is related to CL in this way, for a 14-f-t-diameter pipe (which applies to both branches): v2 hL = CL 2 = CL 2g 155, since area of 14-ft pipe = 155 sq ft = 0.647 CLQ2; - K = 0.647 CL o We now consider the two branches: K1 Main 1' + Kr = K2 + Kv Pump. Station 22

The University of Michigan ~ Engineering Research Institute K1 is the (constant) loss coefficient in the main line, estimated at 6.6. K2 is the loss coefficient in the branch line, estimated at 4.75 (without vanes)o Kv is the extra loss coefficient added to the branch line by the vanes. Kr = K2 + Kv Now if Qo = total flow, 1,= main flow, and Q2 = branch flow, we wish to obtain the effective loss coefficient, Ko, of the two branches combined. Now K hL K1Q12 Qo2 and Q2 K1 Q= Q1 +..2 1 +;.... K, (1 +K1/Kr)2 The second part of Table II is then found by taking the extra CL, and therefore Kv, introduced by the vanes, obtaining Kr and hence Ko. The increase in Ko over the original Ko gives the increased hL at each discharge, and hence increased cost in dollars. In the particular case dealt with in Table II, this increased cost is $449 p.a. leaving a net gain of $3387 - $449 = $2938 p.a. Table III summarizes the results of Table II and applies it to all vane arrangements that were tried. It also gives the values of CL, Kv, etc., which are applied to the calculations in Table II. All the results of Table III can readily be obtained from the single result of Table II because the gross saving in the pumping cycle is directly proportional to the decrease in CL, and the loss in the gravity-flow cycle is directly proportional to the increase in KOD 23

The University of Michigan Engineering Research Institute ~~~~~~~~~~~~~~ n,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Z """~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~........... PlteI Ve o odlfrm-usremshwngmnoeercnncios

The University of Michigan ~ Engineering Research Institute Plate II. View of model from downstream. upstream of Pump No. 50 _::e.S..'~: iK::

The University of Michigan ~ Engineering Research Institute Plate IV. Recommended design-behavior of woolen tufts und-er Pump No. 3 intake. 26:. i.; f 1;:i. ~:i: Plate V. Recommended design-behavior of woolen tufts under Pump No, 1 intake.

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ADDENDUM TO REPORT 2564-1-F "A Model Study of City of Detroit Booster Pwaping Station" Four further runs were made to test two new features: a systen of vertical guide vanes at each pump intake, and a new type of bafile installed in the pit. Both features are detailed in the attached sketch, which should be regarded as an addendum to Fig. 4, and results are suimarized in the attached table, which is an addendum to Table V. For all of these four runs, the "tnew vanes at the pit entry were used, as well as the short partition at the end of the pit, shown in Fig. 4. The table makes it clear that the baffles, and to a lesser extent the intake guiide vanes, were responsible for a large increase in the overall loss coefficient - from 1.40 in the recoumendecl design (No. 17, Table V) to 3.57, which is greater fthan for the original design at the start of the model study. The conditions in the pit and the pump intakes, brie-fly described in the table, were if anything vworse than in the recommended des ign.o The spots of turbulence in the pump intLakes were as numerous, and a little more severe, than in the recommended design and as the table shows, the velocity distribution within pump line No. 2 was much more unleven.

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