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Solution 11.9
The following are observed:
(a) The discharge Q is almost linearly proportional to speed and slightly less for the higher
heads (H or p).
Problem 11.10
Suppose that the pump of Fig. P11.9 is run at 1100 r/min against a pressure rise of 210 bar.
(a) Using the measured displacement, estimate the theoretical delivery in gal/min. From the
chart, estimate (b) the actual delivery; and (c) the overall efficiency.
Solution 11.10
(a) From Fig. P11.9, the pump displacement is 41 cm3. The theoretical delivery is
Problem 11.11
A pump delivers 1500 L/min of water at 20C against a pressure rise of 270 kPa. Kinetic and
potential energy changes are negligible. If the driving motor supplies 9 kW, what is the overall
efficiency?
Solution 11.11
With pressure rise given, we don’t need density. Compute “water” power:
Problem 11.12
In a test of the pump shown in Fig. P11.12, the following data are taken: p1 = 100 mmHg
(vacuum), p2 = 500 mmHg (gage). The pipe diameters are D1 = 12 cm, and D2 = 5 cm. The
flow rate is 180 gal/min of light oil (SG = 0.91). Estimate (a) the head developed in meters,
and (b) the input power required at 75 percent efficiency.
Solution 11.12
Convert 100 mmHg = 13332 Pa, 500 mmHg = 66661 Pa, 180 gal/min = 0.01136 m3/s. Compute
Problem 11.13
A 3.5 hp pump delivers 1140 lbf of ethylene glycol at 20C in 12 seconds, against a head of
17 ft. Calculate the efficiency of the pump.
Solution 11.13
From Table A.3 for ethylene glycol,
= 1117 kg/m3 = 2.167 slug/ft3. The specific weight is thus
Problem 11.14
A pump delivers gasoline at 20C and 12 m3/h. At the inlet, p1 = 100 kPa, z1 = 1 m, and
V1 = 2 m/s. At the exit p2 = 500 kPa, z2 = 4 m, and V2 = 3 m/s. How much power is required if
the motor efficiency is 75 percent?
Solution 11.14
For gasoline, take
g 680(9.81) = 6671 N/m3. Compute head and power:
Problem 11.15
A lawn sprinkler can be used as a simple turbine. As shown in Fig. P11.15, flow enters normal to
the paper in the center and splits evenly into Q/2 and Vrel leaving each nozzle. The arms rotate at
angular velocity
and do work on a shaft. Draw the velocity diagram for this turbine. Neglecting
friction, find an expression for the power delivered to the shaft. Find the rotation rate for which the
power is a maximum.
Solution 11.15
Utilizing the velocity diagram at right, we apply the Euler turbine formula:
max
Problem 11.16
The centrifugal pump in Fig. P11.16 has r1 = 15 cm, r2 = 25 cm, b1 = b2 = 6 cm, and rotates
counterclockwise at 600 r/min. A sample blade is shown. Assume
1 = 90. Estimate the
theoretical flow rate and head produced, for water at 20C, and comment.
Solution 11.16
For water, take
= 998 kg/m3. For counterclockwise rotation, this is a forward-facing impeller,
Problem 11.17
A centrifugal pump has d1 = 7 in, d2 = 13 in, b1 = 4 in, b2 = 3 in,
1 = 25, and
2 = 40 and rotates at
1160 r/min. If the fluid is gasoline at 20C and the flow enters the blades radially, estimate the
theoretical (a) flow rate in gal/min, (b) horsepower, and (c) head in ft.
Solution 11.17
For gasoline, take
1.32 slug/ft3. Compute
= 1160 rpm = 121.5 rad/s.
Problem 11.18
A jet of velocity V strikes a vane that moves to the right at speed Vc, as in Fig. P11.18. The vane
has a turning angle
. Derive an expression for the power delivered to the vane by the jet. For
what vane speed is the power maximum?
Solution 11.18
The jet approaches the vane at relative velocity (V − Vc). Then the force is
Problem 11.19
A centrifugal pump has r2 = 9 in, b2 = 2 in, and
2 = 35 and rotates at 1060 r/min. If it generates a
head of 180 ft, determine the theoretical (a) flow rate in gal/min and (b) horsepower. Assume
near-radial entry flow.
Solution 11.19
For water take
= 1.94 slug/ft3. Convert
= 1060 rpm = 111 rad/s. Then
Problem 11.20
Suppose that Prob. 11.19 is reversed into a statement of the theoretical power P ≈ 153 hp. Can
you then compute the theoretical (a) flow rate; and (b) head? Explain and resolve the difficulty
that arises.
Problem 11.19
A centrifugal pump has r2 = 9 in, b2 = 2 in, and
2 = 35 and rotates at 1060 r/min. If it generates a
head of 180 ft, determine the theoretical (a) flow rate in gal/min and (b) horsepower. Assume
near-radial entry flow.
Solution 11.20
With power known, the basic theory becomes quadratic in flow rate:
Problem 11.21
The centrifugal pump of Fig. P11.21 develops a flow rate of 4200 gpm with gasoline at 20C and
near-radial absolute inflow. Estimate the theoretical (a) horse-power; (b) head rise; and
(c) appropriate blade angle at the inner radius.
Solution 11.21
For gasoline take
1.32 slug/ft3. Convert
Problem 11.22
A 37-cm-diameter centrifugal pump, running at 2140 rev/min with water at 20C produces the
following performance data:
Q, m3/s:
0.0
0.05
0.10
0.15
0.20
0.25
0.30
H, m:
105
104
102
100
95
85
67
P, kW:
100
115
135
171
202
228
249
(a) Determine the best efficiency point. (b) Plot CH versus CQ. (c) If we desire to use this same
pump family to deliver 7000 gal/min of kerosene at 20C at an input power of 400 kW, what pump
speed (in r/min) and impeller size (in cm) are needed? What head will be developed?
Solution 11.22
Efficiencies, computed by
=
gQH/Power, are listed above. The best efficiency point (BEP) is
approximately 92% at Q = 0.2 m3/s. Ans. (a)
Problem 11.23
When pumping water, (a) at what speed should the 11-inch Bell and Gossett centrifugal pump of
Prob. P11.8 be run, at best efficiency, to deliver 800 gal/min? Estimate the resulting (b) head,
and (c) brake horsepower.
Problem 11.8
A Bell and Gossett pump at best efficiency, running at 1750 r/min and a brake horsepower of
32.4, delivers 1050 gal/min against a head of 105 ft. (a) What is its efficiency? (b) What type of
pump is this?
Solution 11.23
Recall the P11.8 data: n = 1750 r/min, H = 105 ft, Q = 1050 gal/min, P = 32.4 hp. Scale the
problem using our similarity rules, Eqs. (11.28):
Problem 11.24
Figure P11.24 shows performance data for the Taco, Inc., model 4013 pump. Compute the ratios
of measured shutoff head to the ideal value U2/g for all seven impeller sizes. Determine the
average and standard deviation of this ratio and compare it to the average for the six impellers in
Fig. 11.7.
Solution 11.24
All seven pumps are run at 1160 rpm = 121 rad/s. The 7 diameters are given. Thus we can easily
compute U =
r =
D/2 and construct the following table:
Problem 11.25
At what speed in r/min should the 35-in-diameter pump of Fig. 11.7(b) be run to produce a head of
400 ft at a discharge of 20000 gal/min? What brake horsepower will be required? Hint: Fit H(Q) to a
formula.
Solution 11.25
A curve-fit formula for H(Q) for this pump is H(ft) 235 − 0.125Q2, with Q in kgal/min. Then,
Problem 11.26
Would the smallest, or the largest, of the seven Taco Inc. pumps in Fig. P11.24 be better (a) for
producing, near best efficiency, a water flow rate of 600 gal/min and a head of 95 ft? (b) At
what speed, in r/min, should this pump run? (c) What input power is required?
Solution 11.26
First try the smallest pump, D = 10.00 in. Read Fig. P11.24: Q* = 390 gal/min, H* = 41 ft,
max = 65%. To scale up to 600 gpm, use the similarity rules for constant D:
Problem 11.27
The 11-in Bell and Gossett pump of Prob. P11.8 is to be scaled up to provide, at best efficiency,
a head of 250 ft and a flow rate of 3000 gal/min. Find the appropriate (a) impeller diameter;
(b) speed in r/min; and (c) horsepower required.
Problem 11.8
A Bell and Gossett pump at best efficiency, running at 1750 r/min and a brake horsepower of
32.4, delivers 1050 gal/min against a head of 105 ft. (a) What is its efficiency? (b) What type of
pump is this?
Solution 11.27
For water take ρ = 1.94 slug/ft3. Compute the BEP dimensionless values and apply them to the
new head and flow rate to find the new n and D and P:
Problem 11.28
Tests by the Byron Jackson Co. of a 14.62-in-diameter centrifugal water pump at 2134 rpm yield
the following data.
Q, ft3/s:
0
2
4
6
8
10
H, ft:
340
340
340
330
300
220
bhp:
135
160
205
255
330
330
What is the BEP? What is the specific speed? Estimate the maximum discharge possible.
Solution 11.28
The efficiencies are computed from
=
gQH/(550 bhp) and are as follows:
Problem 11.29
If the scaling laws are applied to the pump of Prob. 11.28 for the same impeller diameter,
determine (a) the speed for which the shutoff head will be 280 ft; (b) the speed for which the BEP
flow rate will be 8.0 ft3/s; and (c) the speed for which the BEP conditions will require 80 hp.
Problem 11.28
Tests by the Byron Jackson Co. of a 14.62-in-diameter centrifugal water pump at 2134 rpm yield
the following data.
Q, ft3/s:
0
2
4
6
8
10
H, ft:
340
340
340
330
300
220
bhp:
135
160
205
255
330
330
What is the BEP? What is the specific speed? Estimate the maximum discharge possible.
Solution 11.29
From the table in Prob. 11.28, the shut-off head at 2134 rpm is 340 ft. Thus
Problem 11.30
A pump, geometrically similar to the 12.95-in model in Fig. P11.24, has a diameter of 24 in and
is to develop 30 hp at BEP when pumping gasoline (not water). Determine (a) the appropriate
speed, in r/min; (b) the BEP head, in ft; and (c) the BEP flow rate, in gal/min.
Solution 11.30
For gasoline, from Table A.3, ρ = 680 kg/m3 = 1.32 slug/ft3. Read Fig. P11.24 for the BEP
values:
* * *
1 1 1
72 , 525 / , 0.80.H ft Q gal min
= = =
Compute the power from this data:
Problem 11.31
A centrifugal pump with backward-curved blades has the following measured performance when
tested with water at 20C:
Q, gal/min:
0
400
800
1200
1600
2000
2400
H, ft:
123
115
108
101
93
81
62
P, hp:
30
36
40
44
47
48
46
(a) Estimate the best efficiency point and the maximum efficiency. (b) Estimate the most
efficient flow rate, and the resulting head and brake horsepower, if the diameter is doubled and
the rotation speed increased by 50 percent.
Solution 11.31
(a) Convert the data above into efficiency. For example, at Q = 400 gal/min,
