Problem 11.35
An 18-in-diameter centrifugal pump, running at 880 r/min with water at 20C, generates the
following performance data:
Q, gal/min:
0.0
2000
4000
6000
8000
10000
H, ft:
92
89
84
78
68
50
P, hp:
100
112
130
143
156
163
Determine (a) the BEP; (b) the maximum efficiency; and (c) the specific speed. (d) Plot the
required input power versus the flow rate.
Solution 11.67
(a) There is no elevation change, so the pump head matches the friction:
2 2 2 2
75 [ / ( (0.2) /4)] 4 0.15
19366 , , 0.00075
2 0.2 2(9.81) 200
pd
L V Q Q
H f f fQ Re
d g d d
= = = = = =
Problem 11.68
A popular small aircraft cruises at 230 km/h at 8500 ft altitude. It weighs 2200 lbf, has a 180 hp
engine, a 76-in diameter propeller, and a drag-area CDA ≈ 5.6 ft2. The propeller data in Fig.
P11.68 is proposed to drive this aircraft. Estimate the required rotation rate, in r/min, and power
delivered, in hp. [NOTE: Simply use the coefficient pairs. The actual advance ratio is too high.]
Solution 11.68
First convert to BG units: V = 230 km/hr = 210 ft/s, ρ at 8500 ft ≈ 0.00184 slug/ft3,
D = 76/12 = 6.33 ft. The weight is immaterial because we know the drag-area. The two
coefficients are
Problem 11.69
The pump of Prob. 11.38, running at 3500 rpm, is used to deliver water at 20C through 600 ft of cast
iron pipe to an elevation 100 ft higher. Find (a) the proper pipe diameter for BEP operation; and
(b) the flow rate that results if the pipe diameter is 3 in.
Problem 11.38
A 6.85-in pump, running at 3500 r/min, has the following measured performance for water at
20C.
Q, gal/min:
50
100
150
200
250
300
350
400
450
H, ft:
201
200
198
194
189
181
169
156
139
, %:
29
50
64
72
77
80
81
79
74
(a) Estimate the horsepower at BEP. If this pump is rescaled in water to provide 20 bhp at
3000 r/min, determine the appropriate (b) impeller diameter; (c) flow rate; and (d) efficiency for
this new condition.
Solution 11.69
For water at 20C, take
= 1.94 slug/ft3 and
= 2.09E−5 slug/fts. For cast iron, take
Problem 11.70
The pump of Prob. 11.28, operating at 2134 r/min, is used with 20C water in the system of
Fig. P11.70. (a) If it is operating at BEP, what is the proper elevation z2? (b) If z2 = 225 ft, what
is the flow rate if d = 8 in?
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 11.70
For water at 20C, take
= 1.94 slug/ft3 and
= 2.09E−5 slug/fts. For cast iron, take
Problem 11.71
The pump of Prob. 11.38, running at 3500 r/min, delivers water at 20C through 7200 ft of
horizontal 5-in-diameter commercial-steel pipe. There are a sharp entrance, sharp exit, four 90
elbows, and a gate valve. Estimate (a) the flow rate if the valve is wide open and (b) the valve
closing percentage which causes the pump to operate at BEP. (c) If the latter condition holds
continuously for 1 year, estimate the energy cost at 10 ¢/kWh.
Problem 11.38
A 6.85-in pump, running at 3500 r/min, has the following measured performance for water at
20C.
Q, gal/min:
50
100
150
200
250
300
350
400
450
H, ft:
201
200
198
194
189
181
169
156
139
, %:
29
50
64
72
77
80
81
79
74
(a) Estimate the horsepower at BEP. If this pump is rescaled in water to provide 20 bhp at
3000 r/min, determine the appropriate (b) impeller diameter; (c) flow rate; and (d) efficiency for
this new condition.
Solution 11.71
For water at 20C, take
= 1.94 slug/ft3 and
= 2.09E−5 slug/fts. For commercial steel, take
0.00015 ft, or
/d 0.00036. The data above show BEP at 350 gal/min. The minor losses are a
Problem 11.72
Performance data for a small commercial pump are shown as follows:
Q, gal/min:
0
10
20
30
40
50
60
70
H, ft:
75
75
74
72
68
62
47
24
The pump supplies 20C water to a horizontal 5/8-in-diameter garden hose (
0.01 in), that is
50 ft long. Estimate (a) the flow rate; and (b) the hose diameter which would cause the pump to
operate at BEP.
Solution 11.72
For water at 20C, take
= 1.94 slug/ft3 and
= 2.09E−5 slug/fts. Given
Problem 11.73
The Bell and Gossett pump of Prob. P11.8, running under the same conditions, delivers water at
20ºC through a long, smooth, 8-in-diameter pipe. Neglect minor losses. How long is the pipe?
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 11.73
For water at 20ºC, from Table A.3, take ρ = 998 kg/m3 = 1.94 slug/ft3 and
μ = 0.0010 kg/m·s = 2.09E-5 slug/ft·s. “Exact same” means Q = 1050 gal/min = 2.34 ft3/s and
Problem 11.74
The 32-in-diameter pump in Fig. 11.7a is used at 1170 r/min in a system whose head curve is
Hs(ft) = 100 + 1.5Q2, with Q in thousands of gallons of water per minute. Find the discharge and
brake horsepower required for (a) one pump; (b) two pumps in parallel; and (c) two pumps in
series. Which configuration is best?
Figure 11.7a:
Solution 11.74
Assume plain old water,
g 62.4 lbf/ft3. A reasonable curve-fit to the pump head is taken from
Problem 11.75
Two 35-inch pumps from Fig. 11.7b are installed in parallel for the system of Fig. P11.75.
Neglect minor losses. For water at 20C, estimate the flow rate and power required if (a) both
pumps are running; and (b) one pump is shut off and isolated.
Solution 11.75
For water at 20C, take
= 1.94 slug/ft3 and
= 2.09E−5 slug/fts. For cast iron,
0.00085 ft,
Problem 11.76
Two 32-inch pumps from Fig. 11.7a are combined in parallel to deliver water at 60°F through
1500 ft of horizontal pipe. If f = 0.025, what pipe diameter will ensure a flow rate of
35,000 gal/min at 1170 r/min?
Solution 11.76
For water at 20C, take
= 1.94 slug/ft3 and
= 2.09E−5 slug/fts. As in Prob. 11.74, a
Problem 11.77
Two pumps of the type tested in Prob. 11.22 are to be used at 2140 r/min to pump water at 20C
vertically upward through 100 m of commercial-steel pipe. Should they be in series or in
parallel? What is the proper pipe diameter for most efficient operation?
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 11.77
For water take
= 998 kg/m3 and
= 0.001 kg/ms. For commercial steel take
= 0.046 mm.
Parallel operation is not feasible, as the pump can barely generate 100 m of head and the
Problem 11.78
Consider the axial-flow pump of Fig. 11.13, running at 4200 r/min, with an impeller diameter of
36 in. The fluid is propane gas (molecular weight 44.06). (a) How many pumps in series are
needed to increase the gas pressure from 1 atm to 2 atm? (b) Estimate the mass flow of gas.
Solution 11.78
Find the gas constant and initial density of the propane. Assume T = 68F = 528R.
Problem 11.79
Two 32-inch pumps from Fig. 11.7a are to be used in series at 1170 rpm to lift water through
500 ft of vertical cast iron pipe. What should the pipe diameter be for most efficient operation?
Neglect minor losses.
Figure 11.7a:
Solution 11.79
For water at 20C, take
= 1.94 slug/ft3 and
= 2.09E−5 slug/fts. For cast iron,
0.00085 ft.
Problem 11.80
Determine if either (a) the smallest, or (b) the largest of the seven Taco pumps in Fig.P11.24,
running in series at 1160 r/min, can efficiently pump water at 20C through 1 km of horizontal
12-cm-diameter commercial steel pipe.
Solution 11.80
For water at 20C, take
= 998 kg/m3 and
= 0.001 kg/m-s. For commercial steel pipe, from
Table 6.1,
= 0.046 mm. Then
/D = 0.046 mm/120 mm = 0.000383.
Problem 11.81
Reconsider the system of Fig. P6.62. Use the Byron Jackson pump of Prob. 11.28 running at
2134 r/min, no scaling, to drive the flow. Determine the resulting flow rate between the
reservoirs. What is the pump efficiency?
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 11.81
For water take
= 1.94 slug/ft3 and
= 2.09E−5 slug/fts. For cast iron take
= 0.00085 ft, or
/d = 0.00085/0.5 = 0.0017. The energy equation, written between reservoirs, is the same as in
Prob. 6.62:
Problem 11.82
The S-shaped head-versus-flow curve in Fig. P11.82 occurs in some axial-flow pumps. Explain how a
fairly flat system loss curve might cause instabilities in the operation of the pump. How might we avoid
instability?
Solution 11.82
The stability of pump operation is nicely covered in the review article by Greitzer (Ref. 41 of Chap.
11). Generally speaking, there is little danger of instability if the slope of the pump-head curve,
dH/dQ, is negative, unless there are two such points. In Fig. P11.82 above, a flat system curve
Problem 11.83
The low-shutoff head-versus-flow curve in Fig. P11.83 occurs in some centrifugal pumps.
Explain how a fairly flat system-loss curve might cause instabilities in the operation of the pump.
What additional vexation occurs when two of these pumps are in parallel? How might we avoid
instability?
Solution 11.83
As discussed, for one pump with a flat system curve, point a is statically unstable, point b is stable.
A ‘better’ system curve only passes through b.
Problem 11.84
Turbines are to be installed where the net head is 400 ft and the flow rate is 250,000 gal/min.
Discuss the type, number, and size of turbine which might be selected if the generator selected is
(a) 48-pole, 60-cycle (n =150 r/min); or (b) 8-pole (n = 900 r/min). Why are at least two turbines
desirable from a planning point of view?
Solution 11.84
We select two turbines, of about half-flow each, so that one is still available for power generation
Problem 11.85
For a high-flow site with a head of 45 ft, it is desired to design a single 7-ft-diameter turbine that
develops 4000 bhp at a speed of 360 r/min and 88 percent efficiency. It is decided first to test a
geometrically similar model of diameter 1 ft, running at 1180 r/min. (a) What likely type of
turbine is the prototype? What are the appropriate (b) head, and (c) flow rate for the model test?
(d) Estimate the power expected to be delivered by the model turbine.
Solution 11.85
For water, take
= 1.94 slug/ft3. (a) We have enough information to determine power specific
speed:
Problem 11.86
The Tupperware hydroelectric plant on the Blackstone River has four 36-inch-diameter turbines,
each providing 447 kW at 200 r/min and 205 ft3/s for a head of 30 ft. What type of turbines are
these? How does their performance compare with Fig. 11.20?