Problem 11.32
The data of Prob. 11.31 correspond to a pump speed of 1200 r/min. (Were you able to solve
Prob. 11.31 without this knowledge?) (a) Estimate the diameter of the impeller [HINT: See Prob.
11.24 for a clue.]. (b) Using your estimate from part (a), calculate the BEP parameters
* * *
, , and
QHP
C C C
and compare with Eq. (11.27). (c) For what speed of this pump would the BEP
head be 280 ft?
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.
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 11.32
Yes, we were able to solve Prob. 11.31 by simply using ratios.
(a) Prob. 11.24 showed that, for a wide range of centrifugal pumps, the shut–off head
Problem 11.33
In Prob. P11.31, the pump BEP flow rate is 2000 gal/min, the impeller diameter is 16 in, and the
speed is 1200 r/min. Scale this pump with the similarity rules to find (a) the diameter and (b) the
speed that will deliver a BEP water flow rate of 4000 gal/min and a head of 180 ft. (c) What
brake horsepower will be required for this new condition?
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 11.33
Take the specific weight of water to be
= 62.4 lbf/ft3. Find the efficiency:
2
Problem 11.34
You are asked to consider a pump geometrically similar to the 9-in-diameter pump of
Fig. P11.34 to deliver 1200 gal/min at 1500 rpm. Determine the appropriate (a) impeller
diameter; (b) BEP horsepower; (c) shut-off head; and (d) maximum efficiency. The fluid is
kerosene, not water.
Solution 11.34
For kerosene, take
1.56 slug/ft3, whereas for water
1.94 slug/ft3. From Fig. P11.34, at
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 11.35
We have computed the efficiencies and listed them. The BEP is the next–
Problem 11.36
The pump of Prob. P11.35 has a maximum efficiency of 88 percent at 8000 gal/min. (a) Can we
use this pump, at the same diameter but a different speed, to generate a BEP head of 150 ft and a
BEP flow rate of 10,000 gal/min? (b) If not, what diameter is appropriate?
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 11.36
We are still pumping water,
= 1.94 slug/ft3. Try scaling laws for head and then for flow:
Problem 11.37
Consider the two pumps of Problems P11.28 and P11.35. If the diameters are not changed,
which is better for delivering water at 3000 gal/min and a head of 400 ft? What is the
appropriate rotation speed for the better pump?
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.
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 11.37
Unless we are brilliant, what can we do but try them both? The scaling law for constant diameter
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 11.38
The BEP of 81% is at about Q = 350 gpm and H = 169 ft. Hence the power is
Problem 11.39
The Allis-Chalmers D30LR centrifugal compressor delivers 33,000 ft3/min of SO2 with a
pressure change from 14.0 to 18.0 lbf/in2 absolute using an 800-hp motor at 3550 r/min. What is
the overall efficiency? What will the flow rate and p be at 3000 r/min? Estimate the diameter of the
impeller.
Solution 11.39
For SO2, take M = 64.06, hence R = 49720/64.06 776 ftlbf/(slugR). Then
Problem 11.40
The specific speed Ns, as defined by Eq. (11.30), does not contain the impeller diameter. How
then should we size the pump for a given Ns? An alternate parameter is called the specific
diameter DS, which is a dimensionless combination of Q, (gH), and D. (a) If DS is proportional
to D, determine its form. (b) What is the relationship, if any, of DS to CQ*, CH*, and CP*?
(c) Estimate DS for the two pumps of Figs. 11.8 and 11.13.
Solution 11.40
If we combine CQ and CH in such a way as to eliminate speed n, and also to make the result
Problem 11.41
It is desired to build a centrifugal pump geometrically similar to Prob. 11.28 to deliver
6500 gal/min of gasoline at 1060 r/min. Estimate the resulting (a) impeller diameter; (b) head;
(c) brake horsepower; and (d) maximum 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 11.41
For gasoline, take
1.32 slug/ft3. From Prob. 11.28, BEP occurs at
Problem 11.42
An 8-in model pump delivering water at 180F at 800 gal/min and 2400 r/min begins to cavitate
when the inlet pressure and velocity are 12 lbf/in2 and 20 ft/s, respectively. Find the required
NPSH of a prototype that is 4 times larger and runs at 1000 r/min.
Solution 11.42
For water at 180F, take
g 60.6 lbf/ft3 and pv 1600 psfa. From Eq. 11.19,
Problem 11.43
The 28–in–diameter pump in Fig. 11.7a at 1170 r/min is used to pump water at 20C through a
piping system at 14,000 gal/min. (a) Determine the required brake horsepower. The average
friction factor is 0.018. (b) If there is 65 ft of 12-in-diameter pipe upstream of the pump, how far
below the surface should the pump inlet be placed to avoid cavitation?
Solution 11.43
For water at 20F, take
g 62.4 lbf/ft3 and pv 49 psfa. From Fig. 11.7a (above), at 28 and
14000 gpm, read H 320 ft,
0.81, and P 1400 bhp. Ans.
Problem 11.44
The pump of Prob. 11.28 is scaled up to an 18-in-diameter, operating in water at best efficiency
at 1760 rpm. The measured NPSH is 16 ft, and the friction loss between the inlet and the pump is
22 ft. Will it be sufficient to avoid cavitation if the pump inlet is placed 9 ft below the surface of
a sea-level reservoir?
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 11.44
For water at 20C, take
g = 62.4 lbf/ft3 and pv = 49 psfa. Since the NPSH is given, there is no
need to use the similarity laws. Merely apply Eq. 11.20:
Problem 11.45
Determine the specific speeds of the seven Taco, Inc. pump impellers in Fig. P11.24. Are they
appropriate for centrifugal designs? Are they approximately equal within experimental
uncertainty? If not, why not?
Solution 11.45
Read the BEP values for each impeller and make a little table for 1160 rpm:
Problem 11.46
The answer to Prob. 11.40 is that the dimensionless “specific diameter” takes the form
Ds = D(gH*)1/4/Q*1/2, evaluated at the BEP. Data collected by the author for 30 different pumps
indicates, in Fig. P11.46, that Ds correlates well with specific speed Ns. Use this figure to
estimate the appropriate impeller diameter for a pump which delivers 20,000 gal/min of water
and a head of 400 ft when running at 1200 r/min. Suggest a curve-fitted formula to the data.
Hint: Use a hyperbolic formula.
Problem 11.40
The specific speed Ns, as defined by Eq. (11.30), does not contain the impeller diameter. How
then should we size the pump for a given Ns? An alternate parameter is called the specific
diameter DS, which is a dimensionless combination of Q, (gH), and D. (a) If DS is proportional
to D, determine its form. (b) What is the relationship, if any, of DS to CQ*, CH*, and CP*?
(c) Estimate DS for the two pumps of Figs. 11.8 and 11.13.
Solution 11.46
We see that the data are very well correlated by a single curve. (NOTE: These are all centrifugal
pumps—a slightly different correlation holds for mixed- and axial-flow pumps.) The data are
well fit by a hyperbola:
Problem 11.47
A pump must be designed to deliver 6 m3/s of water against a head of 28 m. The specified shaft
speed is 20 r/s. What type of pump do you recommend?
Solution 11.47
Change units to suit the practicing-engineer version of specific speed: 6 m3/s = 95,100 gal/min,
Problem 11.48
Using the data for the pump in Prob. P11.8, (a) determine its type: PDP, centrifugal, mixed-flow,
or axial-flow. (b) Estimate the shutoff head at 1750 r/min. (c) Does this data fit on Fig. 11.14?
(d) What speed and flow rate would result if the head were increased to 160 ft?
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 11.48
Recall the P11.8 data: n = 1750 r/min, H = 105 ft, Q = 1050 gal/min, P = 32.4 hp.
Problem 11.49
Data collected by the author for flow coefficient at BEP for 30 different pumps are plotted in
Fig. P11.49. Determine if the values of
Q
*
C
fit this correlation for the three pumps of
Problems P11.28, P11.35, and P11.38. If so, suggest a curve-fitted formula for the data.
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.
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.
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 11.49
Make a table of these values:
Q*, gpm
D, inches
n, rpm
NS
3
Q
*
C Q*/(nD )
=
Prob. 11.28:
2692
14.62
2134
1430
0.0933
Prob. 11.35:
880
3320
Prob. 11.38:
3500
1400