For the pumped fluid flow system shown in Fig. 13.41, select a suitable pump to enable the system to deliver at least 225 gal/min of water at 60°F at the total head of 299.8 ft as found in Example Problem 13.4. Then show the operating point for the pump in that system. Also, list the efficiency

Question

For the pumped fluid flow system shown in Fig. 13.41, select a suitable pump to enable the system to deliver at least 225 gal/min of water at 60°F at the total head of 299.8 ft as found in Example Problem 13.4. Then show the operating point for the pump in that system. Also, list the efficiency of the pump at the operating point, the power required to drive the pump, and the [latex] NPSH_R[/latex]. Analyze the suction line part of the system to determine the [latex] NPSH_A[/latex] and ensure that it is adequate for the chosen pump. Recommend desirable adjustments to the piping system to accommodate the selected pump.

Accepted Answer

Given From Example Problem 13.4, we need to select a pump that can deliver 225 gal/min at 299.8 ft of total head.

Step 1 Figure 13.28 shows the performance curves for a suitable centrifugal pump, the [latex] 2 imes 3 - 10[/latex] operating at 3500 rpm. The desired operating point lies between the curves for the 8-in and 9-in impellers. We specify the 9-in impeller that has a capacity slightly greater than the minimum of 225 gal/min.

We find the following data near the desired operating point:

■ The pump efficiency is approximately 58 percent, near the BEP for this pump.

■ The suction port is 3 in and the discharge port is 2 in.

Step 2 Figure 13.45 shows the pump curve for the selected pump on the graph of the SRC that is shown in Fig. 13.43 as the result of Example Problem 13.4. The intersection of the pump curve and the SRC defines the operating point for this pump in this system.

Step 3 From Fig. 13.45, at the operating point, the following data are found:

Capacity = Q = 229 gal/min

Total head [latex] h_a = 303 ft[/latex]

Input power = P = 30.0 hp

[latex] NPSH_R = 8.8 ft[/latex]

Step 4 We can now compute the NPSHA for the system at the suction port of the pump, using the equation,

[latex] NPSH_A = h_{sp}\pm h_s-h_f-h_{vp}.[/latex]

Assume [latex] p_{sp} = 14.7[/latex] psia (atmospheric) above the water in the source reservoir. Then,

[latex] h_{sp} = \frac{p_{sp}}{\gamma} =\frac{14.7lb}{in^2} \frac{144in^2}{ft^2} \frac{ft^3}{62.4lb} =33.9ft[/latex]

[latex] h_s[/latex] = + 8.0 ft (positive because the pump is below source level)

[latex] h_f[/latex] = Total energy loss in suction line = Entrance loss + Loss in valve + Loss in pipe

[latex] h_f[/latex] = 0.421 ft + 0.114 ft + 0.436 ft = 0.971 ft (values found in Fig. 13.42)

[latex] h_{vp}[/latex] = 0.5917 ft (from Table 13.2)

The values for head loss, [latex] h_f[/latex], used above were determined using the spreadsheet shown in Figure 13.42, but with the flow rate of 229 gal/min, instead of 225 gal/min. Then,

[latex]NPSH_A = 33.9 ft + 8.0 ft - 0.971 ft - 0.5917 ft = 40.34 ft [/latex]

Step 5 Now the value for the [latex] NPSH_A[/latex] can be compared with the [latex]NPSH_R[/latex] for the selected pump. It is recommended that the [latex] NPSH_A[/latex] be at least 10 percent greater than the [latex] NPSH_R[/latex] given by the manufacturer. Compute

[latex] 1.10 NPSH_R = 1.10\left(8.8ft ight) =9.68ft[/latex]

Then, because [latex] NPSH_A[/latex] = 40.34 ft, the pump is acceptable.

Step 6 Now we can see if any issues exist for placing the selected pump in the system shown in Fig. 13.41. The sizes of the suction and discharge pipes are different from the sizes of the pump ports.A gradual reducer must be used from the 3½–in Schedule 40 suction line pipe to the 3–in suction port.A gradual enlargement must be used from the 2-in discharge port to the 2½–in Schedule 40 discharge pipe. These elements add energy losses that should be evaluated. The diameter ratio for each is approximately 1.2. Referring to Fig. 10.6 for a gradual enlargement and Fig. 10.11 for a gradual reducer, and specifying a 15° included angle, we find the K value will be 0.09 for the enlargement and 0.03 for the reducer. The additional energy losses are

[latex] h_{Ls}=0.03\left(v^2/2g ight) =0.03\left(0.842ft ight) =0.025ft[/latex]

[latex] h_{Ld}=0.09\left(v^2/2g ight) =0.09\left(3.587ft ight) =0.323ft[/latex]

These values are negligible compared to the other energy losses in the suction and discharge lines and, therefore, should not significantly affect the pump selection or its performance. Also, the [latex] NPSH_A[/latex] will still be acceptable.

TABLE 13.2 Vapor pressure and vapor pressure head of water

Vapor Pressure Head (ft)	Specific Weight ([latex]lb/ft^3[/latex])	Vapor Pressure (psia)	Temperature °F	Vapor Pressure Head (m)	Specific Weight [latex] (kN/m^3)[/latex]	Vapor Pressure kPa (abs)	Temperature °C
0.2043	62.24	0.08854	32	0.06226	9.806	0.6105	0
0.2807	62.43	0.1217	40	0.08894	9.807	0.8722	5
0.4109	62.41	0.1781	50	0.1253	9.804	1.228	10
0.5917	62.37	0.2563	60	0.2388	9.789	2.338	20
0.8393	62.3	0.3631	70	0.4345	9.765	4.243	30
1.173	62.22	0.5069	80	0.758	9.731	7.376	40
1.618	62.11	0.6979	90	1.272	9.69	12.33	50
2.205	62	0.9493	100	2.066	9.642	19.92	60
3.948	61.71	1.692	120	3.25	9.589	31.16	70
6.775	61.38	2.888	140	4.967	9.53	47.34	80
11.18	61	4.736	160	7.405	9.467	70.1	90
17.55	61.58	7.507	180	10.78	9.399	101.3	100
27.59	60.12	11.52	200
35.36	59.83	14.69	212

Question 13.5: For the pumped fluid flow system shown in Fig. 13.41, select...

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