Figure 13.41 shows a pumped fluid flow system that is being designed to transfer 225 gal/min of water at 60°F from a lower vented reservoir to an elevated tank at a pressure of 35.0 psig. The suction line has 8.0 ft of steel pipe and the discharge line has 360 ft of pipe. Pipe sizes are shown

Question

Figure 13.41 shows a pumped fluid flow system that is being designed to transfer 225 gal/min of water at 60°F from a lower vented reservoir to an elevated tank at a pressure of 35.0 psig. The suction line has 8.0 ft of steel pipe and the discharge line has 360 ft of pipe. Pipe sizes are shown in the figure. Prepare the SRC for this application, considering flow rates from zero to 250 gal/min, computing head values in 50 gal/min increments.

Accepted Answer

Objective: Develop the SRC for the pumped system shown in Fig. 13.41.

Given: Fluid: Water at 60° F: [latex] \gamma = 62.4 lb/ft^3; u = 1.21 imes 10^{-5} ft^2/s; h_{vp} = 0.5917 ft.[/latex]

(Appendix A.2 and Table 13.2)

Range of volume flow rates: Q = 0 to 250 gal/min at increments of 50 gal/min

Select reference point 1 for the energy equation at the surface of the lower reservoir and point 2 at the surface of the upper tank.

Source: Lower reservoir; [latex] p_1[/latex] = 0 psig;Elevation = 8.0 ft above the pump inlet

Destination: Upper reservoir; [latex] p_2[/latex] = 35.0 psig; Elevation = 88 ft above pump inlet

Suction pipe is 3½–in Schedule 40 steel pipe; D = 0.2957 ft, A = 0.06868 [latex]ft^2[/latex] ; L = 8.0 ft

Discharge line is 2½– in Schedule 40 steel pipe; D = 0.2058 ft, A = 0.03326 [latex]ft^2[/latex] ; L = 360 ft

Step 1 Figure 13.41 shows the proposed layout.

Step 2 For the static head: [latex]z_2 – z_1[/latex] = 88.0 ft – 8.0 ft = 80.0 ft; [latex]p_2[/latex] = 35.0 psig; [latex]p_1[/latex]= 0

Then,

[latex] \frac{P_2}{\gamma} =\frac{35.0lb}{in^2} imes \frac{ft^3}{62.4lb} imes \frac{144in^2}{ft^2} =80.77ft.[/latex]

The total static head [latex] h_o = \left(p_2-p_1 ight)/\gamma + \left(z_2-z_1 ight) =80.77ft+80ft=160.77ft.[/latex]

Step 3 To compute the total head at many different flow rates, it is convenient to use the spreadsheet shown in Fig. 13.42, adapted from Chapter 11. The data shown in the figure are for the total dynamic head [latex] h_a[/latex] at the design flow rate of 225 gal/min , given by

[latex] h_a = \left(z_2 -z_1 ight) +p_2/\gamma +h_L=80.0ft+80.8ft +139.0ft = 299.8ft[/latex]

Step 4 Points on the SRC are shown in Table 13.3, computed using the spreadsheet and varying only the volume flow rate from zero to 250 gal/min in 50 gal/min increments (zero to 0.557 [latex]ft^3/s[/latex] in 0.111 [latex]ft^3/s[/latex] increments ).

Step 5 Figure 13.43 shows the system resistance curve.

Note the static head of 166.77 ft at the left axis for zero flow, the 2nd order shape of the curve, and the total head of 299.8 ft at the design flow rate of 225 gal/min.

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

TABLE 13.3 Data points on the system resistance curve (SRC)

[latex] h_a[/latex] (ft)	Q (cfs)	Q (gal/min)
160.8	0	0
168.6	0.111	50
189.9	0.223	100
224.1	0.334	150
271.3	0.445	200
299.8 (Design point)	0.501	225
331.4	0.557	250

Question 13.4: Figure 13.41 shows a pumped fluid flow system that is being ...

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