You want to control the flow rate of a liquid in a transfer line at $350 \mathrm{gpm}$. The pump in the line has the characteristics shown in Figure 8.2, with a 5 1/4 in. impeller. The line contains $150 \mathrm{ft}$ of 3 in. sch 40 pipe, 10 flanged elbows, four gate valves, and a $3 \times 3$ control valve. The pressure and elevation at the entrance and exit of the line are the same. The valve has an equal percentage trim. What should the value of $C_{\mathrm{v}}$ be for the valve to achieve the desired flow rate? The fluid has a viscosity of $5 \mathrm{cP}$ and an $\mathrm{SG}$ of 0.85 .

Figure 8.2

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Size 23 R & C 1% in. Pedestal 3500 rpm 4' minimum NPSH 400 Impeller Total head feet 8% in 300 200 8% ins 7% in 7% in 6% in. 6% in. 1 100 50 0 S1 MISSION VALVE AND PUMP CO. M Semi-open impeller Dia. 6%-8% in. Eye area 9.8 in. Max. sphere 1% in. Maximum normal capacity for slurries and abrasive fluids Curve 8 7 ft 30% 10ft 40% 15 ft 145% 50% 20 f 25 ft 50% 45% 15 HP 20 HP 50 100 200 300 40HP 30 HP 25 HP 60 HP 50 HP 400 40% 500 600 700 Capacity-U.S. gallons per minute