A water pump is used to pump water from one large reservoir to another large reservoir that is at a higher elevation. The free surfaces of both reservoirs are exposed to atmospheric pressure, as sketched in Fig. P14–43. The dimensions and minor loss coefficients are provided in the figure. The pump’s performance is approximated by the expression H_available = H₀ – aV̇², where shutoff head H₀ = 24.4 m of water column, coefficient a = 0.0678 m/Lpm², available pump head H_available is in units of meters of water column, and capacity V̇ is in units of liters per minute (Lpm). Estimate the capacity delivered by the pump.

Data from FIGURE P14–43

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22- 22-21 7.85 m (elevation difference) D = 2.03 cm (pipe diameter) KL. , entrance = 0.50 (pipe entrance) KL, valve KL, elbow KL, exit L Z2-21 P₁V₁=0 V₁ = 0 Reservoir = 17.5 (valve) = 0.92 (each elbow-there are 5) = 1.05 (pipe exit) = 176.5 m (total pipe length) ε = 0.25 mm (pipe roughness) E 21 Valve Pump V₂=0 Reservoir -D