In a chemical processing plant a liquid is pumped from an open tank, through a 0.1-m-diameter vertical pipe, and into another open tank as shown in Fig. P12.31(a). A valve is located in the pipe, and the minor loss coefficient for the valve as a function of the valve setting is shown in Fig. P12.31(b). The pump head-capacity relationship is given by the equation h_a = 52.0 - 1.01 × 10³ Q² with h_a in meters when Q is in m³/s. Assume the friction factor ƒ = 0.02 for the pipe, and all minor losses, except for the valve, are negligible. The fluid levels in the two tanks can be assumed to remain constant.

(a) Determine the flowrate with the valve wide open.

(b) Determine the required valve setting (percent open) to reduce the flowrate by 50%.