In a chemical processing plant, a liquid hydrogen peroxide solution at 15°C (p = 1450 kg/m' and Pu= 1.6 kPa) is pumped from an open tank, through a 0.1 m diameter vertical pipe, and into another open tank. A valve is located in the pipe, and the minor loss coefficient for the valve is KL= 1. The pump head-capacity relationship is given by the equation: H_{\text {available }}=52-1.01 \times 10^{3} \dot{V}^{2} with Hin meters when the volume flow rate is in m'/s. Assume the friction factor f= 0.03 for the pipe to be constant, 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 expression of the required head as function of the volume flow rate b) Determine the flowrate in the system. c) Is there a risk of cavitation if the required NPSH of the pump is 2.4 m at the operating point?