Problem $2$ Underground water is to be pumped by a $78$ percent efficient $5-kW$ submerged pump to a pool whose free surface is $30m$ above the underground water level. The diameter of the pipe is $7cm$ on the intake side and $5cm$ on the discharge side. Determine $($a$)$ the maximum flow rate of water and $($b$)$ the pressure difference across the pump. Assume the elevation difference between the pump inlet and the outlet and the effect of the kinetic energy correction factors to be negligible.