A centrifugal water pump, with 15 -cm-diameter impeller and axial inlet flow, is driven at \(1750 \mathrm{rpm}\). The impeller vanes are backward curved \(\left(\beta_{2}=65^{\circ}\right)\) and have axial width \(b_{2}=2 \mathrm{~cm}\). For a volume flow rate of \(225 \mathrm{~m}^{3} / \mathrm{hr}\) determine the theoretical head rise and power input to the pump.