A centrifugal pump having an internal and external diameter of impeller \(150 \mathrm{~mm}\) and \(450 \mathrm{~mm}\), respectively, is running at \(1,000 \mathrm{rpm}\). It has a constant velocity of flow of \(5 \mathrm{~m} / \mathrm{sec}\) and discharges through the pump is \(0.04 \mathrm{~m}^{3} / \mathrm{sec}\). The diameters of suction and delivery pipes are 100 and \(80 \mathrm{~mm}\), respectively and suction and delivery heads are 8 and \(20 \mathrm{~m}\) of water, respectively. If outlet vane angle is \(30^{\circ}\) and power required to drive the pump is \(18 \mathrm{~kW}\). Determine: (i) vane angle at the inlet, (ii) overall efficiency of the pump, and (iii) manometric efficiency of the pump.