Asingle stage, radial flow, and double suction centrifugal pump having the following data: Discharge $72$ liters$/$s; Inner diameter $90$ mm; Outer diameter $280$ mm; Speed $1650$ revolutions$/$minute; Head $25$ m; Width at inlet $20$ mm$/$side; Width at outlet $18$ mm$/$side;Absolute velocity angle at inlet $90\backslash$deg ; Leakage losses $2$ liters$/$s; Mechanical losses $1$:$50$ kW; Contraction factor due to vane thickness $0$:$85$; Relative velocity angle measured from tangential direction $35\backslash$deg ; Overall efficiency of the pump $0$:$56.$ Determine $(1)$ inlet vane angle, $(2)$ the angle at which the water leaves the wheel, $(3)$ the absolute velocity of water leaving impeller, $(4)$ manometric efficiency, and $(5)$ the volumetric and mechanical efficiencies.