A centrifugal pump has an impeller of $50$ cm outer diameter and $25$ cm inner diameter. When running at $6000$ rpm$,$ the pump discharges $130$ liters of water per second against a gross head of $12$m$.$ At this discharge, water enters the impeller without stock. The vane angle at outlet is $45$deg to the tangent at outlet, and the outlet, and the area of flow which is constant from inlet to outlet of the impeller is $0\mathrm{.}61$ m$2.$ Determine a$)$ The manomertic efficiency of the pump and b$)$ The loss of head at inlet to the impeller when the discharge is reduced by $50\%$ the speed of rotation being unchanged