A turbine discharges \(40 \mathrm{~m}^{3} / \mathrm{s}\) of water and generates \(42 \mathrm{MW}\) of power. The rotational speed is 24 r.p.s. Fluid enters at a radius of \(1.6 \mathrm{~m}\) with a tangential velocity of \(9 \mathrm{~m} / \mathrm{s}\). The pump operates at 1200 r.p.m. The fluid exits the impeller in a radial direction near the center.

Determine the velocity of the entering stream and the head of fluid required by the Bernoulli equation. Find the power output of the turbine.