A hydroelectric power station is required to generate a total of 4.2 MW from a number of single-jet Pelton wheel turbines each operating at the same rotational speed of 650 rpm, at the same power output and at a power specific speed of 1.0 rev. The nozzle efficiency ηN of each turbine can be assumed to be 0.98, the overall efficiency ηo is assumed to be 0.88, and the blades speed to jet speed ratio v is to be 0.47. If the effective head HE at the entry to the nozzles is 250 m, determine

a. the number of turbines required (round up the value obtained);

b. the wheel diameter;

c. the total flow rate.