A water turbine delivering $$10$$ $$MW$$ power is to be tested with the help of a geometrically similar $$1:8$$ model, which runs at the same speed as the proto-type.

(a) Find the power developed by the model assuming the efficiencies of the model and the proto-type are equal.

(b) Find the ratio of the heads and the ratio of mass flow rates between the proto-type and the model.