A performance of a prototype water pump is to be tested using a scale model. The prototype will have an impeller of diameter 260 mm, and when delivering 990 L/s, the difference in water pressure...

A performance of a prototype water pump is to be tested using a scale model. The prototype will have an impeller of diameter 260 mm, and when delivering 990 L/s, the difference in water pressure between the inlet and the outlet of the pump is expected to be 350 kPa. The impeller diameter in the model is to be 50 mm, and the model tests are to use water at the same temperature as that used in the prototype. (a) What dimensionless functional relationship would describe the performance of the pump? Express this relationship in terms of conventional dimensionless groups. (b) What flow rate should be used in the model to achieve dynamic similarity? (c) What would be the expected pressure rise between the inlet and the outlet in the model?