A hydroelectric power station requires water to be pumped from its' feeder dam to a secondary dam, using two pumps (each supplying 250MW within a 32 metre diameter silo) to elevate the water to approximately 100m. At full power, the secondary dam can be filled from empty to full 28700 ML capacity in 14 hours. To determine the operational speed of the pumps, each pump is modelled by a 10kW scale model that is 80cm in diameter and spins at 60Hz.
A) Derive the appropriate non-dimensional pi-groups for this case.
B) Determine the operating angular speed of each dam's pump and the volume flow rate and lift required in the scale model.
c) Calculate the specific speed of each pump.