Question: Dimensional analysis is useful in the design of centrifugal pumps. The pressure rise across a pump (proportional to the head developed by the pump) is affected by the fluid density, p, the angular velocity, o, the impeller diameter, D, the volumetric flow rate, Q, and the fluid viscosity, µ. Find the pertinent dimensionless groups, choosing them so the Δp, Q, and µ each appear in one group only. Find similar expressions replacing the pressure rise fust by the power input to the pump, and then by the efficiency of the pump.