The purpose of a centrifugal pump is to increase the pressure of a liquid in order to move it through a piping system. The pump is driven by a motor, which must provide sufficient power to operate the pump at the desired conditions. You wish to find the pressure developed by a pump operating at a flow rate of $300 \mathrm{gpm}$ with an oil having a specific gravity (SG) of 0.8 and a viscosity of $20 \mathrm{cP}$, and the required horsepower for the motor to drive the pump. The pump has an impeller diameter of $10 \mathrm{in}$., and the motor runs at $1200 \mathrm{rpm}$.

(a) Determine the dimensionless groups that would be needed to completely describe the performance of the pump.

(b) You want to determine the pump pressure and motor horsepower by measuring these quantities in the lab on a smaller-scale model of the pump that has a 3 in. diameter impeller and a $1800 \mathrm{rpm}$ motor, using water as the test fluid. Under the operating conditions for both the lab model and the field pump, the value of the Reynolds number is very high, and it is known that the pump performance is independent of the fluid viscosity under these conditions. Determine the proper flow rate at which the lab pump should be tested and the ratio of the pressure developed by the field pump to that of the lab pump operating at this flow rate as well as the ratio of the required motor power in the field to that in the lab.

(c) The pump efficiency $\left(\eta_{e}\right)$ is the ratio of the power delivered by the pump to the fluid (as determined by the pump pressure and flow rate) to the power delivered to the pump by the motor. Because this is a dimensionless number, it should also have the same value for both the lab and field pumps when they are operating under equivalent conditions. Is this condition satisfied?