The power required to drive a centrifugal pump and the pressure that the pump will develop depends upon the size (diameter) and speed (angular velocity) of the impeller, the volumetric flow rate through the pump, and the fluid properties. However, if the fluid is not too viscous (e.g., less than about $100 \mathrm{cP}$ ), the pump performance is essentially independent of the fluid viscosity. Under these conditions:

(a) Perform a dimensional analysis to determine the dimensionless groups that would be required to define the pump performance. Arrange the groups so that the power and pump pressure each appear in only one group.

You have a pump with an $8 \mathrm{in}$. diameter impeller that develops a pressure of $15 \mathrm{psi}$ and requires $1.5 \mathrm{hp}$ to operate when running at $1150 \mathrm{rpm}$ with water at a flow rate of $100 \mathrm{gpm}$. You also have a similar pump with a 13 in. diameter impeller, driven by a $1750 \mathrm{rpm}$ motor, and you would like to know what pressure this pump would develop with water and what power would be required to drive it.

(b) If the second pump is to be operated under equivalent (similar) conditions to the first one, what should the flow rate be?

(c) If this pump is operated at the proper flow rate, what pressure will it develop, and what power will be required to drive it when pumping water?