Power P of a centrifugal pump is assumed to be a function of the volume flow rate Q, the impeller diameter D, angular rotation rate , density p, and viscosity of the fluid. Using Buckingham II theorem, rewrite this as a dimensionless relationship between three II groups using: (a) p, and D as the repeated variables. (b) Q, , and p as the repeated variables. (c) Let's call the set of non-dimensional groups from (a) as II, I and II3 and from (b) as N, N, and N3. It may be possible, through appropriate algebraic manipulations, to transform II groups into the N groups. Find how II, Pi2, and Pi3 are related to N, N2, N3.