The power input P of a rotary pump is a function of the volumetric flow rate Q, the diameter of the pump D, the rotational rate 12, the fluid density p, and fluid viscosity u. Use dimensional analysis to demonstrate thatP /pΩ^3 D^5 = f (Q/ΩD^3, u/ pΩ^2Use Ω, p, and D as the repeating parameters and Use M, L, t as the primary dimensional. Hint: The dimensions of P and Ω are mL^2t^3 and t^-1, respectively.
