The power input P to a centrifugal pump is assumed to be a function of the volume flow rate, Q, impeller diameter, d, angular velocity, theta, and the density, row, and viscosity, u, of the fluid.
(i) How many (non-dimensional) Pi-groups are there?
(ii) Find these non-dimensional groups.
(iii) Can one of the Pi-groups be considered a Reynolds number?
(iv) Express the non-dimensional power in terms of its dependence on the other non-dimensional groups.
(v) Consider two pumps, #1 and #2, both operating in the same fluid. If each pump has the same power input P and the same volume flow rate Q, but pump #1 has a diameter that is twice that of pump #2, i.e. d1 = 2d2, can full similarity between the pumps be achieved?