The energy per unit mass (of fluid), e, added by a pump of a given shape depends on the pump size, D, volume flow rate, Q, speed of the rotor, ω, density of the fluid, ρ, and dynamic viscosity of the...

The energy per unit mass (of fluid), e, added by a pump of a given shape depends on the pump size, D, volume flow rate, Q, speed of the rotor, ω, density of the fluid, ρ, and dynamic viscosity of the fluid, µ. This functional relation can be stated as

        e = f(D, Q, ω, ρ, µ)

Express this as a relationship between dimensionless groups. What is gained by expressing the pump performance as an empirical relationship between dimensionless groups versus expressing the pump performance as a relationship between the given dimensional variables?