The pressure difference ∆p produced by a water pump, and the power P required to operate it, each depend on the size of the pump, measured by the diameter D of the impeller, the volume flow rate ˙q, the rate of rotation ω, the water density ρ and dynamic viscosity µ. (a) Express the non-dimensional pressure difference and power as separate functions of the other non-dimensional groups. (b) Tests on a model pump are performed at 0.5 × full scale, at a rotation rate that is 2 × the full-scale value. To achieve dynamic similarity in the model test: (i) what would the volume flow rate of the water need to be in the model test compared to the full-scale? (ii) What would the pressure difference be compared to the full scale? (iii) What would the power consumption be relative to the full scale?
The pressure difference ∆p produced by a water pump, and the power P required to operate it, each depend on the size of the pump, measured by the diameter D of the impeller, the volume flow rate ˙q, the rate of rotation ω, the water density ρ and dynamic viscosity µ.
(a) Express the non-dimensional pressure difference and power as separate functions of the other non-dimensional groups.
(b) Tests on a model pump are performed at 0.5 × full scale, at a rotation rate that is 2 × the full-scale value. To achieve dynamic similarity in the model test:
(i) what would the volume flow rate of the water need to be in the model test compared to the full-scale?
(ii) What would the pressure difference be compared to the full scale? (iii) What would the power consumption be relative to the full scale?
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