The affinity law modified for viscosity effects is further extended to include the power input and efficiency. The power input and efficiency data generated using computational fluid dynamics (CFD) are utilized to represent dimensionless power coefficient and efficiency for the pump under consideration. The goal of modifying the affinity laws for power input is achieved by developing a new relationship where the power coefficient is modified by multiplying it by rotational Reynolds number raised to a power $Π*Rew−Pat$. This new relationship is then represented as a function of a modified flow coefficient $ф*Rew−Mo$. All the data collapse onto a single curve for varying values of the exponents Morrison number (Mo) and Patil number (Pat). Pat is further characterized as a function of flow regime and specific speed. The method also holds true for efficiency prediction, however, with different values of Mo and Pat. The proposed method is validated by using data collected from published literature.

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