The purpose of this research is to investigate the flow behavior inside a mixed flow type pump operating with fluids of different viscosities using computational fluid dynamics (CFD) with the goal to establish additional terms for the pump affinity laws to scale pump performance including the effects of viscosity. Several sets of fluids of different viscosities and densities are simulated under various operating conditions. The effect of viscosity on the performance of the impeller and diffuser is discussed. Changes in the pump performance due to fluid viscosity are characterized using the dimensionless flow coefficient, head coefficient, and rotational Reynolds number. The result, which can be regarded as the modified pump affinity laws for viscosity flows, was obtained based on the relationships between dimensionless coefficients. The modified affinity laws agreed well with the CFD results. Further study was conducted to validate the relationships using previously published test data for a semi axial pump design (specific speed, $Ns$: 3869) tested with fluid viscosity ranging from 1 cp to 1020 cp and in-house testing of a split vane impeller pump ($Ns$: 3027) and a helicoaxial pump ($Ns$: 5281) using 1 cp and 5 cp viscosity fluid. The modified affinity laws accurately models the performance dependence upon viscosity. As with the standard affinity laws, a pump's functional relationship varies with each pump design. Yet the modified affinity laws produce a single common curve for all operating conditions and viscosities for a specific pump.

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