In the previous paper, the optimum meridian profile of impeller was obtained for various specific speed by means of eight shape factors, that is, inlet relative flow angle β1, turning angle Δβ, axial velocity ratio kc = Cm2/Cm1, impeller diameter ratio kd = D1c/D2c, outlet hub-tip ratio ν2, tip solidity σtimp, mid span solidity σcimp and hub solidity σhimp. In this paper, the optimum meridian profile of multi-stage impeller with guidevane was obtained by means of twelve shape factors. The additional four shape factors are guidevane tip solidity σtgv, mid span solidity σcgv, hub solidity σhgv and coefficient of peripheral velocity at impeller inlet or guidevane outlet kCu1c. In the optimum method, the hydraulic efficiency and suction specific speed are calculated by diffusion factor. In the optimum condition, the best hydraulic efficiency or the best suction specific speed is obtained. In the cyclic flow condition of multi-stage impeller with guidevane, the absolute flow velocity of guidevane outlet is equal to that of impeller inlet, and the diameter of guidevane outlet is equal to that of impeller inlet. In this calculation, the diameter of impeller outlet is equal to that of guidevane inlet. The total calculation number of case study is very large, so the number of each parameter is about between four and seven. The best 1000 optimum meridian profiles and the best design parameter are selected for few kinds of specific speed using twelve dimensional optimum method. As the result of this calculation, the optimum meridian profile of multi-stage impeller and guidevane. The more detailed optimum multi-stage mixed flow impeller and guidevane profile is drawn. For, example, the 1000 specific speed is selected for case study of multi-stage mixed flow impeller. At first, the approximate optimum shape factors are present shape factors. And the optimum shape factors which have better efficiency are tried to find near the present shape factors. Then the study of shape factor changes is the objective of this paper.

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