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In centrifugal rotary blood pumps (RBP), clearances are a critical parameter in determining blood trauma. This study investigates the effect of axial clearance (Cax) and radial clearance (Crad) on the hydrodynamic and hemolytic performance of a centrifugal RBP. A centrifugal pump was parameterized so that it could be defined by geometric variables Cax and Crad. Optimal Latin hypercube sampling was used to determine design points based on Cax, Crad, and rotor speed (ω). For each design point, a computational simulation was conducted to determine efficiency (η) and normalized index of hemolysis (NIH). Next, a response surface (RS) was created to estimate these performance parameters based on the design variables. The results show that for a given Cax, when Crad is decreased, η increases until Crad = 0.15 mm, beyond which η deceases. For a given Crad, Cax has a unimodal relationship with η. The NIH has a unimodal relationship with both Cax and Crad. The mechanisms behind these relationships were investigated by various analytical methods. It was found that vortices in the secondary flow paths were a critical factor in determining efficiency and hemolysis. The optimal clearance values discerned in this study are only valid for the specific impeller geometry and operating conditions analyzed.