This study proposes a method of predicting hemolysis induced by turbulent shear stress (Reynolds stress) in a simplified orifice pipe flow. In developing centrifugal blood pumps, there has been a serious problem with hemolysis at the impeller or casing edge; because of flow separation and turbulence in these regions. In the present study, hemolysis caused by turbulent shear stress must occur at high shear stress levels in regions near the edge of an orifice pipe flow. We have computed turbulent shear flow using the low-Reynolds number k-epsilon model. We found that the computed turbulent shear stress near the edge was several hundreds times that of the laminar shear stress (molecular shear stress). The peak turbulent shear stress is much greater than that obtained in conventional hemolysis testing using a viscometer apparatus. Thus, these high turbulent shear stresses should not be ignored in estimating hemolysis in this blood flow. Using an integrated power by shear force, it is optimal to determine the threshold of the turbulent shear stress by comparing computed stress levels with those of hemolysis experiments or pipe orifice blood flow.