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The flow of blood as a viscous, Newtonian, incompressible liquid in an expanding spherical cavity with a ball-type inlet valve was examined. This type of flow can serve as a model of the phase of ventricular diastole in a sac-type artificial heart. The critical values of Reynolds numbers at which flow interruption behind the valve occurs were found. The optimum geometric ratios of the dimensions of the ventricular cavity and valve that permit a decrease in the input resistance of the cavity, the size of the valve, and the surface tensions in the bloodstream were determined.