Since the efficiency of a positive-displacement pump or motor depends, to a great extent, upon the slip flow and the drag developed by moving surfaces, it is essential to proportion slip passages in such a manner that the energy losses are kept to a minimum. In this presentation, the slip flow and the drag on the moving elements are determined on the basis of a theory of laminar flow which takes into consideration the internal heating of the liquid and consequent reduction in viscosity. The optimum clearance, under various operating conditions is determined. It is shown that, under certain circumstances, the optimum clearance is not materially different from that predicted by the constant-viscosity theory. Under other circumstances, the minimum clearance that is physically possible is shown to be the optimum.