Steady, turbulent two-phase fluid flow in a rotating annular seal with no eccentricity is analyzed. The fluid is assumed to be a homogeneous mixture of liquid and vapor in thermodynamic equilibrium. Further, the flow is assumed to be adiabatic, but the effects due to heat generation by viscous dissipation are accounted for fully. Solution of the model governing differential equations is accomplished by use of a fourth-order Runge-Kutta numerical integration scheme.