Pressure calculation for a fluid flowing in a plane wedge-shaped layer with account for inertial forces

The Reynolds equations are solved with account for inertial forces in a plane wedge-shaped layer using the Slezkin-Targ method. The analytical expressions determining the dimensionless longitudinal velocity, hydrodynamic pressure, and total pressure force as functions of the lubricating Reynolds number and dimensionless parameter of the problem are obtained. A new method for solving the Reynolds equations is proposed accounting for inertial forces and avoiding averaging the inertial terms with respect to the gap height. The numerical analysis of the proposed method shows that in the first and second approximations, the deviations for the total hydrodynamic pressure force in a plane wedge-shaped layer differ little from each other in the considered range of the lubricating Reynolds number for varying dimensionless parameter of the problem, but exceed the deviation obtained using the Slezkin-Targ method. The coincidence of the first approximation with the second one gives ground to believe that the proposed method is more accurate for calculating the total hydrodynamic pressure force in the fluid flow occurring in a plane wedge-shaped layer.