An Integral of the Two-Dimensional Stationary Viscous Fluid Flow Equations

This study demonstrates that the equations for a two-dimensional steady flow of a viscous fluid contain an integral of motion, i.e., they have some function whose gradient is zero in the solutions of hydrodynamic equations A system of partial differential equations has been derived to calculate this function. It has been established that, at a certain integral of motion, the calculation of hydrodynamic fields is reduced to the solution of a system consisting of three first-order partial differential equations with a characteristic manifold. (paper)