Simulation of viscous fluid flow with consideration of boundary outflow and pressure drop

The problem of modeling a viscous fluid flow over the surface of a plate under the condition of pressure changes according to a linear law along the longitudinal coordinate is considered. The boundary conditions for the problem are formulated. The Navier–Stokes equations are solved exactly for the problem of flow past the plate in the case of fluid outflow and a longitudinal pressure drop. Several formulas to determine the velocity profile are derived. The limiting cases are analyzed to study the consistency between various models. The corresponding pressure conditions are proposed for the case when the Navier–Stokes system has an exact solution.