Abstract
A second-order nonlinear differential equation is derived for the pressure of a compressible flow with slip at the wall through a constricted cylinder. The ideal gas equation of state is used, and the Karman-Pohlhausen method is utilised to derive the pressure differential equation from the Navier-Stokes equations of motion for a Newtonian viscous fluid. The solution for pressure is determined numerically and assessed in various flow geometries. This work is an extension of existing assessments in that nonlinear terms are kept in the differential equation for pressure, as well as second-order derivative terms. Additionally, wall slip and compressibility are incorporated in the equations, as well as geometries that are asymmetric with respect to the location of maximum constriction.
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