Investigation of velocity field of gas flow moving behind a piston in rectangular branch pipe

The two-dimensional boundary-value problem of the unsteady flow of an incompressible viscous gas moving behind the piston in a “long” rectangular branch pipe is solved. An analytic solution is constructed for two velocity components with a refining polynomial, which reduces to a system of nonlinear algebraic equations after the substitution into the governing system of equations. By virtue of the solution uniqueness of the boundary-value problem under study, the only solution is found from obtained values of the refining polynomial constants for each point of the branch pipe internal space for the velocity components in analytic form.