An exact partial solution to the compressible flow problems of jet formation and penetration in plane, steady flow

A partial solution to the problem of the symmetric impact of two compressible fluid streams is derived. The plane, two-dimensional flow is assumed to be steady, and the inviscid, compressible fluid is of the Chaplygin (tangent gas) type. The equations governing this flow are transformed to the hodograph plane where an exact, closed-form solution for the stream function is obtained. The distribution of fluid properties along the plane of symmetry and the shape of free surface streamlines are determined by transformation back to the physical plane. The problem of a compressible fluid jet penetrating an infinite target of similar material is also solved by considering a limiting case of this solution. Differences between compressible and incompressible flows of the type considered are illustrated.