New boundary-layer equations are developed and the solutions match all of the boundary-layer properties, except for the normal velocity, exactly with the corresponding inviscid properties. The numerical procedure solves tridiagonal matrices at each marching station. As part of the solution an inviscid transpiration velocity at the surface is calculated from the boundary-layer solution. This transpiration velocity could be used as a boundary condition to calculate a new inviscid solution. If the inviscid/boundary-layer solutions are interacted, then the normal velocity from the boundary-layer solution will match the inviscid values exactly.
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