New boundary-layer equations are developed and the solutions match all
of the boundary-layer properties, except for the normal velocity, exa
ctly with the corresponding inviscid properties. The numerical procedu
re solves tridiagonal matrices at each marching station. As part of th
e solution an inviscid transpiration velocity at the surface is calcul
ated from the boundary-layer solution, This transpiration velocity cou
ld be used as a boundary condition to calculate a new inviscid solutio
n. If the inviscid/moundary-layer solutions are interacted, then the n
ormal velocity from the boundary-layer solution will match the invisci
d values exactly. Solutions are calculated for shear flows over a flat
plate, Results from the present method compared well with Navier-Stok
es solutions for incompressible constant shear flow and sinusoidal she
ar Bow. Iterations of the inviscid/boundary-layer solutions were not n
ecessary. Compressible flow of an exponential shear at Mach 3 was calc
ulated for cold and hot walls. It was found that inviscid/boundary-lay
er interactions were significant for hot walls but negligible for cold
walls. The present method should yield accurate boundary-layer soluti
ons at Reynolds numbers lower than the traditional boundary-layer equa
tions.