Laminar boundary layers at the interface of co-current parallel streams

The approximate solution of Keulegan (1) for the steady flow of a stream of viscous incompressible fluid over another at rest is extended to the case where both fluids are moving co-current but at different velocities. This solution utilizes a sextic polynomial for the velocity distribution in the boundary layers. The solutions depend only on the ratio U₂/U₁ of the velocities of the two streams and on the product of the corresponding viscosity and density ratios. Numerical results are given for seven values of μ₂ ρ₂/(μ₁ρ₁) at one value of U₂/U₁. Lock (2) has published an exact solution with a numerical result for μ₂ρ₂/(μ₁ρ₁) = 1, U₂/U₁ = 0.501 and the sextic polynomial solution is evaluated for this case also. Comparison indicates that in general the sextic polynomial is more accurate than the quartic polynomial but that the advantage is not great.