On the solution of the laminar boundary layer equations

Summary

In the first part of paper, the momentum equation of the incompressible laminar boundary layer is solved for the velocity distribution outside the boundary layer of the form U = U ₀ — bxⁿ. It is found from results of solution that the frequently used parameter λ = (θ²/v) (d U/d x) cannot exactly fix the velocity profile, its value at separation becoming less negative as d² U/x² becomes more positive. In the second part, a simple approximate method of solution is developed, in which the velocity profile is expressed as a member of a family of curves, with the parameter α different from λ. It is found that results of sufficient accuracy can be obtained by calculating λ from a quadrature formula and determining the relation between λ and α from the momentum and energy integrals of the boundary layer. The method of solution can easily be extended to the boundary layer of a compressible fluid.