On the solution of the laminar boundary layer equations.

Abstract

For some years after its suggestion an approximate method of solution of the boundary layer equations due to Kármán and Pohlhausen was thought to be reasonably accurate. The present writer (1934) recommended it for general use because it agreed with experiment as far as the point of separation for the flow past a circular cylinder (when the observed pressure distribution was used in the theoretical solution). There seems to be little doubt that this method gives a reasonably accurate solution in a region of accelerated flow, but more recently its adequacy in a region of retarded flow has been questioned. The flow past a circular cylinder is not an exhaustive test for a retarded region because the pressure rises very rapidly from its minimum value leaving little doubt as to the position of separation. Schubauer (1935) has measured the pressure distribution around an elliptic cylinder of fineness ratio 2∙96:1 and also observed, by introducing smoke just beyond the separation point, the actual position of separation. On applying Pohlhausen’s method to his observed pressure distribution Schubauer fails to find any separation at all. By measurements of the velocity distribution in the boundary layer he finds that Pohlhausen’s method agrees reasonably with the observed one up to a point about five-sevenths of the way between the pressure minimum and the observed point of separation; the calculated distribution then diverges from the observed one.