Note on the Calculation of Velocity Profiles in the Laminar Boundary Layer on Circular Cylinder placed in a Uniform Stream

Abstract

§7. In a recent paper, GÖRTLER has calculated, by applying a new method proposed recently by PRANDTL, the velocity profiles in the laminar boundary layer on the surface of a circular cylinder placed in a uniform stream. To do this, use has been made of HIEMENZ'S observed values for the velocity U in the main stream at the edge of the boundary layer. His calculated velocity profiles lave bean compared with those given by BLASIUS-HIEMENZ'S method of series as well as with those calculated by using KÁRMÁN-POHLHAUSEN'S method indirectly through some figures given in HOWARTH'S report. Thus GÖRTLER has concluded that the velocity profile calculated by PRANDTL-GÖRTLER'S method lies between the other two given respectively by BLASIUSHIEMENZ'S and KÁRMÁN-POHLHAUSEN'S method However, the results given by the three methods under consideration for the position of the point of separation of the flow seem to suggest that GÖRTLER'S conclusion just mentioned is not at all quite correct. On the contrary, it seems that at least in the neighbourhood of the point of separation, the velocity profile calculated by KARMAN-POHLHAUSEN'S method lies between the corresponding two profiles given by the other two methods.
Since it is of considerable interest to settle the matter, we have calculated afresh the velocity profiles in the laminar boundary layer on a circular cylinder, by employing both BLASIUS-HIEMENZ'S and KÁRMÁN-POHLHAUSEN'S methods and using HIEMENZ'S observed values as given by the formula (2) for the velocity U in the main stream just outside the layer. The velocity profiles thus calculated have been compared with those given by GÖRTLER. Thus, it has been found that the velocity profiles calculated by KÁRMÁN-POHLHAUSEN'S method are rather nearer to the more accurate profiles given by PRANDTL-GÖRTLER'S method than those calculated by BLASIUS-HIEMENZ'S method and that contrary to GÖRTLER'S conclusion in mentioned before, the velocity profile calculated by KÁRMÁN-POHLHAUSEN'S method lies between the corresponding two profiles given respectively by BLASIUS-HIEMENZ'S and PRANDTL-GÖRTLER'S methods, at least in the neighbourhood of the point of separation