On the momentum equation in laminar boundary-layer flow a new method of uniparametric calculation

Abstract

Summary.--The general method of Pohlhausen, which is discussed in detail in Ref. 1, uses a uniparametric system of velocity distributions of the form u/U = f(y/delta) + lamda.g(y/delta). Pohlhausen, by choosing simple forms for the functions f and g, then uses the momentum equation to find the distribution of delta with x and thence the distributions with x of the other boundary-layer characteristics. Several awkwardnesses exist in his method, especially when it is applied to problems dealing with a normal velocity at the boundary. In this paper, a new method is described of combining velocity distributions in the form y/theta = F(u/U) + lamda.G(u/U), and it is shown that such a combination avoids several difficulties. This method of combination also allows a second parameter apart from lamda, which might be found valuable in certain problems. The method has been briefly described before as part of an investigation into the effect of continuous suction on laminar boundary-layer flow under adverse pressure gradients. In that paper (R&M 2514) a numerical example of its use was given. In this paper no example will be given because, as far as the author can see, the practical use of the method is superseded by the generalised method of Ref. 1 : however it possessed considerable analytical interest.