LXXXV.Solutions of the boundary-layer equations

Abstract

30. A particular solution of the boundary-layer equations is given for the case where the tangential velocity at the outer limit of the boundary layer is proportional to a power of the distance measured along the boundary from the stagnation point, and the results are presented graphically for a range of values of the index. Iris shown that Blasius' solution for a flat plate is a particular case of this solution. By a consideration of the necessary agreement between the solutioa of the equations of potential flow and that of the boundary-layer equations as the distance along the boundary from the stagnation point is decreased indefinitely, it is shown that the solution of the boundary-layer equations reduces to the particular solution described as the stagnation point is approached. This particular solution is used as a basis for two approximations of varying complexity to the solution in the general case; the second of these gives the correct value of the surface friction. These solutions are given graphically, and the method of application to problems is described. Close agreement is found between the calculated and experimental values of the tangential velocity in the boundary layer for a flat plate and a cylinder and of the surface friction for a cylinder.