Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/146

§ 96 efflux system, even when the edges are given quite an easy radius. Before discussing this difficulty further another example of motion with a free surface may be given.

'''§ 97. Discontinuous Flow. Pressure on a Normal Plane.'''—In Fig. 47 the stream lines are given for a normal plane on the assumption of continuity. We now have to deal with the same example under different conditions, the form of flow involving discontinuity; a stream of infinite breadth impinges normally on a fixed plane, from the edge of which springs a free surface. The solution to this problem is only known in the particular case of two-dimensional motion where the plane is a lamina of infinite lateral breadth, and is, in the main, due to Kirchhoff. The form of the resulting free surface is given in Fig. 54, in which the direction of flow is taken as vertical. The pressure force for one unit width of the lamina is given by the expression