© 1948 by Oxford University Press
ON THE HODOGRAPH TRANSFORMATION FOR HIGH-SPEED FLOW
I. A FLOW WITHOUT CIRCULATION
( Department of Mathematics, The University Manchester )
In ref. (4) a solution is given to the problem of finding, by use of the hodograph transformation, steady plane isentropic flows round contours, reducing to given incompressible flows when the Mach number at infinity tends to zero. The solution contains an arbitrary function and therefore gives an infinity of such flows for each incompressible flow, when circulation is absent: with circulation, however, only one determination of this arbitrary function is permissible.
In this paper an alternative method of solution is indicated. This method is not so easy to put into a general form, so it is set out for the case when the incompressible flow is the symmetrical one about a circle. Various possible generalizations are indicated. The approach is presented as one which helps to clarify understanding of the use of the hodograph transformation for the study of the flow around bodies and as one which may suggest future investigations on the application of the transr formation. It is shown also how the results obtained for the case studied follow from the method of ref. (4). (We understand that this case is among those studied by Cherry in a paper to appear in the Proceedings of the Royal Society;
the method there used, however, is similar to that of ref. (4): our interest here is in describing the alternative method.)