| Summary: | By means of finite Fourier transtorms the Green's function and hence the general solution is found for the Chaplygin equation of motion for an important class of flows i.e. 2-dimensional non-viscous compressible 'simple wedge flows' with circular sector hodographs (these flows have been defined and classified according to their hodograph diagrams by Birkhoff and Zarantonello). From the particular case of Réthy flows the solution is used to find the drag coefficient, firstly in an exact analytical form and then, for sonic jet flows past thin wedges, as a series inascending powers of the wedge angle; comparisons are made with the results obtained from the approximate equations of Tricomi and of Tomotika and Tamada. The study of sonic Réthy flows of small wedge angle is taken further and series which are uniformly valid for all possible source velocities are found for the wedge length and stand-off (i.e. distance of the wedge from the channel) in terms of the (small) wedge angle. From these series certain limitations on the lengths and pressure differences can be determined. Some examples of the general solution (including the solution for Réthy flows) are discussed in relation to earlier published papers and a discrepancy in some Russian papers is explained. The thesis ends with a theorem on sonic jets. This states that for simple wedge flows involving sonic jets, the physical changes due to the presence of solid boundaries in the flow are compared withina finite distance in those directions in which sonic jet flow prevails.
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