Studies on Two - Dimensional Transonic Flows of Compressible Fluid . — Part Iii

13. The introduction of a second new hypothetical gas. In the foregoing sections, we have investigated some transonic fields of flow by employing a hypothetical gas which closely approximates the real gas during an isentropic flow in the transonic range. Although such a hypothetical gas has a merit that the fundamental equation governing its flow assumes a rather simple form and can be solved exactly in several cases, it has the drawback that it can approximate the real gas obeying the isentropic law only for a limited (transonic) range of velocities. Thus, the method of analysis as developed in the foregoing sections has a rather narrow application; it can be applied only to nearly uniform transonic flows. In Part III, an attempt is made to develop a theory which is applicable even to a transonic flow containing limited supersonic regions as well as stagnation points. For this purpose, we have introduced a second hypothetical gas which is capable of representing the real gas subject to the isentropic law with a better degree of approximation than that used in Parts I and II. For the sake of convenience, we start from the linearized equations of motion in the hodograph plane which are valid for any compressible perfect fluid. They can be written in the following forms: