ABSTRACT
The fundamental equations for the velocity components of a compressible flow in terms of the space coordinates are nonlinear because the coefficients of the derivatives of the velocity components are themselves functions of the velocity. Since there is no general method for solving the nonlinear differential equations, it is necessary, in the theoretical investigation of compressible flow problems to linearize the fundamental equations. For two-dimensional steady irrotational flow, the fundamental equations can be linearized by inverting the roles of the dependent and the independent variables, i.e., by expressing the space coordinates or their equivalent in terms of the velocity components. Since the streamline in the plane with velocity components u and v as coordinates, i.e., hodograph plane, is known as hodograph, the method with u and v or q and θ as independent variables is called the hodograph method. The quantity q is the magnitude of the velocity vector, and θ is the angle between the velocity vector and the x-axis, i.e., https://www.w3.org/1998/Math/MathML"> u = q cos θ , v = q sin θ (8.1) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003062158/3c801ad2-7941-4aec-8e9b-25f05722827e/content/math800.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>
