摘要: Firstly, this paper presents a new expression which changes the isentropic flow equation into Cauchy-Riemann quation, and the exact solution of subsonic flow around an arbitrary two dimensional body is obtained. Secondly, another new affine transformation is employed, with a coordinate transformation, to change the isentropic flow equation into the hyperbolic equation through the transformations. Therefore, an exact solution of transonic flow is obtained. And the two solutions make the variables of velocity, pressure and density contain continuity near the sonic line.