The flow of a compressible fluid through a channel having locally supersonic regions is studied by using the Trinomial equation in the hodograph variables as an approximation in the sonic region to the equation of flow of an irrigational, inviscid gas. It is shown that this is equivalent to studying the flow of a gas having a pressure-density relation matching the isentropic relation to the third derivative at the sonic point. A one-parameter family of solutions of the Trachoma equation is used which provides symmetrical accelerated-decelerated flows. The variation of this parameter alters the Mach number at the center of the throat, the velocity distribution and gradient along the center streamline, as well as the shape of the channel, that is, the curvature of the bounding streamline.
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