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3) (25 points) Transonic flow is a mixed subsonic-supersonic flow where the local Mach number is near one. A typical example is the flow over the wing of a high-speed subsonic transport, such as the Boeing 777. When the airplane is flying at a free-stream Mach number 0.8 <M 1.0, there will be a pocket of locally supersonic flow over the wing. This pocket is terminated by a weak shock wave, as illustrated in the figure. Early numerical calculations of such transonic flows over an Shock wave airfoil assumed the flow to be isentropic, hence ignoring the M> entropy increase and total pressure loss across the shock 0.8 <M«<1.0 wave. Assuming the shock wave in the figure is locally a normal shock, M<1 M<1