Consider a system of governing equations for 1-D, isentropic, inviscid, PROBLEM 1 (35 points) compressible flow др ap au

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Consider a system of governing equations for 1-D, isentropic, inviscid, PROBLEM 1 (35 points) compressible flow др ap au + u + p = 0 ax ди 1 др +0+ = 0 at р дх 15313 дх = Where, p = Cp(C=const.) and a? = v. Here a is the speed of sound and y = ratio of specific heats. Problem 1-1) Show that this system of equation is hyperbolic type of PDE (10 points) Problem 1-2) Show that the characteristics are given by a = u fa (10 points) Problem 1-3) Show that the given equations can be written as follows: (15 points) 2a dx -+u) = 0 along dt Ly - 1 dt – u) = 0 along dt d = u + a d 2a dx =U - a dt - 1