In a laboratory test rig, air flows from a high pressure upstream supply, through a convergent-divergent nozzle, and into a test section (with some area change) where heat is added to the flow. The downstream end of the test section is terminated by a convergent nozzle which serves the function of back-pressuring the system. A schematic diagram of this system is given in the Figure 1, below. Both throats (stations 1 and 4) are choked. The flow in the two convergent sections may be taken as isentropic, but a shock exists in the divergent section of the C-D nozzle (between Stations 1 and 2). The force (Fx) acting on the test section (between Stations 2 and 3) is known from measurement. (a) Given stagnation conditions in the upstream supply reservoir (p0, T0) and the areas (A1, A2, A3, and A4), develop the equations to compute the stagnation pressure at Stations 2, 3 and 4 for various amounts of heat addition, where To = To,3 To,2. Explain your steps and state all assumptions. Your formulation should be explicit (i.e. iteration should not be required) apart from having to solve a Mach number function for the Mach number at specific locations