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Consider isentropic flow through a converging nozzle. The total (reservoir) pressure and temperature are p, and Ty, respectively, and the ambient pressure is p,. A static pressure gauge at the nozzle exit measures the exit static pressure p,. (a) Nozzle choking is a compressible flow effect that obstructs the flow, setting a limit to fluid velocity because the flow becomes supersonic and perturbations cannot move upstream; in a subsonic flow, choking takes place when the exit Mach number reaches 1. Derive and calculate the critical pressure ratio 3 = p,/py at which the nozzle is choked. (b) Find an expression or expressions for p./po in terms of p,/po and sketch (in a plot) Pe/Po versus p,/py. (c) Find an expression or expressions for the exit Mach number M, in terms of p,/p, and sketch M. versus p,/po. (d) Find an expression for the dimensionless exit velocity u./+/RT, in terms of M, and sketch w, versus pa/po. [n all the above relations and plots, p,/py will range from 0 to 1. Mark clearly any critical values/points, including the starting and ending values on both the abscissa and ordinate in your plots