The mass flow rate of a calorically perfect gas (Cp = constant) through a Convergent-Divergent nozzle is given by, m = A Pt R m= y + 1 +²²) 2(x-1) M (1+ (a) Derive the above relation from fundamental principals. Here, P₁, is total (or Stagnation) pressure and T, is total temperature, M is Mach number, A is local area of nozzle. (b) Prove mathematically that the maximum airflow limit occurs when the Mach number is equal to one and obtain below relation. A Pt R (Y+¹) y + 1 2(y-1) √Tt Note: The limiting of the maximum mass flow rate when M =1, is called choking of the flow or Choked flow.

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