An aircraft engine is operating at an ambient pressure and temperature of P_∞ and T_∞. The mass flow rate through the engine is m˙ and the air enters with a velocity of u_∞. Consider the following two choices for the nozzle:

• Convergent with the flow choked at the exit, and

• Convergent divergent with the flow at the exit correctly expanded.

In each case, express the thrust in terms of the quantities given above as well the stagnation pressure P₀ and temperature T₀ in the nozzle. Simplify the expressions by substituting γ = 4/3. Demonstrate that the thrust produced by the convergent divergent nozzle is always greater. You may assume the flow in the nozzle to be isentropic.