3 Control volume analysis (40 pts) In lecture, we derived an expression for thrust using a control volume whose left edge was upstream of the engine intake and whose right edge

was at the exit plane. Now consider a control volume (depicted in Figure 2), where the left edge is at the intake and whose right edge is far downstream of the engine outlet. Ambient air moving at speed u relative to the aircraft slows down and compresses as it moves into the inflow duct of the engine. We measure the state and velocity of the air at station i, inside the inlet, and at station d. some distance downstream where the pressure phas returned to atmospheric AEROSP 335 (Winter 2024) AEROSP 335 (Winter 2024) "₂ Pa A₂ 44, P A₁ 2 "₂ Pa = Pa A₂ Jorns Jormes Figure 1: Engine diagram for problem 3 pressure på. The fuel fraction of the engine is f. Use this control volume to answer the following questions: a) (15 pts) Write down the integral form of conservation of momentum in this control volume. Label all terms. b) (15 pts) Starting from your answer in part (a), derive an expression for the thrust in terms of ui, ud. Pi, Pa, Ai, f, and ma. c) (10 pts) Compare your result to the expression we derived in class. Why do you think we use the expression derived in class rather than the one from part (b)?