4. You are responsible for the design of the convergent nozzle for a turbojet engine fitted to a civil aircraft, as shown in Figure Q4. During operation at an altitude of 10,000 m, the aircraft flies at 300 m/s and the flow exhausts to atmosphere, where the pressure is 26.5 kPa and the temperature is 223 K. In this question, you should treat the flow as quasi-one-dimensional and inviscid. a) The radius of the nozzle satisfies the equation R(x) = 2-0.44x² where both x and R are expressed in metres. What is the area ratio between the nozzle inlet (x = 0.0 m) and the nozzle exit (x = 1.5 m)? b) The turbine exit temperature is the stagnation temperature, To = 400 K, of the flow in the nozzle. Similarly, the turbine exit pressure is the stagnation pressure, Po, of the flow in the nozzle. When the turbine exit pressure is 35 kPa, what is the Mach number at the nozzle exit? c) In a different scenario, the turbine exit pressure is 70 kPa. What is the Mach number of the flow at the nozzle exit? Also determine the Mach number at the nozzle inlet. d) The turbo-machinery team within the company have asked you to specify what exit pressure of the turbines results in perfectly expanded flow, with minimal expansion and compression waves outside the nozzle. What is this turbine exit pressure? p=26.5 kPa T=223 K capture streamtube 100 m combustion compressor chamber turbine nozzle nozzle nozzle inlet. exit. x=0.0 m x=1.5 m Figure Q4: Diagram of turbojet engine p=26.5 kPa T=223 K

4. You are responsible for the design of the convergent nozzle for a turbojet engine fitted to a civil aircraft, as shown in Figure Q4. During operation at an altitude of 10,000 m, the aircraft flies at 300 m/s and the flow exhausts to atmosphere, where the pressure is 26.5 kPa and the temperature is 223 K. In this question, you should treat the flow as quasi-one-dimensional and inviscid. a) The radius of the nozzle satisfies the equation R(x) = 2-0.44x² where both x and R are expressed in metres. What is the area ratio between the nozzle inlet (x = 0.0 m) and the nozzle exit (x = 1.5 m)? b) The turbine exit temperature is the stagnation temperature, To = 400 K, of the flow in the nozzle. Similarly, the turbine exit pressure is the stagnation pressure, Po, of the flow in the nozzle. When the turbine exit pressure is 35 kPa, what is the Mach number at the nozzle exit? c) In a different scenario, the turbine exit pressure is 70 kPa. What is the Mach number of the flow at the nozzle exit? Also determine the Mach number at the nozzle inlet. d) The turbo-machinery team within the company have asked you to specify what exit pressure of the turbines results in perfectly expanded flow, with minimal expansion and compression waves outside the nozzle. What is this turbine exit pressure? p=26.5 kPa T=223 K capture streamtube 100 m combustion compressor chamber turbine nozzle nozzle nozzle inlet. exit. x=0.0 m x=1.5 m Figure Q4: Diagram of turbojet engine p=26.5 kPa T=223 K