Question 1 Air ( 1.4, R = 287 J/(kg K)) flows from a very large reservoir...

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Question 1 Air ( 1.4, R = 287 J/(kg K)) flows from a very large reservoir through a convergent- divergent nozzle. The air in the reservoir is kept at a constant temperature of To =300 K. The exit area is AE = 10 cm and the throat area is AT = 6.45 cm. When the back pressure is P100 kPa (absolute), the pressure distribution as measured along the centre-line shows a discontinuity at the exit as shown schematically in Figure 1. The flow may be assumed adiabatic for all conditions and isentropic in the absence of shocks. To P/P air AT A m Pb Figure 1: Top: Convergent-divergent nozzle attached to a large air reservoir. Bottom: Pressure distribution along the nozzle centre-line for a back pressure of Pb. (a) What is the total pressure Po in the reservoir. (b) What is the speed of the flow and the temperature directly downstream of the exit? (c) What is the mass flow rate? (d) What is the lowest back pressure for which the flow will be subsonic throughout the channel? What will be the mass flow rate at this back pressure? Question 1 Air ( 1.4, R = 287 J/(kg K)) flows from a very large reservoir through a convergent- divergent nozzle. The air in the reservoir is kept at a constant temperature of To =300 K. The exit area is AE = 10 cm and the throat area is AT = 6.45 cm. When the back pressure is P100 kPa (absolute), the pressure distribution as measured along the centre-line shows a discontinuity at the exit as shown schematically in Figure 1. The flow may be assumed adiabatic for all conditions and isentropic in the absence of shocks. To P/P air AT A m Pb Figure 1: Top: Convergent-divergent nozzle attached to a large air reservoir. Bottom: Pressure distribution along the nozzle centre-line for a back pressure of Pb. (a) What is the total pressure Po in the reservoir. (b) What is the speed of the flow and the temperature directly downstream of the exit? (c) What is the mass flow rate? (d) What is the lowest back pressure for which the flow will be subsonic throughout the channel? What will be the mass flow rate at this back pressure?