LEICESTER 4. Air flows from a reservoir through a converging/diverging nozzle, as shown in Figure~Q4.1. At...

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LEICESTER 4. Air flows from a reservoir through a converging/diverging nozzle, as shown in Figure~Q4.1. At the exit the cross sectional area of the nozzle is Aex=2 cm and the pressure is atmospheric. The pressure and temperature in the reservoir are po=1.6X 105 Pa and To=293 K respectively. A manometer containing mercury (SG=13.56) is connected between the reservoir and section 1 of the nozzle, where the cross sectional area is 1.5 cm, and gives a reading of h=99 cm. The flow between the reservoir and section 1 may be assumed to be isentropic. [Atmospheric pressure may be taken to be 1X 105 Pa] P=1.6x105 Pa T=293 K A=1.5 cm P=105 Pa Ax2 cm h Figure Q4.1 (a) Deduce that the flow must be sonic at the throat. Hence show that the cross-sectional area at the throat, At, is approximately 1.05 cm [5 Marks] (c) Show that a normal shock must lie in the nozzle between the throat and the exit. [3 Marks] (d) If the exit temperature is measured to be 280 K, estimate the exit Mach number. [4 Marks] (e) What is the Mach number of the flow immediately upstream of the shock? [7 Marks] LEICESTER 4. Air flows from a reservoir through a converging/diverging nozzle, as shown in Figure~Q4.1. At the exit the cross sectional area of the nozzle is Aex=2 cm and the pressure is atmospheric. The pressure and temperature in the reservoir are po=1.6X 105 Pa and To=293 K respectively. A manometer containing mercury (SG=13.56) is connected between the reservoir and section 1 of the nozzle, where the cross sectional area is 1.5 cm, and gives a reading of h=99 cm. The flow between the reservoir and section 1 may be assumed to be isentropic. [Atmospheric pressure may be taken to be 1X 105 Pa] P=1.6x105 Pa T=293 K A=1.5 cm P=105 Pa Ax2 cm h Figure Q4.1 (a) Deduce that the flow must be sonic at the throat. Hence show that the cross-sectional area at the throat, At, is approximately 1.05 cm [5 Marks] (c) Show that a normal shock must lie in the nozzle between the throat and the exit. [3 Marks] (d) If the exit temperature is measured to be 280 K, estimate the exit Mach number. [4 Marks] (e) What is the Mach number of the flow immediately upstream of the shock? [7 Marks]