Gas Dynamics and Jet Propulsion – Unit 3 Problem: When a convergent divergent nozzle is operated at off design condition, a normal shock occurs at a section where the cross sectional area is 18.75 cm2 in the diverging position. At inlet to the nozzle, stagnation state is given as 0.21 MPa and 36 0C. The throat area is 12.5 cm2 and exit area is 25 cm2. Estimate the exit mach number, exit pressure and loss in the stagnation pressure for the flow through nozzle.

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Gas Dynamics and Jet Propulsion – Unit 3 Problem: A convergent divergent nozzle is designed to expand air from a reservoir in which the pressure is 800 kPa and temperature is 40 0C to give a mach number at exit of 2.5. The throat area is 25 cm2. Find (a) mass flow rate, (b) exit area and (c ) when normal shock appears at a section where the area is 40 cm2, determine the pressure and temperature at exit.

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Gas Dynamics and Jet Propulsion – Unit 3

Problem: A bow shock occurs in front of a pitot tube when it is used in a supersonic flow field. It measures 16 kPa and 70 kPa for static pressure upstream of the shock and the pressure at the mouth of the tube respectively. Estimate the mach number of the supersonic flow. If the stagnation temperature is 300 0C. Calculate the static temperature and total pressure upstream and down stream of the pitot tube.

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Gas Dynamics and Jet Propulsion – Unit 3

Problem: The ratio of the exit to entry area in a subsonic diffuser is 4.0. the mach number of a jet of air approaching the diffuser at P0 = 1.013 bar, T = 290 K is 2.2. There is a standing normal shock wave just outside the diffuser entry. The flow in the diffuser is isentropic. Determine at the exit of the diffuser (a) mach number, (b) temperature, and (c ) pressure. What is the stagnation pressure loss between the initial and final state of the flow.

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Gas Dynamics and Jet Propulsion – Unit 3 Problem: Air at M = 2.5 enters a convergent duct with a area ratio of A2/A1= 0.5. Normal shock occurs at a test section where At/A1 = 0.6. For this condition find exit mach number and pressure ratio across the duct.

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Gas Dynamics and Jet Propulsion – Unit 3

Problem: A gas (γ = 1.3) at P1 = 345 mbar, T1 = 350 K and M1 = 1.5 is to be isentropically expanded to 138 mbar. Determine (a) the deflection angle, (b) final mach number and temperature of the gas.

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Gas Dynamics and Jet Propulsion – Unit 3

Problem: A jet of air at mach number 2.5 is deflected inwards at the corner of a curved wall. The wave angle at the corner is 60 0. Determine the deflection angle on the wall, pressure and temperature ratios and final mach number.

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Gas Dynamics and Jet Propulsion – Unit 3

An oblique shock wave at angle of 330 occurs at the leading edge of a symmetrical wedge. Air has mach number of 3.2 upstream temperature of 300 K and upstream pressure of 11 bar. Determine (a) Downstream pressure, (b) Downstream temperature, (c ) wedge angle, and (d) downstream mach number.

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Gas Dynamics and Jet Propulsion – Unit 3

Problem: An explosion in air (γ=1.4) creates a spherical shockwave propagating radially into still air at standard conditions. At that instant the pressure just inside the shock is 13.789 bar(abs). Estimate (a) shock speed c ab, (b) air velocity c just inside the shock. Given: Px=1.01325 bar; Tx= 150C = 288 K; Py=13.789 bar

** ** 13.6087 **** ****

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1. Show the shock process in Fanno and Rayleigh line. 2. Why shock is impossible in a subsonic flow?

3. Why rarefaction shocks are not possible?

4. Write the equation for strength of shock. 5. Write the change in entropy across a shock. 6. How would you measure irreversibility of a shock?

7. Is shock an irreversible process?Why?

8. Write the Prandtl Meyer relation. 9. Write the Rankine Hugoniot equation. 10. Differentiate between normal and oblique shocks 11. Define a simple wave. 12. What is a wave motion?

13. Define shock wave. 14. What are the effects of a shock wave?

15. What is a normal shock wave?

16. How do the properties change across a normal shock?

17. Is the flow process across a normal shock equilibrium one?

18. What are the applications of a moving shock?

19. Are the shock waves created by supersonic aircraft desirable?

20. What is a shock polar?

21. Define oblique shock. 22. Differentiate between normal shock and oblique shock. 23. Show Rankine Hugoniot curve.

Gas Dynamics and Jet Propulsion – Unit 3

END of Unit 3

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