8/19/2019 AE221_16_Tut_04

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AE221 Gas dynamics(2015-16, II Semester)

Tutorial – 4

1. A normal shock moves into still air with a velocity of 1,000 m/s. The motionless air is at101 kPa and 20◦C; calculate the following: (a) the velocity of the air flow behind the wave,(b) the static pressure behind the wave, and (c) the stagnation temperature and pressure

 behind the wave.

2. A normal shock traveling at 1,000 m/s into still air at 0◦C and 101 kPa reflects from a planewall. Determine the velocity of the reflected shock. Compare the pressure ratio across thereflected shock with that across the incident shock. Find the stagnation pressure thatwould be measured by a stationary observer behind the reflected wave.

3. A normal shock moves down a tube with a velocity of 600 m/s into a gas with staticpressure of 50 kPa and static temperature of 300 K. At the end of the tube, a piston is

moving with a velocity of 60 m/s. Calculate the velocity of the reflected wave and thestatic pressure behind the reflected wave.

4. A shock tube is to be used to subject an object to momentary conditions of high pressureand temperature. To provide an adequate measuring time, the tube is to be made longenough so that a period of 100 ms is provided between the time of passage over the bodyof the initial shock and the time of passage of the shock reflected from the closed endof the tube. The initial pressure ratio across the diaphragm is 400 to 1 (pressure ratioacross the shock wave is 9.29), with the object located 3 m from the diaphragm. Theinitial temperature of the air in the shock tube is 35◦C. Determine a suitable length for thelow-pressure end of the tube.

5. A projectile moves down a gun barrel with a velocity of 500 m/s. Calculate the veloc-ity of the normal shock that would precede the projectile. Assume the pressure in theundisturbed air to be 101 kPa and the temperature to be 25◦C.

6. A piston in a tube is suddenly accelerated to a velocity of 25 m/s causing a normal shockto move into air at rest in the tube and at a temperature of 27◦C in the tube. One secondlater, the piston is suddenly accelerated from 25 to 50 m/s causing a second shock to movedown the tube. How much time will elapse from the initial acceleration of the piston tothe intersection of the two shocks?

7. Air at 100 kPa and 290 K is flowing in a constant- area tube with a velocity of 50 m/s

which is connected to large tank. The length of the tube is 1 m. Suddenly the end of thetube is closed, which causes a normal shock to propagate back through the airstream. (a)Find the absolute velocity of this shock and (b) How long it will take for the flow to stopin the tube.

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