Question

17 Marks Shock QUESTION 2 A piston in a tube is suddenly accelerated to a velocity of 50 m's, which causes a normal shock to move into the air at rest in the tube. Several seconds later, the piston is suddenly accelerated from 50 to 100 m's, which, causes a second shock to move down the tube. Calculate the velocities of the two shock waves for an initial air temperature of 300 K. QUESTION 3 50 T2 TOT Air at fet 17 Marks

Answer 1

The air next to the piston must move at the same velocity as the piston, since it can neither move through the face of the piston nor move away from the piston and leave a vacuum behind. Therefore, for a fixed observer, the air velocities are as shown in Figure (13.7).

al = RT1 = V1.4 x 287 x 300 = 347.2m/s

V = (2+1) Vg t 4 tx, 2 4 Vs, = (1.4+1) 50 I (14+1) SD +347.2² 4 V - 30 +348.5=378.5 m/s Msi Vsi & 378.5 =1.090 347.2 tiguse. setting VI Vogt from normal shock table, at M, = 1.090 72 = 1.859 Ti T2 = 300 x 1059=317.7k for second shock, situation is showw in on second ware, (8+1) Mir (8.1) MP +2 Where, V = Vs, - 50 Vg =Vs, -100 Mr. (Ver-50) NRTI suhostituting yields

[248 +2 n VS2-50 2.4x (Vs. -30)" Vsr-10 1.482874317.7 0.4x (voz-50) 1-4X X61X317.7 7 2.4l Vs 2-5o)" 0.4 ( VS-50)+2x 127651.86 selving quadratic equ let na = (Vs₂ - 50) 2.4x² 0.42² +235303.72 0.42 +255303.12 = 2.4m3_120m² In? 1800-275303.12 = 0 Тр — n-50 n= -b I V b²-4ac 120 t 190² + 4xgx 225303.12 ga 2x2 n=120I / 120 tuxrx 255303-7 2x2 - 120 Hyzy. 165 n Vsz-50-388-543 Vs 2 = 438.54m/s

Thus, the second wave travels at a greater velocity than the first and eventually overtakes it. This result is a demonstration of the principles formation of normal shock. Compression waves are able to overtake and reinforce one another. In this example problem, the second wave travels at a greater velocity because it is both moving into the compressed, higher-temperature gas behind the first wave and also moving into a gas stream already traveling in the same direction with a velocity of . A new set of gas properties now can be computed before and after the second shock.