Q5 - Moving shock

Question 1

Derive general relations for a moving shock using the general relations for a steady-state
normal shock.

Answer 1

Mass : rho1s = rho2(s-v)

Energy : T1 + (s^2/(2cp)) = T2 + ((s-v)^2/(2cp))

Momentum: P1 + rho1s^2 = P2 + rho2(s-v)^2

Question 2

A normal shock is observed to move through a constant-area tube into air at rest at 20 Degrees C. The
velocity of the air behind the wave is measured to be 170 m/s.
b) Calculate the shock velocity.

Answer 2

% Prandtl relation: v1v2 = cc^2 = (1/k2)c0^2 = (k/k2)RgT0

% v1 = v’1-s = -s, v2 = v’2-s = v-s

% Thus: -s(v-s) = (k/k2)Rg*T0 (1)

% T0 = T1 + v1^2/(2cp) = T1 + s^2/(2cp)

% Substituting T0 into Eq.(1) we obtain an eq.

% with the single unknown s:

% -s(v-s) = (k/k2)Rg(T1 + s^2/(2cp))

% Solving it and selecting the positive root

% s = (1/2)vk2+(1/2)sqrt(v^2k2^2/2+4T1Rg*k)

Question 3

A normal shock is observed to move through a constant-area tube into air at rest at 20 Degrees C. The
velocity of the air behind the wave is measured to be 170 m/s.
(c) Calculate the temperature after the shock.

Answer 3

Find c1 = Sqrt(kRgT1)
Find M1 = s/c1

Find M2^2 = k1M1^2+1)/(kM1^2-k1)

(T2/T1) = (1+k1M1^2)/(1+k1M2^2)
and arrange to find T2

Question 4

(d) Calculate the ratio of pressures across the shock

Answer 4

Calculate (P2/P1)= (k*M1^2 -k1)/k2

Question 5

(e) Calculate the ratio of stagnation pressures across the shock

Answer 5

Calculate (P02/P01) = (T1/T2)^(k/(k-1)) * (P2/P1)

Question 6

(f) Calculate the change in the specific entropy across the shock.

Answer 6

As this is an adiabatic process, the formula

s2-s1 = -Rg * Ln(P02/P01) can be used.