The GATE Grind

GATE 2021 AE – Question 43

Aerodynamics · Compressible flows: isentropic flow, normal and oblique shocks, Prandtl-Meyer flow, nozzles and diffusers · 2 marks · Multiple select

A normal shock moves into stationary gas. Unprimed properties use the laboratory frame; primed properties use the shock-fixed frame. Subscripts 1,2 denote upstream,downstream and 0 stagnation. Which sets hold?

source diagram and its labels are reproduced in the attached image.
  1. $T_1^\prime>T_1,\ T_{01}^\prime>T_{01},\ p_{01}^\prime>p_{01},\ \rho_2^\prime>\rho_1^\prime$
  2. $T_1^\prime=T_1,\ T_2^\prime<T_{01}^\prime,\ p_{01}^\prime>p_{01},\ \rho_2^\prime=\rho_2$
  3. $T_1^\prime<T_1,\ p_1^\prime>p_1,\ p_{01}^\prime>p_{01},\ \rho_2^\prime>\rho_1$
  4. $T_1^\prime=T_1,\ p_2^\prime>p_{01},\ T_{01}^\prime>T_{01},\ p_{01}^\prime>p_{01}$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (B) $T_1^\prime=T_1,\ T_2^\prime<T_{01}^\prime,\ p_{01}^\prime>p_{01},\ \rho_2^\prime=\rho_2$; (D) $T_1^\prime=T_1,\ p_2^\prime>p_{01},\ T_{01}^\prime>T_{01},\ p_{01}^\prime>p_{01}$

Explanation

Static thermodynamic properties are invariant under Galilean transformation, so T1′=T1 and ρ2′=ρ2. The stationary upstream gas has p01=p1; the shock raises p2 and upstream-relative kinetic energy raises T01′ and p01′.