Chapter 11 - Shocks

Question 1

Shock wave definition

Answer 1

A discontinuity in a fluid separating regions of different thermodynamic properties and velocities.

Question 2

Why discontinuity occurs

Answer 2

Supersonic flows cannot receive information upstream via pressure waves traveling at sound speed.

Question 3

Key conserved quantities across a shock

Answer 3

Mass, momentum, and energy (in the shock-fixed frame).

Question 4

Mass conservation equation

Answer 4

ρ1 u1 = ρ2 u2

Question 5

Momentum conservation equation

Answer 5

p1 + ρ1 u1^2 = p2 + ρ2 u2^2

Question 6

Energy conservation equation

Answer 6

h1 + u1^2/2 = h2 + u2^2/2

Question 7

Mach number relation across shock

Answer 7

M2^2 = (1 + (γ-1)/2 M1^2) / (γ M1^2 - (γ-1)/2)

Question 8

Behavior of Mach number across shock

Answer 8

Supersonic before shock (M1>1), subsonic after shock (M2<1).

Question 9

Density ratio limit for strong shocks

Answer 9

(ρ2/ρ1)max = (γ+1)/(γ-1)

Question 10

Weak shock definition

Answer 10

Shock where M1 ≈ 1 so changes in properties are very small.

Question 11

Entropy change significance

Answer 11

Entropy increases across a real shock; stagnation pressure decreases.

Question 12

Can a shock turn subsonic to supersonic?

Answer 12

No, forbidden by second law because entropy would decrease.