What is the continuity equation for a moving shock wave?
A. ρ1W = ρ2up
B. ρ1W = ρ2(W – up)
C. ρ1(W + up) = ρ2up
D. ρ1W = ρ2(W + up)
Answer:A
What is the continuity equation for a moving shock wave?
A. ρ1W = ρ2up B. ρ1W = ρ2(W – up) C. ρ1(W + up) = ρ2up D. ρ1W = ρ2(W + up)
Explanation: Continuity equation across a shock wave is given by the formula ρ1u1 = ρ2u2 Where, subscripts 1 and 2 are the sections behind and ahead of the shock wave. The above formula is valid only for stationary wave. For a moving wave, there is a induced gas formation behind the shock wave resulting in (W – up) being the velocity behind the shock wave which is relative to the wave, and W is the velocity of the gas ahead of the shock wave. Thus, the continuity equation becomes: ρ1W = ρ2(W – up) up is the velocity of induced mass motion due to the gas W is the velocity of the normal shock wave.