Correct Answer : ρ1W = ρ2(W – up)
Explaination : 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.