A shock wave moves down a pipe as shown below. The fluid properties change across the shock,

Question:

A shock wave moves down a pipe as shown below. The fluid properties change across the shock, but they are not functions of time. The velocity of the shock is v_w. Write the continuity equation and obtain the relation between p₂, p₁, v₂, and v_w. The mass in the control volume at any time is M = p₂Ax + p₁Ay. Use a control volume that is moving to the right at velocity v_w.