If the shock-wave velocity in Problem 5-13 is approximated by the speed of sound, determine the pressure

Question:

If the shock-wave velocity in Problem 5-13 is approximated by the speed of sound, determine the pressure change causing a velocity change of 10 fps in
a. Air at standard conditions
b. Water

Data From Problem 5.13

The shock wave illustrated below is moving to the right at v_w fps. The properties in front and in back of the shock are not a function of time. By using the illustrated control volume, show that the pressure difference across the shock is

P₂ - P₁= p₁ v_w v₂

P1 Uw P2 P1 P2 V1 = 0 U2