Moving shock

A knowledge of moving shocks is important for studying the phenomena surrounding detonation, among other applications.

This is shown in the figure, with the shock wave propagating to the right.

The velocity of the gas is denoted by u, pressure by p, and the local speed of sound by a.

The speed of the shock wave relative to the gas is W, making the total velocity equal to u1 + W. Next, suppose a reference frame is then fixed to the shock so it appears stationary as the gas in regions 1 and 2 move with a velocity relative to it.

Redefining region 1 as x and region 2 as y leads to the following shock-relative velocities: With these shock-relative velocities, the properties of the regions before and after the shock can be defined below introducing the temperature as T, the density as ρ, and the Mach number as M: Introducing the heat capacity ratio as γ, the speed of sound, density, and pressure ratios can be derived: One must keep in mind that the above equations are for a shock wave moving towards the right.