# Moving shock

In fluid dynamics, a **moving shock** is a shock wave that is travelling through a fluid (often gaseous) medium with a velocity relative to the velocity of the fluid already making up the medium.^{[1]} As such, the normal shock relations require modification to calculate the properties before and after the moving shock. A knowledge of moving shocks is important for studying the phenomena surrounding detonation, among other applications.

## Contents

## TheoryEdit

To derive the theoretical equations for a moving shock, one may start by denoting the region in front of the shock as subscript 1, with the subscript 2 defining the region behind the shock. 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 *u _{1}* +

*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. For a shock moving towards the left, the *x* and *y* subscripts must be switched and:

## See alsoEdit

## ReferencesEdit

**^**Shapiro, Ascher H.,*Dynamics and Thermodynamics of Compressible Fluid Flow,*Krieger Pub. Co; Reprint ed., with corrections (June 1983), ISBN 0-89874-566-7.