Propagation of shock waves in a dusty gas with density obeying the power law

Shock velocity and Mach number are obtained for a shock wave propagating in a dusty gas (mixture of a gas and small solid particles)by use of Whitham's method. The initial density of the medium is assumed to be varying and obeying the power law due to action of a force. The solid particles are considered as a pseudo fluid, and it is assumed that the equilibrium flow conditions are maintained. It is found that the shock velocity and Mach number decrease as the shock radius increases, and the presence of small solid particles in the medium has decaying effect on the shock wave.