A simple approximate method for determining the self-similarity exponent for concentric shock waves

A very simple formula is derived for the self-similarity exponent for a convergent concentric shock wave in gas. The agreement with the accurate solution is very good, the error being below 5%. The formula obtained enables us to avoid the tedious procedure of determining the self-similarity exponent by solving a boundary value problem for a complicated set of nonlinear equations. The present method is based on the analogy with the plane wave problem in a nonhomogeneous body of decreasing density. (author)