On an invariant transformation of equations of one-dimensional non-steady gas flows

Reciprocal relations are constructed for the unsteady one-dimensional flow of an inviscid gas using suitable transformations under which the basic equations of gasdynamics remain invariant. A new flow plane, (x prime, t prime) is introduced in addition to the initial space-time flow plane, (x,t). A very general class of solutions is obtained in the (x prime, t prime) plane by linking a known solution on the (x,t) plane with a four-parameter class of solutions in the (x prime, t prime) plane, each with its own equation of state. The procedure is extended to the case of (n plus 1) dimensional spherically symmetrical flows.