Symmetries of fluid dynamics with polytropic exponent

The symmetries of the general Euler equations of fluid dynamics with polytropic exponent are determined using the Kaluza-Klein type framework of Duval et $al$. In the standard polytropic case the recent results of O’Raifeartaigh and Sreedhar are confirmed and generalized. Similar results are proved for polytropic exponent $\gamma =-1$, which corresponds to the dimensional reduction of $d$-branes. The relation between the duality transformation used in describing supernova explosion and Cosmology is explained.