The Substitution Principle established by Munk and Prim for flows of a gas having constant specific heats is extended to the wider class of fluids having a state equation of the form &rgr;=P(p)S(s). The equations of motion for this class of fluids is reduced to a canonical form involving only the reduced velocity vector and the pressure. It is shown that explicit elimination of the pressure from these equations is possible only for those fluids whose state equation has the form &rgr;=pkS(s) withk<1. Relations between the Mach number and stagnation pressure and the reduced velocity field are discussed for the class of fluids under investigation.