text: Potential flow theory can also be used to model irrotational compressible flow. The derivation of the governing equation for  from Eulers equation is quite straightforward. The continuity and the (potential flow) momentum equations for steady flows are given by
  where the last equation follows from that fact that entropy is constant for a fluid particle and that square of the sound speed is . Eliminating  from the two governing equations results in
  The incompressible version emerges in the limit . Substituting here  results in
  where  is expressed as a function of the velocity magnitude . For a polytropic gas, , where  is the specific heat ratio and  is the stagnation enthalpy. In two dimensions, the equation simplifies to 
  Validity: As it stands, the equation is valid for any inviscid potential flows, irrespective of whether the flow is subsonic or supersonic (e.g. Prandtl–Meyer flow). However in supersonic and also in transonic flows, shock waves can occur which can introduce entropy and vorticity into the flow making the flow rotational. Nevertheless, there are two cases for which potential flow prevails even in the presence of shock waves, which are explained from the (not necessairly potential) momentum equation written in the following form
  where  is the specific enthalpy,  is the vorticity field,  is the temperature and  is the specific entropy. Since in front of the leading shock wave, we have a potential flow, Bernoulli's equation shows that  is constant, which is also constant across the shock wave (Rankine–Hugoniot conditions) and therefore we can write
  1) When the shock wave is of constant intensity, the entropy discontinuity across the shock wave is also constant i.e.,  and therefore vorticity production is zero. Shock waves at the pointed leading edge of two-dimensional wedge or three-dimensional cone (Taylor–Maccoll flow) has constant intensity. 2) For weak shock waves, the entropy jump across the shock wave is a third-order quantity in terms of shock wave strength and therefore  can be neglected. Shock waves in slender bodies lies nearly parallel to the body and they are weak.
  Nearly parallel flows: When the flow is predominantly unidirectional with small deviations such as in flow past slender bodies, the full equation can be further simplified. Let  be the mainstream and consider small deviations from this velocity field. The corresponding velocity potential can be written as  where  characterizes the small departure from the uniform flow and satisfies the linearized version of the full equation. This is given by
  where  is the constant Mach number corresponding to the uniform flow. This equation is valid provided  is not close to unity. When  is small (transonic flow), we have the following nonlinear equation
  where  is the critical value of  and  is the specific volume. The transonic flow is completely characterized by the single parameter , which for polytropic gas takes the value . Under hodograph transformation, the transonic equation in two-dimensions becomes the Euler–Tricomi equation.