The most general form of the equation, suitable for use in thermodynamics in case of (quasi) steady flow, is:
Here  is the enthalpy per unit mass (also known as specific enthalpy), which is also often written as  (not to be confused with "head" or "height").
Note that
where  is the thermodynamic energy per unit mass, also known as the specific internal energy. So, for constant internal energy  the equation reduces to the incompressible-flow form.
The constant on the right-hand side is often called the Bernoulli constant and denoted . For steady inviscid adiabatic flow with no additional sources or sinks of energy,  is constant along any given streamline. More generally, when  may vary along streamlines, it still proves a useful parameter, related to the "head" of the fluid (see below).
When the change in  can be ignored, a very useful form of this equation is:
where  is total enthalpy. For a calorically perfect gas such as an ideal gas, the enthalpy is directly proportional to the temperature, and this leads to the concept of the total (or stagnation) temperature.
When shock waves are present, in a reference frame in which the shock is stationary and the flow is steady, many of the parameters in the Bernoulli equation suffer abrupt changes in passing through the shock. The Bernoulli parameter remains unaffected. An exception to this rule is radiative shocks, which violate the assumptions leading to the Bernoulli equation, namely the lack of additional sinks or sources of energy.