For a compressible fluid, with a barotropic equation of state, and under the action of conservative forces,
where:
* is the pressure
* is the density and  indicates that it is a function of pressure
* is the flow speed
* is the potential associated with the conservative force field, often the gravitational potential
In engineering situations, elevations are generally small compared to the size of the Earth, and the time scales of fluid flow are small enough to consider the equation of state as adiabatic. In this case, the above equation for an ideal gas becomes:
where, in addition to the terms listed above:
* is the ratio of the specific heats of the fluid
* is the acceleration due to gravity
* is the elevation of the point above a reference plane
In many applications of compressible flow, changes in elevation are negligible compared to the other terms, so the term  can be omitted. A very useful form of the equation is then:
where:
* is the total pressure
* is the total density