where g is the gravity acceleration constant (9.81 m/s2; 32.2 ft/s2), V is the velocity of the fluid, and z is the height above an arbitrary datum. C remains constant along any streamline in the flow, but varies from streamline to streamline. If the flow is irrotational, then C has the same value for all streamlines.
The function is the "pressure per density" in the fluid, and follows from the barotropic equation of state, p = p(r).
For an incompressible fluid, the function simplifies to p/r, and the incompressible Bernoulli Equation becomes: