In most flows of liquids, and of gases at low Mach number, the density of a fluid parcel can be considered to be constant, regardless of pressure variations in the flow. Therefore, the fluid can be considered to be incompressible, and these flows are called incompressible flows. Bernoulli performed his experiments on liquids, so his equation in its original form is valid only for incompressible flow.
A common form of Bernoulli's equation is:
where:
* is the fluid flow speed at a point,
* is the acceleration due to gravity,
* is the elevation of the point above a reference plane, with the positive -direction pointing upward—so in the direction opposite to the gravitational acceleration,
* is the pressure at the chosen point, and
* is the density of the fluid at all points in the fluid.
Bernoullis equation and the Bernoulli constant are applicable throughout any region of flow where the energy per unit mass is uniform. Because the energy per unit mass of liquid in a well-mixed reservoir is uniform throughout, Bernoullis equation can be used to analyze the fluid flow everywhere in that reservoir (including pipes or flow fields that the reservoir feeds) except where viscous forces dominate and erode the energy per unit mass.
The following assumptions must be met for this Bernoulli equation to apply:
* the flow must be steady, that is, the flow parameters (velocity, density, etc.) at any point cannot change with time,
* the flow must be incompressible—even though pressure varies, the density must remain constant along a streamline;
* friction by viscous forces must be negligible.
For conservative force fields (not limited to the gravitational field), Bernoulli's equation can be generalized as:
where  is the force potential at the point considered. For example, for the Earth's gravity .
By multiplying with the fluid density , equation () can be rewritten as:
or:
where
* is dynamic pressure,
* is the piezometric head or hydraulic head (the sum of the elevation  and the pressure head) and
* is the stagnation pressure (the sum of the static pressure  and dynamic pressure ).
The constant in the Bernoulli equation can be normalized. A common approach is in terms of total head or energy head :
The above equations suggest there is a flow speed at which pressure is zero, and at even higher speeds the pressure is negative. Most often, gases and liquids are not capable of negative absolute pressure, or even zero pressure, so clearly Bernoulli's equation ceases to be valid before zero pressure is reached. In liquids—when the pressure becomes too low—cavitation occurs. The above equations use a linear relationship between flow speed squared and pressure. At higher flow speeds in gases, or for sound waves in liquid, the changes in mass density become significant so that the assumption of constant density is invalid.