After free falling through a height  in a vacuum from an initial velocity of 0, a mass will have reached a speed
where  is the acceleration due to gravity. Rearranged as a head:
The term  is called the velocity head, expressed as a length measurement. In a flowing fluid, it represents the energy of the fluid due to its bulk motion.
The total hydraulic head of a fluid is composed of pressure head and elevation head. The pressure head is the equivalent gauge pressure of a column of water at the base of the piezometer, and the elevation head is the relative potential energy in terms of an elevation. The head equation, a simplified form of the Bernoulli principle for incompressible fluids, can be expressed as:
where
* is the hydraulic head (Length in m or ft), also known as the piezometric head.
* is the pressure head, in terms of the elevation difference of the water column relative to the piezometer bottom (Length in m or ft), and
* is the elevation at the piezometer bottom (Length in m or ft)
In an example with a 400 m deep piezometer, with an elevation of 1000 m, and a depth to water of 100 m: z = 600 m, ψ = 300 m, and h = 900 m.
The pressure head can be expressed as:
where
 is the gauge pressure (Force per unit area, often Pa or psi),
* is the unit weight of the liquid (Force per unit volume, typically N·m or lbf/ft),
* is the density of the liquid (Mass per unit volume, frequently kg·m), and
* is the gravitational acceleration (velocity change per unit time, often m·s)