Hydraulic head (hydrology and fluid mechanics)

Components of head

The total hydraulic head is traditionally decomposed into three parts:

• Elevation head (z): the vertical position of the point relative to a chosen datum.
• Pressure head (p/γ): the height of a fluid column whose weight would produce the local static pressure (pressure divided by specific weight).
• Velocity head (v²/2g): the energy equivalent of fluid motion; often negligible in slow groundwater flow but important in open-channel and pipe flows.

Measurement and practical use

In hydrogeology, hydraulic head is measured with piezometers or wells: the elevation of the water level in the pipe or well above the chosen datum gives the piezometric head. For a well, the head equals the elevation of the measuring point minus the measured depth to water, plus any needed correction for well construction. Engineers use hydraulic head maps (potentiometric surfaces) to determine flow direction—water moves from high head toward low head—and to compute hydraulic gradients that drive flow according to Darcy's law.

Theoretical context and conservation

Hydraulic head is central to Bernoulli's equation and energy-balance descriptions of fluid flow. In ideal, inviscid flows the total head is conserved along a streamline; in real flows head losses occur due to friction and turbulence. In porous media, differences in hydraulic head between two points divided by distance define the hydraulic gradient, which, together with the medium's conductivity, determines volumetric flux.

Applications and notable facts

Hydraulic head underpins tasks such as groundwater resource assessment, contaminant transport studies, design of pumping schemes, and seepage analysis beneath dams. A useful conceptual point is that equipotential lines of equal head are perpendicular to streamlines of flow. Because head values are relative to a datum, absolute numbers matter less than differences and gradients. For more technical background see further reading.