How to Calculate the Piezometric Head

Water bubbling up from the ground seems downright magical. Water flowing uphill through pipes seems to contradict the laws of gravity. While these may seem like miraculous events, they occur due to ​piezometric or hydraulic head​.

Piezometric Head Definition

The ​piezometric head definition​ from the American Meteorological Society glossary is "the pressure that exists in a confined aquifer." The definition continues by stating that piezometric head " the elevation above a datum plus the pressure head."

The piezometric surface is described as "an imaginary or hypothetical surface of the piezometric pressure or hydraulic head throughout all or part of a confined or semi-confined aquifer; analogous to the water table of an unconfined aquifer."

Piezometric head synonyms include hydraulic head and hydraulic head pressure. The piezometric surface may also be called the ​potentiometric surface​. Piezometric head is a measure of the ​potential energy of water​.

What Piezometric Head Actually Measures

Piezometric head indirectly measures the potential energy of water by measuring the height of water at a given point. Piezometric head is measured using the elevation of the water surface in a well or the height of water in a standpipe attached to a pipe containing water under pressure.

Piezometer head combines three factors: the potential energy of the water due to the water's height above a given point (usually average or mean sea level), any additional energy applied by pressure and velocity head.

The pressure may be due to gravity, as with flow through the pipes in a hydroelectric dam, or by confinement, as in a confined aquifer. The equation for calculating head can be written as head ​h​ equals elevation head ​z​ plus pressure head ​Ψ​ plus velocity head ​v.

h=z+\Psi +v

Velocity head, while an important factor in pipe and pump flow calculations, is negligible in calculations of groundwater piezometric head because the velocity of groundwater is very slow.

Determining Piezometric Head in Groundwater

Determining piezometric head is accomplished by measuring the elevation of the water level in a well. Piezometric total head calculations in groundwater use the formula ​h=z+Ψ​ where ​h​ means total head or height of the groundwater level above the datum, usually sea level, while ​z​ represents the elevation head and ​Ψ​ represents the pressure head.

The elevation head, ​z​, is the height of the bottom of a well above the datum. The pressure head equals the height of the water column above ​z​. For a lake or pond, ​Ψ​ equals zero so the hydraulic or piezometric head simply equals the potential energy of the water surface height above the datum. In an unconfined aquifer, the water level in the well will approximately equal the groundwater level.

In confined aquifers, however, the water level in wells rises above the level of the confining rock layer. The total head is directly measured at the surface of the water in the well. Subtracting the elevation of the bottom of the well from the elevation of the water surface yields the pressure head.

For example, the water surface in a well lies at an elevation of 120 feet above mean sea level. If the elevation at the bottom of the well lies at 80 feet above mean sea level, then the pressure head equals 40 feet.

Calculating Piezometric Head in Hydroelectric Dams

The piezometric pressure definition shows that the potential energy at the surface of a reservoir equals the elevation of the lake's surface above a datum. In the case of a hydroelectric dam, the datum used can be the surface of the water just below the dam.

The total head equation simplifies to the difference in elevation from the reservoir surface and the outflow surface. For example, if the reservoir surface is 200 feet above the river level immediately below the dam, the total hydraulic head equals 200 feet.



About the Author

Karen earned her Bachelor of Science in geology. She worked as a geologist for ten years before returning to school to earn her multiple subject teaching credential. Karen taught middle school science for over two decades, earning her Master of Arts in Science Education (emphasis in 5-12 geosciences) along the way. Karen now designs and teaches science and STEAM classes.