Hydraulic head or piezometric head is a specific measurement of above a

^{−3} or lbf/ft³),
:$\backslash rho$ is the ^{−3}), and
:$g$ is the ^{−2})

^{−3})

vertical datum
A vertical datum, altimetric datum, or height datum is a reference surface for vertical position
Vertical position or vertical location is a position along a vertical direction
In astronomy
Astronomy (from el, ἀστρονομία, ...

., 410 pages. See pp. 43–44., 650 pages. See p. 22.
It is usually measured as a liquid surface elevation, expressed in units of length, at the entrance (or bottom) of a piezometer
A piezometer is either a device used to measure liquid pressure
Pressure (symbol: ''p'' or ''P'') is the force
In physics
Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ...

. In an aquifer
An aquifer is an underground layer of -bearing , rock fractures or unconsolidated materials (, , or ). can be extracted using a water . The study of water flow in aquifers and the characterization of aquifers is called . Related terms include a ...

, it can be calculated from the depth to water in a piezometric well (a specialized water well
A well is an excavation or structure created in the ground by digging
Digging, also referred to as excavation, is the process of using some implement such as claws, hands, manual tools or heavy equipment, to remove material from a solid surf ...

), and given information of the piezometer's elevation and screen depth. Hydraulic head can similarly be measured in a column of water using a standpipe piezometer by measuring the height of the water surface in the tube relative to a common datum. The hydraulic head can be used to determine a ''hydraulic gradient'' between two or more points.
"Head" in fluid dynamics

Influid dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) and ...

, ''head'' is a concept that relates the energy
In physics
Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regula ...

in an incompressible
In fluid mechanics
Fluid mechanics is the branch of physics concerned with the mechanics
Mechanics (Ancient Greek, Greek: ) is the area of physics concerned with the motions of physical objects, more specifically the relationships among ...

fluid to the height of an equivalent static column of that fluid. From Bernoulli's principle
File:Venturi Tube en.webm, Video of a Venturi effect, venturi meter used in a lab experiment
In fluid dynamics, Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure, static press ...

, the total energy at a given point in a fluid is the energy associated with the movement of the fluid, plus energy from static pressure
In fluid mechanics
Fluid mechanics is the branch of physics concerned with the mechanics
Mechanics (Ancient Greek, Greek: ) is the area of physics concerned with the motions of physical objects, more specifically the relationships among for ...

in the fluid, plus energy from the height of the fluid relative to an arbitrary datum
Data (; ) are individual facts
A fact is something that is truth, true. The usual test for a statement of fact is verifiability—that is whether it can be demonstrated to correspond to experience. Standard reference works are often use ...

. Head is often expressed in units of height such as meters or feet. On Earth, additional height of fresh water adds a static pressure of about 9.8 kPa per meter (0.098 bar/m) or 0.433 psi per foot of water column height.
The ''static head'' of a pump is the maximum height (pressure) it can deliver. The capability of the pump at a certain RPM can be read from its Q-H curve (flow vs. height).
A common misconception is that the head equals the fluid's energy per unit weight
In science
Science () is a systematic enterprise that Scientific method, builds and organizes knowledge in the form of Testability, testable explanations and predictions about the universe."... modern science is a discovery as well as ...

, while, in fact, the term with pressure does not represent any type of energy (in the Bernoulli equation for an incompressible fluid this term represents work
Work may refer to:
* Work (human activity), intentional activity people perform to support themselves, others, or the community
** Manual labour, physical work done by humans
** House work, housework, or homemaking
* Work (physics), the product of ...

of pressure forces). Head is useful in specifying centrifugal pump
Centrifugal pumps are used to transport fluids by the conversion of rotational kinetic energy to the hydrodynamic energy of the fluid flow. The rotational energy typically comes from an engine or electric motor. They are a sub-class of dynamic ...

s because their pumping characteristics tend to be independent of the fluid's density.
There are four types of head used to calculate the total head in and out of a pump:
#''Velocity head
Fluid flows from the tank at the top to the basin at the bottom under the pressure of the hydraulic head.
Hydraulic head or piezometric head is a specific measurement of liquid pressure above a vertical datum
A vertical datum, altimetric dat ...

'' is due to the bulk motion of a fluid (kinetic energy
In physics
Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular ...

). Its pressure head correspondent is the dynamic pressure
In incompressible fluid dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including aerodynamics (the study of air a ...

.
#''Elevation head'' is due to the fluid's weight, the gravitational force
Gravity (), or gravitation, is a natural phenomenon
Types of natural phenomena include:
Weather, fog, thunder, tornadoes; biological processes, decomposition, germination
seedlings, three days after germination.
Germination is th ...

acting on a column of fluid.
#''Pressure head
In fluid mechanics
Fluid mechanics is the branch of physics concerned with the mechanics
Mechanics (Ancient Greek, Greek: ) is the area of physics concerned with the motions of physical objects, more specifically the relationships among fo ...

'' is due to the static pressure
In fluid mechanics
Fluid mechanics is the branch of physics concerned with the mechanics
Mechanics (Ancient Greek, Greek: ) is the area of physics concerned with the motions of physical objects, more specifically the relationships among for ...

, the internal molecular motion of a fluid that exerts a force on its container.
#''Resistance head'' (or ''friction head'' or Head Loss
File:Headpressure.GIF, Fluid flows from the tank at the top to the basin at the bottom under the pressure of the hydraulic head.
Hydraulic head or piezometric head is a specific measurement of Fluid pressure#Hydrostatic pressure, liquid pressure ...

) is due to the frictional forces acting against a fluid's motion by the container.
Components of hydraulic head

Afterfree fall #REDIRECT Free fall
In Newtonian physics, free fall is any motion of a body where gravity
Gravity (), or gravitation, is a list of natural phenomena, natural phenomenon by which all things with mass or energy—including planets, star ...

ing through a height $h$ in a vacuum
A vacuum is a space
Space is the boundless three-dimensional
Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameter
A parameter (from the Ancient Gree ...

from an initial velocity of 0, a mass will have reached a speed
In everyday use and in kinematics
Kinematics is a subfield of physics, developed in classical mechanics, that describes the Motion (physics), motion of points, bodies (objects), and systems of bodies (groups of objects) without considerin ...

:$v=\backslash sqrt$
where $g$ is the acceleration due to gravity. Rearranged as a ''head'':
:$h=\backslash frac$.
The term $\backslash frac$ 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
Gauge (US: , UK: or ) may refer to:
Measurement
* Gauge (instrument)
A gauge, in science
Science (from the Latin word ''scientia'', meaning "knowledge") is a systematic enterprise that Scientific method, builds and Taxonomy (general), o ...

pressure
Pressure (symbol: ''p'' or ''P'') is the force
In physics, a force is an influence that can change the motion (physics), motion of an Physical object, object. A force can cause an object with mass to change its velocity (e.g. moving fr ...

of a column of water at the base of the piezometer, and the elevation head is the relative potential energy
In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.
Common types of potential energy include the gravitational potentia ...

in terms of an elevation. The ''head equation'', a simplified form of the Bernoulli Principle for incompressible fluids, can be expressed as:
:$h\; =\; \backslash psi\; +\; z\; \backslash ,$
where
:$h$ is the hydraulic head (Length
Length is a measure of distance
Distance is a numerical measurement
'
Measurement is the number, numerical quantification (science), quantification of the variable and attribute (research), attributes of an object or event, which can be us ...

in m or ft), also known as the piezometric head.
:$\backslash psi$ is the pressure head
In fluid mechanics
Fluid mechanics is the branch of physics concerned with the mechanics
Mechanics (Ancient Greek, Greek: ) is the area of physics concerned with the motions of physical objects, more specifically the relationships among fo ...

, in terms of the elevation difference of the water column relative to the piezometer bottom (Length
Length is a measure of distance
Distance is a numerical measurement
'
Measurement is the number, numerical quantification (science), quantification of the variable and attribute (research), attributes of an object or event, which can be us ...

in m or ft), and
:$z$ is the elevation at the piezometer bottom (Length
Length is a measure of distance
Distance is a numerical measurement
'
Measurement is the number, numerical quantification (science), quantification of the variable and attribute (research), attributes of an object or event, which can be us ...

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:
:$\backslash psi\; =\; \backslash frac\; =\; \backslash frac$
where
:$P$ is the gauge pressure (Force per unit area, often Pa or psi),
:$\backslash gamma$ is the unit weightThe specific weight, also known as the unit weight, is the weight per unit volume of a material.
A commonly used value is the specific weight of water on Earth at 4°C, which is 9.807 kN/m3 or 62.43 Pound (force), lbf/ft3.National Council of Examine ...

of the liquid (Force per unit volume, typically N·mdensity
The density (more precisely, the volumetric mass density; also known as specific mass), of a substance is its per unit . The symbol most often used for density is ''ρ'' (the lower case Greek letter ), although the Latin letter ''D'' can also ...

of the liquid (Mass per unit volume, frequently kg·mgravitational acceleration
In physics, gravitational acceleration is the acceleration of an object in free fall within a vacuum (and thus without experiencing air drag, drag). This is the steady gain in speed caused exclusively by the force of ''gravitational attraction' ...

(velocity change per unit time, often m·sFresh water head

The pressure head is dependent on thedensity
The density (more precisely, the volumetric mass density; also known as specific mass), of a substance is its per unit . The symbol most often used for density is ''ρ'' (the lower case Greek letter ), although the Latin letter ''D'' can also ...

of water, which can vary depending on both the temperature and chemical composition (salinity
Salinity () is the saltiness or amount of dissolved in a body of , called (see also ). It is usually measured in g/L or g/kg (grams of salt per liter/kilogram of water; the latter is dimensionless and equal to ‰).
Salinity is an important ...

, in particular). This means that the hydraulic head calculation is dependent on the density of the water within the piezometer. If one or more hydraulic head measurements are to be compared, they need to be standardized, usually to their ''fresh water head'', which can be calculated as:
:$h\_\backslash mathrm\; =\; \backslash psi\; \backslash frac\; +\; z$
where
:$h\_\backslash mathrm\; \backslash ,$ is the fresh water head (Length, measured in m or ft), and
:$\backslash rho\_\backslash mathrm\; \backslash ,$ is the density
The density (more precisely, the volumetric mass density; also known as specific mass), of a substance is its per unit . The symbol most often used for density is ''ρ'' (the lower case Greek letter ), although the Latin letter ''D'' can also ...

of fresh water (Mass per unit volume, typically in kg·mHydraulic gradient

The ''hydraulic gradient'' is a between two or more hydraulic head measurements over the length of the flow path. Forgroundwater
Groundwater is the water
Water (chemical formula H2O) is an , transparent, tasteless, odorless, and , which is the main constituent of 's and the s of all known living organisms (in which it acts as a ). It is vital for all known form ...

, it is also called the 'Darcy slope', since it determines the quantity of a Darcy flux or discharge. It also has applications in open-channel flow
Open-channel flow, a branch of hydraulics
Hydraulics (from Greek: Υδραυλική) is a technology and applied science using engineering, chemistry, and other sciences involving the mechanical properties and use of liquids. At a very ba ...

where it can be used to determine whether a reach is gaining or losing energy. A dimensionless
In dimensional analysis
In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantity, base quantities (such as length, mass, time, and electric curre ...

hydraulic gradient can be calculated between two points with known head values as:
:$i\; =\; \backslash frac\; =\; \backslash frac$
where
:$i$ is the hydraulic gradient (dimensionless),
:$dh$ is the difference between two hydraulic heads (Length, usually in m or ft), and
:$dl$ is the flow path length between the two piezometers (Length, usually in m or ft)
The hydraulic gradient can be expressed in vector notation, using the del
Del, or nabla, is an operator used in mathematics (particularly in vector calculus
Vector calculus, or vector analysis, is concerned with derivative, differentiation and integral, integration of vector fields, primarily in 3-dimensional ...

operator. This requires a hydraulic head field
Field may refer to:
Expanses of open ground
* Field (agriculture), an area of land used for agricultural purposes
* Airfield, an aerodrome that lacks the infrastructure of an airport
* Battlefield
* Lawn, an area of mowed grass
* Meadow, a grassl ...

, which can be practically obtained only from numerical models, such as MODFLOW for groundwater or standard step or HEC-RAS
HEC-RAS is a computer program that models the hydraulics of water flow through natural rivers and other channels. Prior to the 2016 update to Version 5.0, the program was one-dimensional, meaning that there is no direct modeling of the hydraulic ...

for open channels. In Cartesian coordinates
A Cartesian coordinate system (, ) in a plane
Plane or planes may refer to:
* Airplane or aeroplane or informally plane, a powered, fixed-wing aircraft
Arts, entertainment and media
*Plane (Dungeons & Dragons), Plane (''Dungeons & Dragons'') ...

, this can be expressed as:
:$\backslash nabla\; h\; =\; \backslash left(\; ,\; ,\; \backslash right)\; =\; \backslash mathbf\; +\; \backslash mathbf\; +\; \backslash mathbf$
This vector describes the direction of the groundwater flow, where negative values indicate flow along the dimension, and zero indicates 'no flow'. As with any other example in physics, energy must flow from high to low, which is why the flow is in the negative gradient. This vector can be used in conjunction with Darcy's law
Darcy's law is an equation that describes the flow of a fluid
In physics, a fluid is a substance that continually Deformation (mechanics), deforms (flows) under an applied shear stress, or external force. Fluids are a Phase (matter), phase of m ...

and a tensor
In mathematics
Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and their changes ( and ). There is no ...

of hydraulic conductivity
Hydraulics (from Greek language, Greek: Υδραυλική) is a technology and applied science using engineering, chemistry, and other sciences involving the mechanical properties and use of liquids. At a very basic level, hydraulics is the ...

to determine the flux of water in three dimensions.
Hydraulic head in groundwater

The distribution of hydraulic head through anaquifer
An aquifer is an underground layer of -bearing , rock fractures or unconsolidated materials (, , or ). can be extracted using a water . The study of water flow in aquifers and the characterization of aquifers is called . Related terms include a ...

determines where groundwater will flow. In a hydrostatic
Fluid statics or hydrostatics is the branch of fluid mechanics
Fluid mechanics is the branch of physics concerned with the mechanics
Mechanics (Ancient Greek, Greek: ) is the area of physics concerned with the motions of physical object ...

example (first figure), where the hydraulic head is constant, there is no flow. However, if there is a difference in hydraulic head from the top to bottom due to draining from the bottom (second figure), the water will flow downward, due to the difference in head, also called the ''hydraulic gradient''.
Atmospheric pressure

Even though it is convention to usegauge pressure
Pressure measurement is the analysis of an applied force
In physics
Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that st ...

in the calculation of hydraulic head, it is more correct to use total pressure (gauge pressure + atmospheric pressure
Atmospheric pressure, also known as barometric pressure (after the barometer
A barometer is a scientific instrument that is used to measure air pressure
Atmospheric pressure, also known as barometric pressure (after the barometer), is the ...

), since this is truly what drives groundwater flow. Often detailed observations of barometric pressure
Atmospheric pressure, also known as barometric pressure (after the barometer
A barometer is a scientific instrument that is used to measure air pressure
Atmospheric pressure, also known as barometric pressure (after the barometer
A barom ...

are not available at each well
A well is an excavation or structure created in the ground by digging, driving, or drilling to access liquid
A liquid is a nearly incompressible fluid
In physics, a fluid is a substance that continually Deformation (mechanics), defo ...

through time, so this is often disregarded (contributing to large errors at locations where hydraulic gradients are low or the angle between wells is acute.)
The effects of changes in atmospheric pressure
Atmospheric pressure, also known as barometric pressure (after the barometer
A barometer is a scientific instrument that is used to measure air pressure
Atmospheric pressure, also known as barometric pressure (after the barometer), is the ...

upon water levels observed in wells has been known for many years. The effect is a direct one, an increase in atmospheric pressure is an increase in load on the water in the aquifer, which increases the depth to water (lowers the water level elevation). Pascal
Pascal, Pascal's or PASCAL may refer to:
People and fictional characters
* Pascal (given name), including a list of people with the name
* Pascal (surname), including a list of people and fictional characters with the name
** Blaise Pascal, French ...

first qualitatively observed these effects in the 17th century, and they were more rigorously described by the soil physicist Edgar Buckingham
Edgar Buckingham (July 8, 1867 in Philadelphia
Philadelphia, colloquially Philly, is a city in the state of Pennsylvania in the United States. It is the sixth-most populous city in the United States and the most populous city in the state o ...

(working for the United States Department of Agriculture
The United States Department of Agriculture (USDA), also known as the Agriculture Department, is the federal executive department responsible for developing and executing federal laws related to farming, forestry, rural economic development, ...

(USDA)) using air flow models in 1907.
Head loss

In any real moving fluid, energy is dissipated due tofriction
Friction is the force
In physics, a force is an influence that can change the motion (physics), motion of an Physical object, object. A force can cause an object with mass to change its velocity (e.g. moving from a Newton's first law, st ...

; turbulence
In fluid dynamics
In physics
Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities o ...

dissipates even more energy for high Reynolds number
The Reynolds number () helps predict flow patterns in different fluid flow situations. At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow, while at high Reynolds numbers flows tend to be turbulent
In fluid dynam ...

flows. This dissipation, called ''head loss'', is divided into two main categories, "major losses" associated with energy loss per length of pipe, and "minor losses" associated with bends, fittings, valves, etc. The most common equation used to calculate major head losses is the Darcy–Weisbach equation
In fluid dynamics, the Darcy–Weisbach equation is an Empirical research, empirical equation, which relates the head loss, or pressure loss, due to friction along a given length of pipe to the average velocity of the fluid flow for an incompressibl ...

. Older, more empirical approaches are the Hazen–Williams equationThe Hazen–Williams equation is an empirical relationship which relates the flow of water in a pipe with the physical properties of the pipe and the pressure drop caused by friction. It is used in the design of water pipe
Plumbing is any system ...

and the Prony equationThe Prony equation (named after Gaspard de Prony) is a historically important equation in hydraulics, used to calculate the head loss due to friction within a given run of pipe. It is an empirical equation developed by France, Frenchman Gaspard de P ...

.
For relatively short pipe systems, with a relatively large number of bends and fittings, minor losses can easily exceed major losses. In design, minor losses are usually estimated from tables using coefficients or a simpler and less accurate reduction of minor losses to equivalent length of pipe, a method often used for shortcut calculations of pneumatic conveying lines pressure drop.
See also

* Borda–Carnot equation *Dynamic pressure
In incompressible fluid dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of ...

* Minor losses in pipe flow
* Total dynamic head
In fluid dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including aerodynamics (the study of air and other gases in ...

* Stage (hydrology)
* Head (hydrology)
Notes

References

* Bear, J. 1972. ''Dynamics of Fluids in Porous Media'', Dover. . * for other references which discuss hydraulic head in the context of hydrogeology, see that page's Aquifers Water HydrologyFluid dynamics
Fluid dynamics is a mathematical discipline within continuum mechanics
Continuum mechanics is a branch of mechanics
Mechanics (Ancient Greek, Greek: ) is the area of physics concerned with the motions of physical objects, more specifically ...

Water wells
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