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Hydraulic head is a specific measurement of water pressure or total energy per unit weight above a geodetic datum. Fluid pressure is the Pressure at some point within a Fluid, such as water or air In Classical physics, the total energy of an object is the sum of its Potential energy and its Kinetic energy. The specific weight (also known as the unit weight) is the Weight per unit Volume of a material or \gamma = \rho \ g This article describes a concept from Surveying and Geodesy. For other meanings see Datum (disambiguation. It is usually measured as a water surface elevation, expressed in units of length, but represents the energy at the entrance (or bottom) of a piezometer. A piezometer is a small diameter Water well used to measure the Hydraulic head of Groundwater in Aquifers Similarly it may also be a standpipe In an aquifer, it can be calculated from the depth to water in a piezometric well (a specialized water well), 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. In both cases, although the measurement is made at the water surface, the hydraulic head measurement represents the total energy at the entrance (base) of the piezometer. The hydraulic head can be used to determine a hydraulic gradient between two or more points.

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"Head" in fluid dynamics

In fluid dynamics, head is the difference in elevation between two points in a column of fluid, and the resulting pressure of the fluid at the lower point. Fluid dynamics is the sub-discipline of Fluid mechanics dealing with fluid flow: Fluids ( Liquids and Gases in motion The elevation of a Geographic location is its height above a fixed reference point often the mean sea level. FLUID ( F ast L ight '''U'''ser '''I'''nterface D esigner is a graphical editor that is used to produce FLTK Source code Pressure (symbol 'p' is the force per unit Area applied to an object in a direction perpendicular to the surface Head is normally expressed in units of height (e. g. meters), although some texts (incorrectly) refer to it in units of pressure such as pascals (the SI unit of pressure). The metre or meter is a unit of Length. It is the basic unit of Length in the Metric system and in the International Pressure (symbol 'p' is the force per unit Area applied to an object in a direction perpendicular to the surface Head refers to the constant right hand side in the incompressible steady version of Bernoulli's equation. In Fluid dynamics, Bernoulli's principle states that for an Inviscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in

This is best understood by considering a waterwheel: the head is the vertical distance from the top of the waterwheel to the free surface of the millpond. A water wheel is a means of extracting power from the flow (or fall of water otherwise known as Hydropower.

More generally, when considering a flow, one says that head is lost if energy is dissipated, often through turbulence; equations such as the Prony equation and the Darcy-Weisbach equation have been used to calculate the head loss due to friction. In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός In Fluid dynamics, turbulence or turbulent flow is a fluid regime characterized by chaotic Stochastic property changes The Prony equation is a historically important equation in Hydraulics, used to calculate the Head loss due to Friction within a given run of pipe The Darcy-Weisbach equation is an important and widely used phenomenological equation in Hydraulics. Friction is the Force resisting the relative motion of two Surfaces in contact or a surface in contact with a fluid (e In the context of steam trains, one talks of a good head of steam, referring to the pressure in the boiler. A steam locomotive is a Locomotive powered by Steam. The term usually refers to its use on Railways but can also refer to a "road locomotive" A boiler is a closed vessel in which Water or other Fluid is heated

The static head of a pump is the maximum height (pressure) it can deliver. For information on Wikipedia project-related discussions see WikipediaVillage pump. The capacity of the pump can be read from its Q-H curve (flow vs. height).

Head is used to describe the energy in incompressible fluids. In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός Fluid mechanics is the study of how Fluids move and the Forces on them Head has units of distance and equals the fluid's energy per unit weight. In the Physical sciences weight is a Measurement of the gravitational Force acting on an object Head is useful in specifying centrifugal pumps because their pumping characteristics tend to be independent of the fluid's density. A centrifugal pump is a rotodynamic Pump that uses a rotating Impeller to increase the velocity of a fluid

There are four types of head used to calculate the total head in and out of a pump:

Components of hydraulic head

The total hydraulic head is composed of pressure head, velocity head and elevation head. The pressure head is the equivalent gauge pressure of a column of water at the base of the piezometer, the velocity head is the kinetic energy from the motion of water, and the elevation head is the relative potential energy in terms of an elevation. In Engineering, a gauge or gage, is used to make Measurements Various types of gauges include Many techniques have been developed for the measurement of Pressure and Vacuum. The kinetic energy of an object is the extra Energy which it possesses due to its motion Potential energy can be thought of as Energy stored within a physical system This can be expressed as:

h = \psi + h_v + z \,

where

h is the hydraulic head (Length in m or ft),
hv is the velocity head, measured by a Pitot tube (Length in m or ft),
ψ 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
z is the elevation at the piezometer bottom (Length in m or ft)

In groundwater studies, the velocity head is assumed to be zero and is ignored. Length is the long Dimension of any object The length of a thing is the distance between its ends its linear extent as measured from end to end In Fluid dynamics, Bernoulli's principle states that for an Inviscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in A Pitot (ˈpiːtoʊ tube is a Pressure measurement instrument used to measure Fluid flow Velocity. Length is the long Dimension of any object The length of a thing is the distance between its ends its linear extent as measured from end to end Pressure head is a term used in Fluid mechanics to represent the Internal energy of a Fluid due to the Pressure exerted on its container Length is the long Dimension of any object The length of a thing is the distance between its ends its linear extent as measured from end to end Length is the long Dimension of any object The length of a thing is the distance between its ends its linear extent as measured from end to end Groundwater is Water located beneath the Ground surface in Soil pore spaces and in the Fractures of lithologic formations This is because groundwater moves very slowly, and the kinetic energy loss is very low. Thus, for groundwater studies, hydraulic head can be defined simply as:

h = \psi + z \,

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:

\psi = \frac{P}{\gamma} = \frac{P}{\rho g}

where

P is the gauge pressure (Force per unit area, often Pa or psi),
γ is the unit weight of water (Force per unit volume, typically N·m−3 or lbf/ft³),
ρ is the density of the water (Mass per unit volume, frequently kg·m−3), and
g is the gravitational acceleration (velocity change per unit time, often m·s−2)

In faster moving water where the Reynolds number exceeds 10, such as in a river, the velocity head can be calculated using Bernoulli's principles as:

h_v = \frac{v^2}{2g}

where v is relative velocity of the water (distance per unit time, often m·s−1 or ft·s−1)

Fresh water head

The pressure head is dependent on the density of water, which can vary depending on both the temperature and chemical composition (salinity, in particular). The specific weight (also known as the unit weight) is the Weight per unit Volume of a material or \gamma = \rho \ g This article deals with the unit of force For the unit of mass see Pound (mass. The density of a material is defined as its Mass per unit Volume: \rho = \frac{m}{V} Different materials usually have different In Physics, gravitational acceleration is the Acceleration of an object caused by the Force of gravity from another object In Fluid mechanics and Heat transfer, the Reynolds number \mathrm{Re} is a Dimensionless number that gives a measure of the Ratio "Riverine" redirects here For the use of that term in Maritime geography, see there In Fluid dynamics, Bernoulli's principle states that for an Inviscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in In Physics, velocity is defined as the rate of change of Position. The density of a material is defined as its Mass per unit Volume: \rho = \frac{m}{V} Different materials usually have different Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature A chemical substance is a Material with a definite chemical composition. Salinity is the Saltiness or dissolved salt content of a body of Water. 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_{fw} = \psi \frac{\rho}{\rho_{fw}} + z

where

h_{fw} \, is the fresh water head (Length, measured in m or ft), and
\rho_{fw} \, is the density of fresh water (Mass per unit volume, typically in kg·m−3)

Hydraulic gradient

The hydraulic gradient is a vector gradient between two or more hydraulic head measurements over the length of the flow path. The density of a material is defined as its Mass per unit Volume: \rho = \frac{m}{V} Different materials usually have different In Vector calculus, the gradient of a Scalar field is a Vector field which points in the direction of the greatest rate of increase of the scalar It is also called the darcy slope, since it determines the quantity of a darcy flux, or discharge. In Fluid dynamics, Darcy's law is a phenomologically derived Constitutive equation that describes the flow of a Fluid through a Porous medium A dimensionless hydraulic gradient can be calculated between two piezometers as:

i = \frac{dh}{dl} = \frac{h_2 - h_1}{\mathrm{length}}

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 operator. In Dimensional analysis, a dimensionless quantity (or more precisely a quantity with the dimensions of 1) is a Quantity without any Physical units &nablaDel In Mathematics, a differential operator is an Operator defined as a function of the differentiation operator This requires a hydraulic head field, which can only be practically obtained from a numerical model, such as MODFLOW. In Abstract algebra, a field is an Algebraic structure in which the operations of Addition, Subtraction, Multiplication and division MODFLOW is the US Geological Survey modular finite-difference flow model which is a computer code that solves the Groundwater flow equation In Cartesian coordinates, this can be expressed as:

\nabla h = \left( {\frac{\partial h}{\partial x}}, {\frac{\partial h}{\partial y}}, {\frac{\partial h}{\partial z}} \right) = {\frac{\partial h}{\partial x}}\mathbf{i} + {\frac{\partial h}{\partial y}}\mathbf{j} + {\frac{\partial h}{\partial z}}\mathbf{k}

This vector describes the direction of the groundwater flow, where negative values indicate flow along the dimension, and zero indicates no flow. In Mathematics, the Cartesian coordinate system (also called rectangular coordinate system) is used to determine each point uniquely in a plane 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 and a tensor of hydraulic conductivity to determine the flux of water in three dimensions. In Fluid dynamics, Darcy's law is a phenomologically derived Constitutive equation that describes the flow of a Fluid through a Porous medium History The word tensor was introduced in 1846 by William Rowan Hamilton to describe the norm operation in a certain type of algebraic system (eventually Hydraulic conductivity, symbolically represented as K is a property of vascular plants soil or rock that describes the ease with which water can move through pore spaces

Hydraulic head in groundwater

Relation between heads for a hydrostatic case and a downward flow case.

The distribution of hydraulic head through an aquifer determines where groundwater will flow. An aquifer is an underground layer of Water -bearing Permeable rock or unconsolidated materials ( Gravel, Sand, Silt, or Clay In a hydrostatic example (first figure), where the hydraulic head is constant, there is no flow. Fluid pressure is the Pressure at some point within a Fluid, such as water or air 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 use gauge pressure in the calculation of hydraulic head, it is more correct to use total pressure (gauge pressure + atmospheric pressure), since this is truly what drives groundwater flow. Pressure (symbol 'p' is the force per unit Area applied to an object in a direction perpendicular to the surface Often detailed observations of barometric pressure are not available at each well 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 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 first qualitatively observed these effects in the 1600s, and they were more rigorously described by the soil physicist Edgar Buckingham (working for the USDA) using air flow models in 1907. Blaise Pascal (blɛz paskal (June 19 1623 &ndash August 19 1662 was a French Mathematician, Physicist, and religious Philosopher Soil physics is the study of soil physical properties and processes Edgar Buckingham ( July 8, 1867 Philadelphia, PA &ndash April 29, 1940 Washington DC) was a Physicist Year 1907 ( MCMVII) was a Common year starting on Tuesday (link will display the full calendar of the Gregorian calendar (or a Common year

Analogs to other fields

Hydraulic head is a measure of energy, and has many analogs in physics and chemistry, where the same mathematical principles and rules apply:

See also

References

Hydrogeology ( hydro- meaning water and -geology meaning the study of the Earth) is the area of Geology that deals with the distribution and
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