Hydraulic head

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The hydraulic head or piezometric head is a specific measurement of the fluid pressure above the geodetic datum.

This is usually measured as a liquid surface elevation, expressed in units of length, at the entrance (or below) of the piezometer. In aquifers, it can be calculated from depth to water in a piezometric well (a special water well), and given information about the height and depth of the piezometer screen. Hydraulic heads can also be measured in a water column using a standpipe piezometer by measuring the height of the water surface in a tube relative to a common datum. The hydraulic head can be used to define a hydraulic gradient between two or more points.

Video Hydraulic head

"Head" dalam dinamika fluida

In fluid dynamics, head is a concept that connects energy in a liquid that can not be compacted with the equivalent static column height of the fluid. From the Bernoulli Principle, the total energy at a particular point in the fluid is the energy associated with fluid movement, plus the energy of the static pressure in the liquid, plus the energy from the relative fluid altitude to the varying datum. Heads are expressed in high units such as meters or feet.

static head of a pump is the maximum height (pressure) that it can produce. The pump capability of a given RPM can be read from the Q-H (flow vs height) curve.

A common misconception is that the head is equal to the energy of liquid per unit weight, while, in fact, the term with pressure does not represent all kinds of energy (in the Bernoulli equation for the compressed fluid the term is the work of force force). The head is useful in determining the centrifugal pump because its pumping characteristics tend not to depend on the fluid density.

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

1. Head speed is due to the mass movement of a liquid (kinetic energy). The chief correspondent of pressure is dynamic pressure.
2. The elevation head is due to the weight of the fluid, the force of gravity acting on the liquid column.
3. Head pressure is due to static pressure, the internal molecular motion of the fluid that gives force to the container.
4. The head of resistance (or friction head or Head Loss) is caused by the friction force acting against the fluid movement by the container.
Hydraulic head component

Massa bebas jatuh dari ketinggian ${\ displaystyle z \, & gt; \, 0 \,}  ÂÂ$ (dalam ruang hampa) akan mencapai kecepatan

${\ displaystyle v = {\ sqrt {{2g} {z}}},}  ÂÂ$ ketika tiba di ketinggian z = 0, atau ketika kita mengatur ulang sebagai head : ${\ displaystyle h = {\ frac {v ^ {2}} {2g}}}  ÂÂ$

dimana

${\ displaystyle g}  ÂÂ$ adalah akselerasi karena gravitasi

Istilah ${\ displaystyle {\ frac {v ^ {2}} {2g}}}  ÂÂ$ disebut head kecepatan , yang dinyatakan sebagai pengukuran panjang. Dalam cairan yang mengalir, itu mewakili energi dari cairan karena gerakan massalnya.

Total fluid hydraulic heads consist of pressure heads and elevation heads . Head pressure is the equivalent measuring pressure of the water column at the base of the piezometer, and the elevation head is the relative potential energy in terms of height. The equation head , the simplified form of the Bernoulli Principle for compressed fluid, can be expressed as:

${\ displaystyle h = \ psi z \,}$

dimana

$            {\displaystyle         h      }        \{\backslash \; displaystyle\; h\}\;  ÂÂ$ adalah kepala hidraulik (Panjang dalam m atau kaki), juga dikenal sebagai kepala piezometrik.

${\ displaystyle \ psi}  ÂÂ$ adalah kepala tekanan, dalam hal perbedaan elevasi kolom air relatif terhadap dasar piezometer (Panjang dalam m atau ft), dan

${\ displaystyle z}  ÂÂ$ adalah ketinggian di bagian bawah piezometer (Panjang dalam m atau ft)

In an example with a piezometer depth of 400 m, with a height of 1000 m, and a water depth of 100 m: z = 600 m, ? = 300 m, and h = 900 m.

Kepala tekanan dapat dinyatakan sebagai:

${\ displaystyle \ psi = {\ frac {P} {\ gamma}} = {\ frac {P} {\ rho g}}}  ÂÂ$

dimana

${\ displaystyle P}  ÂÂ$ adalah tekanan pengukur (Angkatan per satuan luas, sering Pa atau psi),

${\ displaystyle \ gamma}  ÂÂ$ adalah satuan berat cairan (Angkatan per satuan volume, biasanya NÂ · m ^-3 atau lbf/ft³),

${\ displaystyle \ rho}  ÂÂ$ adalah densitas cairan (Massa per satuan volume, sering kg · m ^-3 ), dan

${\ displaystyle g}  ÂÂ$ adalah percepatan gravitasi (perubahan kecepatan per satuan waktu, seringkali m · s ^-2 )

Kepala air tawar

Head pressure depends on the density of water, which may vary depending on temperature and chemical composition (salinity, in particular). This means the calculation of the hydraulic head depends on the density of the water inside the piezometer. If one or more hydraulic head measurements should be compared, they need to be standardized, usually to their freshwater head , which can be calculated as: ${\ displaystyle h _ {\ mathrm {fw}} = \ psi {\ frac {\ rho} {\ rho _ {\ mathrm {fw}}} } z} Â Â$

dimana

${\ displaystyle h _ {\ mathrm {fw}} \,}  ÂÂ$ adalah kepala air tawar (Panjang, diukur dalam m atau ft), dan

${\ displaystyle \ rho _ {\ mathrm {fw}} \,}  ÂÂ$ adalah densitas air segar (Massa per satuan volume, biasanya dalam kg · m ^-3 )




Maps Hydraulic head





Gradien hidraulik

The hydraulic gradient is the vector gradient between two or more hydraulic head measurements along the flow path. For groundwater, this is also called 'Darcy slope', because it determines the quantity of flux or Darcy release. It also has applications in an open channel flow that can be used to determine whether a range is getting or losing energy. The dimensionless hydraulic gradient can be calculated between two points with a head value known as:

${\ displaystyle i = {\ frac {dh} {dl}} = {\ frac {h_ {2} -h_ {1}} {\ mathrm { length}}}}$

dimana

${\ displaystyle i}  ÂÂ$ adalah gradien hidrolik (tanpa dimensi),

${\ displaystyle dh}  ÂÂ$ adalah perbedaan antara dua kepala hidraulik (Panjang, biasanya dalam m atau ft), dan

${\ displaystyle dl}  ÂÂ$ adalah panjang jalur aliran antara dua piezometers (Panjang, biasanya dalam m atau ft)

Hydraulic gradients can be expressed in vector notation, using del. It requires a hydraulic head field, which can only be obtained practically from a numerical model, such as MODFLOW for groundwater or standard steps or HEC-RAS for open channels. In the Cartesian coordinates, this can be expressed as:

$Â\; ÂÂ\; Â\; Â\; ÂÂ\; Â\; Â\; Â\; Â{\displaystyle Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\mathrm{?}Â\; Â\; Â\; Â\; Â\; Â\; Â\; ÂhÂ\; Â\; Â\; Â\; Â\; Â\; Â\; Â=Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â()\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; ÂÂ\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; ÂÂ\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\frac{Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\mathrm{?}Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; ÂhÂ\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â}{Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\mathrm{?}Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; ÂxÂ\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â}Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â\; Â}$,                                                             ?                   h                                                   ?                   y                                           ,                                                             ?                   h                                                   ?                   z                                                               )                 =                                             ?               h                                       ?               x                                                 me                                                             ?               h                                       ?               y                                                 j                                                             ?               h                                       ?               z                                                 k                   {\ displaystyle \ nabla h = \ left ({\ frac {\ parsial h} {\ parsial x}}, {\ frac {\ partial h} { \ parsial 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}}  Â

This vector explains the direction of 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 in the gradient is negative. This vector can be used in conjunction with Darcy's law and hydraulic conductivity tensor to determine the flux of water in three dimensions.



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Hydraulic head in groundwater

The distribution of the hydraulic head through the aquifer determines where groundwater will flow. In the hydrostatic example (first image), where the hydraulic head is constant, there is no flow. However, if there is a difference in the hydraulic head from top to bottom because of the drainage from below (the second picture), water will flow downward, due to the difference in the head, also called the hydraulic gradient .

atmospheric pressure

Although the convention to use gauge pressure in hydraulic head calculations, it is more appropriate to use the total pressure (pressure of the atmospheric pressure gauge), because this is really what drives groundwater flow. Frequent observations of barometric pressure are not available at each well at all times, so this is often overlooked (contributing to large errors in locations where low hydraulic gradients or angles between wells are acute.)

The effects of changes in atmospheric pressure on water levels observed in wells have been known for years. The effect is immediate, the increase in atmospheric pressure is the increase in water load in the aquifer, which increases the depth to the water (lowers the elevation of the water level). Pascal first qualitatively observed this effect in the 17th century, and they were more strictly described by land physicist Edgar Buckingham (working for the US Department of Agriculture (USDA)) using the airflow model in 1907.



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Loss of head

In a real moving fluid, energy is dissipated by friction; turbulence wastes more energy for the high amount of Reynolds currents. This dissipation, called head loss, is divided into two main categories, "big losses" associated with energy loss per pipeline length, and "small losses" associated with arches, fittings, valves, etc. the most common equation used to calculate the main losses is the Darcy-Weisbach equation. The older and more empirical approach is the Hazen-Williams equation and the Prony equation.

For relatively short pipe systems, with relatively large number of bends and fittings, small losses can easily surpass major losses. In the design, small losses are usually estimated from the table using a simpler and less accurate smaller reduction coefficient or reduction for equivalent pipeline length.



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Analog to other fields

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

• Hydraulic head analogous to:
  • magnetic monopole
  • electric charge
  • heat (ie, temperature)
  • concentration
• The continuous field of the hydraulic head is analogous to:
  • electric field
  • magnetic field
• Similar differential operators can be applied to fields, to find:
  • gradient, or flow direction
  • flow divergence
  • curls, or if the field rotates



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See also

• The Borda-Carnot Equation
• Dynamic pressure
• Total dynamic headers
• Stage (hydrology)
• Head (hydrology)



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Note




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References

• Bear, J. 1972. Fluid Dynamics in Porous Media , Dover. ISBNÃ, 0-486-65675-6.
• for other references that discuss the hydraulic head in a hydrogeological context, see the section further reading the page




Source of the article : Wikipedia