Hydraulic potential

The hydraulic potential describes the energy state of water in the soil at a point defined by the measurement. In the case of groundwater , the hydraulic potential is also called the standpipe or piezometer level . In the case of hydropower plants , the hydraulic head is meant.

Groundwater

In general, the total mechanical energy of groundwater is made up of: ${\displaystyle E}$

• Pressure energy
• Potential energy , also referred to as positional energy , relative to a reference level (e.g. height above sea level ) as well
• Kinetic energy and kinetic energy ,

that is, the Bernoulli equation applies :

${\displaystyle {\begin{aligned}E_{\text{ges}}&=E_{\text{Druck}}+E_{\text{pot}}+E_{\text{kin}}\\&=p\,V+m\,g\,z+{\frac {1}{2}}\,m\,v^{2}\end{aligned}}}$

With

• Water pressure  p (pore water pressure in groundwater) (force per unit area [F / L ² ], often Pa or N · m ⁻² )
• Volume  V
• Mass  m of the water element
• Gravitational acceleration  g (often in ^{ms −2} )
• Position potential  z , d. H. the height of the measuring point above the reference line
• Flow velocity  v .

Since the flow velocities in groundwater are generally very low, the kinetic energy component can be neglected to a good approximation:

${\displaystyle v\approx 0\Rightarrow E_{\text{kin}}\approx 0}$

In addition, the specific energy per weight of a water element from the dimensional analysis corresponds to a geometric height: ${\displaystyle G}$

${\displaystyle {\frac {E_{\text{ges}}}{G}}={\frac {E_{\text{ges}}}{m\,g}}=h}$

The hydraulic potential h in groundwater hydraulics is thus  defined as follows:

${\displaystyle \Rightarrow h=\psi +z={\frac {E_{\text{Druck}}}{m\,g}}+{\frac {E_{\text{pot}}}{m\,g}}}$

The pressure height is expressed as: ${\displaystyle \psi }$

${\displaystyle \psi ={\frac {p}{\gamma }}={\frac {p}{\rho \,g}}}$

With

• ${\displaystyle \gamma }$ specific weight of the fluid (force per unit volume [F / L ³ ], often N · m ⁻³ ),
  • ${\displaystyle \rho }$ Density of the fluid (mass per unit volume [M / L ³ ], often kg · m ⁻³ ).

The hydraulic potential can be measured comparatively easily. For this purpose, a pipe (standpipe) with a filter is inserted into the aquifer (by drilling, ramming , etc.), in poorly permeable soils, the pore water pressure is measured using a pressure cell (piezometer). The hydraulic potential at the measuring point is then represented by

• the height / depth of the water level in the pipe relative to a reference point ( ) ${\displaystyle p=0\Rightarrow \psi =0\Rightarrow h=z}$
• the pressure height measured by the pressure cell, combined with the position of the pressure cell relative to a reference level ( ). ${\displaystyle p\neq 0\Rightarrow \psi \neq 0\Rightarrow h=\psi +z}$

Differences in energy levels at two points on the aquifer lead to groundwater movement between these two points. Groundwater always flows from the higher to the lower hydraulic potential. The decrease in the hydraulic potential (piezometer height) corresponds to an "energy loss", because part of the energy is converted into thermal energy through the internal friction between the water and the solid rock (grains, fissures , etc.) . Depending on the relationship between pressure and positional energy, groundwater can even flow against gravity ( Artesian well ).

Unsaturated area

In order to be able to model water movements in the soil , one would in principle have to know the total potential , which is defined as the sum of all partial potentials acting on water in the soil. Since the total potential is difficult to determine in practice, the hydraulic potential is used instead as an approximation to describe water movements . This is the sum of the easily determinable partial potentials matrix potential and gravitational potential , the gas potential is usually not taken into account: ${\displaystyle \psi }$ ${\displaystyle \psi _{H}}$ ${\displaystyle \psi _{m}}$ ${\displaystyle \psi _{z}}$ ${\displaystyle \psi _{g}}$

${\displaystyle \psi _{H}=\psi _{m}+\psi _{z}(+\psi _{g})}$

The horizontal watershed lies where the gradient of the hydraulic potential disappears . ${\displaystyle \left({\frac {d\psi _{H}}{dz}}=0\right)}$

In order to determine the availability of water for a plant , another combination of partial potentials is used, the water potential . ${\displaystyle \psi _{w}}$

Individual evidence

1. ↑ Scheffer , Schachtschabel : Textbook of soil science. 13th revised edition. 1992, ISBN 3-432-84773-4 , Chapter XVI. Soil water.

literature

• DIN 4049-3 (hydrology, part 3: terms for quantitative hydrology)
• R. Allan Freeze, John A. Cherry: Groundwater. Prentice-Hall, Englewood Cliffs NJ 1979, ISBN 0-13-365312-9 .
• Bernward Hölting , Wilhelm Georg Coldewey: Hydrogeology. Introduction to general and applied hydrogeology. 7th revised and expanded edition. Spektrum Akademischer Verlag, Heidelberg 2009, ISBN 978-3-8274-1713-8 .
• Hanspeter Jordan, Hans-Jörg Weder: Hydrogeology. Basics and methods. Regional hydrogeology: Mecklenburg-Western Pomerania, Brandenburg and Berlin, Saxony-Anhalt, Saxony, Thuringia. 2nd heavily revised and expanded edition. Enke, Stuttgart 1995, ISBN 3-432-26882-3 .
• W. Kinzelbach, R. Rausch : Groundwater modeling. Borntraeger, Berlin et al. 1995, ISBN 3-443-01032-6 .