The groundwater energy balance is the energy balance of a

groundwater Groundwater is the water present beneath Earth's surface in rock and soil pore spaces and in the fractures of rock formations. About 30 percent of all readily available freshwater in the world is groundwater. A unit of rock or an unconsolidated ...

body in terms of incoming hydraulic energy associated with groundwater inflow into the body, energy associated with the outflow, energy conversion into heat due to friction of flow, and the resulting change of energy status and groundwater level.

Theory

When multiplying the horizontal velocity of groundwater (dimension, for example, m3/day per m2 cross-sectional area) with the groundwater potential (dimension energy per m3 water, or ''E''/m3) one obtains an energy flow (flux) in ''E''/day per m2 cross-sectional area. Summation or integration of the energy flux in a vertical cross-section of unit width (say 1 m) from the lower flow boundary (the impermeable layer or base) up to the water table in an

unconfined aquifer An aquifer is an underground layer of water-bearing, permeable rock, rock fractures, or unconsolidated materials (gravel, sand, or silt). Groundwater from aquifers can be extracted using a water well. Aquifers vary greatly in their characterist ...

gives the energy flow ''Fe'' through the cross-section in ''E''/day per m width of the aquifer. While flowing, the groundwater loses energy due to friction of flow, i.e. hydraulic energy is converted into heat. At the same time, energy may be added with the recharge of water coming into the aquifer through the water table. Thus one can make an hydraulic energy balance of a block of soil between two nearby cross-sections. In steady state, i.e. without change in energy status and without accumulation or depletion of water stored in the soil body, the energy flow in the first section plus the energy added by

groundwater recharge Groundwater recharge or deep drainage or deep percolation is a hydrologic process, where water moves downward from surface water to groundwater. Recharge is the primary method through which water enters an aquifer. This process usually occurs ...

between the sections minus the energy flow in the second section must equal the energy loss due to friction of flow. In mathematical terms this balance can be obtained by differentiating the cross-sectional integral of ''Fe'' in the direction of flow using the Leibniz rule, taking into account that the level of the water table may change in the direction of flow. The mathematics is simplified using the Dupuit–Forchheimer assumption. The hydraulic friction losses can be described in analogy to ''Joule's law'' in electricity (see Joule's law#Hydraulic equivalent), where the friction losses are proportional to the square value of the current (flow) and the

electrical resistance The electrical resistance of an object is a measure of its opposition to the flow of electric current. Its reciprocal quantity is , measuring the ease with which an electric current passes. Electrical resistance shares some conceptual paralle ...

of the material through which the current occurs. In groundwater hydraulics ( fluid dynamics, hydrodynamics) one often works with

hydraulic conductivity Hydraulic conductivity, symbolically represented as (unit: m/s), is a property of porous materials, soils and rocks, that describes the ease with which a fluid (usually water) can move through the pore space, or fractures network. It depends on ...

(i.e. permeability of the soil for water), which is inversely proportional to the hydraulic resistance. The resulting equation of the energy balance of groundwater flow can be used, for example, to calculate the shape of the

water table The water table is the upper surface of the zone of saturation. The zone of saturation is where the pores and fractures of the ground are saturated with water. It can also be simply explained as the depth below which the ground is saturated. T ...

between drains under specific

aquifer An aquifer is an underground layer of water-bearing, permeable rock, rock fractures, or unconsolidated materials ( gravel, sand, or silt). Groundwater from aquifers can be extracted using a water well. Aquifers vary greatly in their characteris ...

conditions. For this a

numerical solution Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods th ...

can be used, taking small steps along the impermeable base. The drainage equation is to be solved by trial and error (

iteration Iteration is the repetition of a process in order to generate a (possibly unbounded) sequence of outcomes. Each repetition of the process is a single iteration, and the outcome of each iteration is then the starting point of the next iteration. ...

s), because the hydraulic potential is taken with respect to a reference level taken as the level of the water table at the water divide midway between the drains. When calculating the shape of the water table, its level at the water divide is initially not known. Therefore, this level is to be assumed before the calculations on the shape of the water table can be started. According to the findings of the calculation procedure, the initial assumption is to be adjusted and the calculations are to be restarted until the level of the water table at the divide does not differ significantly from the assumed level. The trial and error procedure is cumbersome and therefore

computer program A computer program is a sequence or set of instructions in a programming language for a computer to execute. Computer programs are one component of software, which also includes documentation and other intangible components. A computer program ...

s may be developed to aid in the calculations.

Application

The energy balance of groundwater flow can be applied to flow of groundwater to subsurface drains. The

''EnDrain'' EnDrain, computer program for drainage design using the energy balance of groundwater flow, free download from

, or from

/ref> compares the outcome of the traditional Drainage equation, drain spacing equation, based on

Darcy's law Darcy's law is an equation that describes the flow of a fluid through a porous medium. The law was formulated by Henry Darcy based on results of experiments on the flow of water through beds of sand, forming the basis of hydrogeology, a branch of ...

together with the continuity equation (i.e.

conservation of mass In physics and chemistry, the law of conservation of mass or principle of mass conservation states that for any system closed to all transfers of matter and energy, the mass of the system must remain constant over time, as the system's mass can ...

), with the solution obtained by the energy balance and it can be seen that drain spacings are wider in the latter case. This is owing to the introduction of the energy supplied by the incoming recharge.

References

External links

*Articles on the energy balance of groundwater flow can be downloaded from

under nr. 3 and 4. {{Agricultural water management Aquifers Hydrology Hydrogeology Hydraulic engineering Conservation laws

Theory

Application

See also

References

External links