- Groundwater energy balance
The

**groundwater energy balance**is the energy balance of agroundwater 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. [

*R.J.Oosterbaan, J.Boonstra and K.V.G.K.Rao, 1996, The energy balance of groundwater flow. In: V.P.Singh and B.Kumar (eds.), Subsurface-Water Hydrology, p. 153-160. Kluwer academic publishers, The Netherlands.*]*For free download see "external links"*.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 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 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 Leibnitz 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 assumption .The hydraulic friction losses can be described in analogy to

Joule's law in electricity, where the friction losses are proportional to the square value of the current (flow) and theelectrical resistance of the material through which the current occurs. In groundwater hydraulics (fluid dynamics ,hydrodynamics ) one often works withhydraulic conductivity (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 under specificaquifer conditions. For this anumerical solution can be used, taking small steps along the impermeable base. The equation is to be solved by trial and error (iteration s), because the hydraulic potential is taken with respect to a reference level for which we use 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 thereforecomputer program s may be developed to aid in the calculations.**Application**The computer program

*EnDrain*[*R.J.Oosterbaan, 1997, The energy balance of groundwater flow applied to subsurface drainage in anisotropic soils by pipes or ditches with entrance resistance. In this article, the confluence of flow (radial flow) towards the drain is taken into account.*] compares the outcome of the traditional*For free download see "external links"*.*drain spacing equation*, based onDarcy's law cumcontinuity equation (i.e.conservation of mass ), 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.**ee also***

Hydrogeology

*Groundwater discharge

*Groundwater flow equation **References****External links***The articles of references 1 and 2 can be viewed and downloaded freely from : [

*http://www.waterlog.info/articles.htm*] .

*The EnDrain software can be downloaded freely from [*http://www.waterlog.info/software.htm*] .**Invitation**The reader is invited to apply the energy balance to the seepage surface along a sloping outlet boundary of an aquifer, at the foot of a river embankment, or at the end of a water conduit from which the water falls down, and improve and expand this article.

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