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Energy balance has the following meanings in several fields:
Additional recommended knowledge
Energy balance of groundwater flow
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 gives us the energy flow through the cross-section gives the energy flow through the cross-section in E/day per m width of the aquifer.
While flowing, the groundwater loses energy due to friction of flow. 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. The energy flow in the first section plus the energy added by recharge 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 E in the direction of flow, taking into account that the level of the water table may change using the Leibnitz rule . The mathematics is simplified by assuming that the horizontal of the flow is constant within the section. This assumption is similar to the Dupuit assumption (the flow is horizontal), but it is more realistic because it only refers to the horizontal component of the flow and it does acknowledge the presence of non-horizontal flow.
The hydraulic friction losses can be described in analogy to the law of Joule in electricity, where the friction losses are proportional to the square value of the current (flow) and the electrical resistance of the material through which the current occurs. In groundwater hydraulics one often works with the hydraulic conductivity (permeability of the soil for water), which is inversely proportional to the 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 specific aquifer conditions. For this we can use a numerical solution, taking small steps along the impermeable base. The equation is to be solved by trial and error (iterations), 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. As we are calculating the shape of the water table, its level at the water divide is initially not known. Therefore we have to assume this level beforehand, start the calculations, adjust the initial assumption according to the findings of the calculation procedure, and restart the calculations from the beginning until the level of the water table at the divide does not differ significantly from the assumed level.
To trial and error procedure is not very inviting to do the calculations by hand. Therefore, a computer program was developed to remove the burden.
A detailed article on "The energy balance of groundwater flow" can be viewed and downloaded freely from www.waterlog.info.
The same holds for an article on "The energy balance of groundwater flow applied to subsurface drainage in anisotropic soils by pipes or ditches with entrance resistance."
Computer program, drain spacing equation
The computer program (EnDrain) can be freely downloaded from the same website.
The computer program compares the outcome of the traditional drain spacing equation based on the Darcy's law with the solution obtained by the energy balance and it can be seen that drain spacings are wider in the latter case than in the first. This is owing to the introduction of the energy supplied by the incoming recharge.
The owner of the referenced website invites the reader to apply the energy balance to the seepage surface along a sloping outlet boundary of the aquifer, or at the foot of a river embankment, or at the end of a water conduit from which the water falls down.
|This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Energy_balance". A list of authors is available in Wikipedia.|