Groundwater energy balance

The groundwater energy balance is the energy balance of a groundwater 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. When multiplying the horizontal velocity of groundwater (dimension, for example, per cross-sectional area) with the groundwater potential (dimension energy per volume of water, or ) one obtains an energy flow (flux) in for the given flow and cross-sectional area. Summation or integration of the energy flux in a vertical cross-section of unit width (say 1m) from the lower flow boundary (the impermeable layer or base) up to the water table in an unconfined aquifer gives the energy flow through the cross-section in 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 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 of the material through which the current occurs.