Groundwater energy balance

cross-sectional area) with the groundwater potential (dimension energy per volume of water, or

[1] 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

Thus one can make an hydraulic energy balance of a block of soil between two nearby cross-sections.

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 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.

The resulting equation of the energy balance of groundwater flow can be used, for example, to calculate the shape of the water table between drains under specific aquifer conditions.

The drainage equation is to be solved by trial and error (iterations), 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.

The trial and error procedure is cumbersome and therefore computer programs may be developed to aid in the calculations.

[2] The computer program EnDrain [3] compares the outcome of the traditional drain spacing equation, based on Darcy's law together with the continuity 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.