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Flow of ground water through porous medium is governed by well-known Darcy’s law which states that the rate of flow, Q through a saturated porous medium is:
(i) Proportional to the difference in hydraulic head Ah between the two flow sections,
(ii) Proportional to the area of flow cross-section A, and
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(iii) Inversely proportional to the length, L between the two sections. Thus,
Q = KA ∆h/L (4.1)
Here, K is a constant of proportionality and is equal to the hydraulic conductivity (or coefficient of permeability). The permeability of a porous medium describes the ease with which a fluid will pass through it. Therefore, it depends on the characteristics of the medium as well as the flowing fluid.
The permeability of a medium is measured in terms of hydraulic conductivity (also known as the coefficient of permeability) which is equal to the volume of water which flows in unit time through a unit cross-sectional area of the medium under a unit hydraulic gradient at the prevailing temperature.
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The hydraulic conductivity, therefore, has the dimensions of [L/T] and is usually expressed as metre per day or metre per hour. It should be noted that an unsaturated medium would have lesser hydraulic conductivity because of resistance to flow of water offered by the air present in void spaces.
The transmissivity, a term generally used for confined aquifers, is obtained by multiplying the hydraulic conductivity of an aquifer with the thickness of the saturated portion of the aquifer. It represents the amount of water which would flow through a unit width of the saturated portion of the aquifer under a unit hydraulic gradient and at the prevailing temperature.
Equation 4.1 is known as Darcy’s law and can also be written as
in which V is the apparent velocity of flow since the area of flow cross-section includes both void space as well as the space occupied by grains. The actual velocity of flow through the void spaces will be greater than the apparent velocity of flow.
When water is pumped from a well (Fig. 4.5), the water table (or the piezometric surface in case of a confined aquifer) is lowered around the well. The surface of a lowered water table resembles a cone and is, therefore, called the cone of depression. The vertical distance between the initial position of stable water table and the lowered water table due to pumping is known as the drawdown.
The drawdown decreases with increase in the distance from the well. The distance between the well and the location at which the drawdown is negligible is termed the radius of influence of the well. Well yield is defined as the volume of water discharged, either by pumping or free flow, per unit time.
With continued pumping of a well, the cone of depression continues to expand in an extensive aquifer until the pumping rate is balanced by the recharge rate. When pumping and recharging rates balance each other, a steady or equilibrium condition exists and there is no further increase in drawdown with continued pumping. For a confined aquifer, the well discharge Q, under equilibrium condition, is obtained as
