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According to Darcy's law, the rate of flow water through soil, for laminar flow condition in a saturated soil is:
(Where, Q = rate of flow, i = hydraulic gradient, k= Darcy's coefficient of permeability
A = total cross-sectional area of soil mass perpendicular to direction of flow.)

  • A.\(Q = k^{2}iA\)
  • B.\(Q = ki^{2}A\)
  • C.\(Q = kiA^{2}\)
  • D.Q = kiA

Answer: D

Darcy's law gives Q = kiA.

For laminar flow through saturated soil, the discharge velocity is proportional to the hydraulic gradient, v = ki, where k is the coefficient of permeability. Multiplying by the total cross-sectional area of the soil perpendicular to the flow gives the rate of flow Q = kiA.

The other options square one of the three quantities, which breaks the linear proportionality on which Darcy's law rests and gives the wrong dimensions for a flow rate.

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