Darcy’s Law & Its Limitations

Darcy’s law states that the discharge or rate of flow per unit time is proportional to hydraulic gradient. Generally the laminar flow velocity through homogeneous soil is represented by Darcy’s law.

It is represented by a simple equation as,

V ∝ i   OR   V = Ki                  ……(eqn 1)

Here, K = coefficient of permeability, V = velocity of flow, i = hydraulic gradient

Limitations of Darcy’s Law

Darcy’s law is generally valid only when the flow is laminar i.e when the reynold’s number is less than on equals to 1.

Re ≤ 1

By calculating all types of soil, Darcy’s law is valid only for clay, silt and sand and not for gravels, cobbles etc. This is because the flow is always turbulant.

When the reynolds number is less than 2000, the flow of water through the pipe remains laminar.

–  Generally, when there is loss of head per unit length of flow through soil, it is usually equal to hydraulic gradient. As said the equation is,

i = h/L

Here, L = length of specimen, h = hydraulic head

–  Superficial velocity or discharge velocity are the results of velocity delivered by Darcys law. When there is discharge through total cross sectional area which is normal in the direction of flow, it is represented as :

Q = V.A = Ki A

Here, Q = total discharge rate, A = cross sectional area, Ki = from eqn 1, i = 1 and hence K = V

Also Read : Soil Stabilization Methods & Necessity
Also Read : California Bearing Ratio Test【CBR Test】of Soil
Also Read : Three Phase System of Soil (Diagram)

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