DHARM118 GEOTECHNICAL ENGINEERINGwhere
q = the rate of flow or discharge
k = a constant, now known as Darcy’s coefficient of permeability
h 1 = the height above datum which the water rose in a standpipe inserted at the en-
trance of the sand bed,
h 2 = the height above datum which the water rose in a stand pipe inserted at the exit
end of the sand bed.
L = the length of the sample.
A = the area of cross-section of the sand bed normal to the general direction of flow.
i = (h 1 – h 2 )/L, the hydraulic gradient.LL SandSandqinArea of cross sectionhh 11hh 22
DatumqoutFig. 5.2 Darcy’s Experiment
Equation 5.11 is known as Darcy’s law and is valid for laminar flow. It is of utmost
importance in geotechnical engineering in view of the its wide range of applicability.
Later researchers have established the validity of Darcy’s law for most types of fluid
flow in soils ; Darcy’s law becomes invalid only for liquid flow at high velocity or gas flow at
very low or at very high velocity.
Darcy’s coefficient of permeability provides a quantitative means of comparison for esti-
mating the facility with which water flows through different soils.
It can be seen that k has the dimensions of velocity; it can also be looked upon as the
velocity of flow for a unit hydraulic gradient. k is also referred to as the ‘coefficient of perme-
ability’ or simply ‘permeability’.
5.4.2 Validity of Darcy’s Law
Reynolds found a lower limit of critical velocity for transition of the flow from laminar to a
turbulent one, as already given by Eq. 5.10.
Many researchers have attempted to use Reynolds’ concept to determine the upper limit
of the validity of Darcy’s law. (Muskat, 1946; Scheidegger, 1957). The values of R for which
the flow in porous media become turbulent have been measured as low as 0.1 and as high as