Armfield Instruction Manual
20
Basic Theory
a. Darcy's
Law
The flow of water through porous media is governed by what is known as
Darcy's Law: "The flow rate through porous media is proportional to head loss
and inversely proportional to the length of the flow path".
Darcy's Law can be expressed mathematically as:
…. (1)
where
Q = flow rate
A = cross-sectional area of flow
K = a proportionality constant, called the "coefficient of permeability"
h = head loss
L = length of the flow path.
A more usual statement of Darcy's Law, however, in terms of velocity of flow.
Since velocity is given as
…. (2)
division of equation (1) by A leads to the familiar statement of Darcy's Law:
…. (3)
Since the ratio
, which is called "hydraulic gradient: and is analogous to
slope, is dimensionless, the coefficient of permeability K must have the
dimensions of velocity for equation (3) to be valid. The coefficient K is
different for different materials and is determined in the laboratory by using
equation (1) in the form:
Note that all the right-hand side terms can be directly measured. A method of
doing so is shown in Figure i below.
