Environmental Engineering Reference
In-Depth Information
Fig. 11.7 Typical set-up of a Darcy-experiment; for examination of Darcy's Law and the determi-
nation of hydraulic conductivity
The left side of the equation denotes the
Darcy velocity
, which is derived from
the real mean interstitial flow velocity by multiplication with the porosity
. It is,
in fact, the same variable as on the left side of (
11.11
); i.e. it is the velocity which
represents the fluid flux. On the right side of equation (
11.12
) the head gradient
y
∇
h
is a generalization of the right side of (
11.11
) replacing the head difference per unit
length.
K
f
is the proportionality factor, which is mostly referred to as hydraulic
conductivity. It has the physical unit of velocity [L/T], [m/s] in MKS units.
K
f
depends on the properties of pore space, such as pore diameter and length,
connectivity and porosity, or pore structure in general. The structure of the pores is
far too complex to predict the
K
f
- value from microscopic properties. For porous
pipe structures the hydraulic conductivity can be estimated on the basis of the
Hagen-Poiseuille formula (see Sidebar 11.1).
The
K
f
- value also depends on the properties of the fluid which flows through
the pore space. It is accepted that the dependencies can be separated by the
approach:
k
r
g
K
f
¼
(11.13)
where
k
represents the permeability (physical MKS unit: [m
2
]) that depends on the
porous medium, while density
r
and dynamic viscosity
are fluid properties.
