Environmental Engineering Reference
In-Depth Information
Chapter 13
Aquifer Baseflow and 2D Meshing
13.1
1D Analysis
In general a flow field, as introduced in Chap. 11, may be different at every location
and, for transient flow, at every time instant. In contrast, one-dimensional base
flow represents a constant vector independent of time and space. Such an idealized
situation is seldom met in environmental compartments, but it may serve as an
approximate description of field situations. An example could be the groundwater
flow between two parallel channels which have a constant but different water level.
However, in parts of a regional watershed often a constant flow field is assumed as
a simplification of the real situation. The 1D assumption is also often justified for
experimental set-ups, for example in column experiments. The simplest flow
pattern for a fluid set-up between two plates is also 1D.
For a basic description, we assume that the
x
-axis is chosen in flow direction.
The flux per unit width results as product of the height
h
of the water column and the
velocity
u
:
q ¼ h u
(13.1)
The unit of
q
is [L
2
/T]. When the fluid fills only part of the space, i.e. in porous
media or in multi-phase situations,
u
is the product of the real velocity
v
multiplied
with the share
of the porespace or the corresponding phase on the total volume:
y
u ¼
y
v
(13.2)
In porous media,
u
is the Darcy-velocity or filter velocity. A slightly more
generalized situation is given if water height and velocity are allowed to change
along the flowpath (in
x-
direction):
q ¼ hðxÞuðxÞ
(13.3)
