Environmental Engineering Reference
In-Depth Information
develop secondary porosity if the rocks become fractured; it
is such fractures that are tapped for water supply.
4.2
Static Water—Hydraulic Head
A fluid is a substance that does not maintain a shear stress; in
contrast, a solid has a definite volume and shape and does
maintain a shear stress, whereas a fluid has a definite volume
but not shape. In other words, fluids continually deform. For
example, if you hit a baseball with a bat, the baseball goes in
a predictable direction. If you hit a balloon filled with water
with a bat, the direction of the water droplets upon the
balloon bursting is far less predictable. Because fluids cannot
maintain shear stresses, the surface of a liquid at equilibrium
is flat, or horizontal. As we saw in Chap. 2, the effects of
surface tension negate this equilibrium if water is placed in a
thin-diameter tube, which usually results in a concave
upward surface.
The pressure,
P
, at any point on the flat surface of a
static fluid is composed of the force,
F
, exerted by the fluid
on the unit area of the point, in ML/T
2
.Inotherwords,
pressure is the force per unit area, or
P
4.1.5 Hydraulic Gradient
As previously noted in the derivation of Darcy's Law, the
hydraulic gradient,
D
l
, is important in driving groundwa-
ter flow through porous media. The head loss between two
wells in the direction of flow represents the energy needed
by groundwater to overcome inertial forces and the friction
of water particles in voids relative to those attached to
sediments by hydroscopic force or tension (Fig.
4.6
). Stearns
(1927) performed laboratory investigations to determine
whether small hydraulic gradients could be responsible for
groundwater flow. He reported that, as expected from
Darcy's Law, groundwater flow could occur even under a
hydraulic gradient of a few inches per mile.
h
/
D
F
/
A
. The pressure
stress in a static fluid is the same in all directions. This was
observed by Pascal as early as 1653. Isaac Newton defined
force as
F
(a vector)
¼
¼
ma
(a vector), where
m
¼
mass and
a
acceleration. Therefore, a body of mass,
m
,under
static conditions accelerates solely because of gravity.
Mass should not be confused with weight; mass is the
same regardless of location, whereas weight is unique to
location because it equals the force of gravity on a particu-
lar object.
But the pressure in a fluid can vary from the pressure at its
surface. For example, in a column of water, the pressure
changes with respect to the height of the column because of
the difference in the weight of the water at various heights in
response to gravity. In other words, the pressure at a partic-
ular location is directly proportional to the depth of the
column of water above it. Generally, the pressure based on
the weight of water is related to the density,
¼
r
, of the fluid,
M/L
3
times the depth,
h,
of the water. The
pressure,
P
, at any height,
h
, in that column is
where
r ¼
P
¼ r
gh
:
(4.7)
In other words, the pressure at a given depth below the
water surface is greater than atmospheric pressure and can
be quantified by
gh
.
Pressure is often defined in pascals (Pa) or Newton per
square meter where 1 Pa
r
1 N/m
2
. In hydrogeology the
effect of atmospheric pressure on water is usually considered
to be negligible under the assumption that it can be consid-
ered constant over time. Under some short-term conditions,
however, this assumption is not always valid, especially for
semi-confined to confined unconsolidated and fractured-
rock aquifers (Landmeyer 1996).
¼
Fig. 4.6
The hydraulic gradient,
Dh
/
Dl
is the force behind ground-
water flow,
Q
.
MSL
is mean sea level.
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