Environmental Engineering Reference
In-Depth Information
Horizontal line,
no flow condition
h
p
Pressure
head h
p
Total
head
h
t
h
t
h
e
Sand-filled
glass tube
Elevation
head h
e
Datum elevation
(a)
Water supply
Hydraulic
head
h
Horizontal line
L
Pressure
surface
Pressure
head
h
p
Total
head
h
t
Elevation
head
h
e
FIGURE 8.22
Diagrams illustrating the hydraulic
gradient of groundwater: (a) no-flow
condition and (b) flow creates an
hydraulic gradient,
i
Reservoir
Tailwater
Datum
(b)
h/L.
Permeability (See Also
Section 3
.3)
Permeability
is the capacity of a material to transmit water.
Darcy's law
expresses the relationship governing the flow of water through a subsurface
medium but is valid only for the conditions of laminar flow through a saturated, incom-
pressible material:
q
kiA
(8.3)
where
q
is the rate of flow or quantity per unit of time (
Q
/
t
), given as L/min, cm
2
/sec,
etc.,
k
the coefficient of permeability in cm/sec,
i
the hydraulic gradient, or total head loss
per flow length,
h
/
L
and
A
the cross section of the material through which the flow
occurs, in cm
2
.
Darcy's initial expression was
v
d
k
i, where
v
d
equals the discharge velocity,
or total volume flow rate per unit of cross section perpendicular to the flow direction
(
V
Q
/
A
).
Values for
k
as used by engineers are given in units of velocity (cm/sec) at a tempera-
ture of 20
C, since temperature affects the viscosity of water. Typical values for various
materials are given in
Section 3.3.
For convenience, engineers refer to permeability as the
superficial
or
discharge velocity
per unit of gradient, as if the flow occurs through the total
volume of the medium, not only the void area.
Geologists use the symbol
K
to signify permeability. It is expressed as a discharge and
defined as “the rate of flow in gallons per day through an area of 1 ft
2
under a hydraulic
gradient of unity (one 1 ft/ft)” by Krynine and Judd (1957), as illustrated in
Figure 8.23.
Transmissibility T
is used by geologists to represent the flow in gallons per day through a
section of aquifer 1 ft in width and extending the full length of the stratum under a unit
head (slope of 1 ft) as shown in Figure 8.23. Transmissibility equals the coefficient of per-
meability of the aquifer times its thickness.
°
