Page 72 - Water Engineering Hydraulics, Distribution and Treatment

50
Water Sources: Groundwater
Chapter 3
Hence,
The ability of an aquifer to transmit water is characterized by
(3.4)
K = k ∕ = k g∕ = kg∕
its coefficient of transmissivity. It is the product of the satu-
where is the specific density and , the kinematic viscosity.
rated thickness of the aquifer, b, and the average value of the
The fluid properties that affect the flow are viscosity and
hydraulic conductivities in a vertical section of the aquifer,
specific weight. The value of K varies inversely as the kine-
K. The transmissivity, T = Kb, gives the rate of flow of water
matic viscosity, , of the flowing fluid. The ratio of specific
through a vertical strip of an aquifer 1 ft wide extending
weight to viscosity is affected by changes in the temperature
the full saturated thickness of the aquifer under a unit of
and salinity of groundwater. Measurements of K are gener-
hydraulic gradient. It has the dimensions of (length) /time,
◦
ally referred to a standard water temperature such as 60 F
2
that is, ft /d or gpd/ft. Equation (3.6) can be rewritten as
◦
or 15.5 C. The necessary correction factor for field temper-
atures other than standard is provided by the relationship 3.8 AQUIFER CHARACTERISTICS 2
Q = TW(dh∕dl) (3.8)
K ∕K = ∕ 2 (3.5) where W is the width of flow.
2
1
1
Most groundwaters have relatively constant tempera- The coefficient of storage is defined as the volume of
tures, and this correction is usually ignored in practice and K water that a unit decline in head releases from storage in
is stated in terms of the prevailing water temperature. Special a vertical prism of the aquifer of unit cross-sectional area
circumstances in which correction may be important include (Fig. 3.3).
influent seepage into an aquifer from a surface-water body The physical processes involved when the water is
where temperature varies seasonally. released from (or taken into) storage in response to head
Darcy’s law is applicable only to laminar flow, and there changes are quite different in cases in which free surface
is no perceptible lower limit to the validity of the law. The is present from those in which it is not. A confined aquifer
volume rate of flow is the product of the velocity given by remains saturated during the withdrawal of water. In the case
Darcy’s law and the cross-sectional area A normal to the of a confined aquifer the water is released from storage by
direction of motion. Thus, virtue of two processes: (a) lowering of the water table in
the recharge or intake area of the aquifer and (b) elastic
Q = KA(dh∕dl) (3.6) response to pressure changes in the aquifer and its confining
and solving for K, beds induced by the withdrawal of water. For this the storage
coefficient is expressed as
K = Q∕[A(dh∕dl)] (3.7)
Hydraulic conductivity may thus be defined as the vol- S = b[ + ( ∕ )] (3.9)
ume of water per unit time flowing through a medium of
unit cross-sectional area under a unit hydraulic gradient. In in which is the average porosity of the aquifer; is the
the standard coefficient used by the US Geological Survey, specific weight of water; is the compressibility of water;
3
2
2
the rate of flow is expressed in gpd/ft (m /d/m ) under a and is the vertical compressibility of aquifer material. In
◦
hydraulic gradient of 1 ft/ft (m/m) at a temperature of 60 F most confined aquifers, storage coefficient values lie in the
◦
(15.5 C). This unit is called the meinzer. For most natural range of 0.00005–0.0005. These values are small and thus
aquifer materials, values of K fall in the range of 10–5000 large pressure changes over extensive areas are required to
meinzers. develop substantial quantities of water.
Ground surface Ground surface
Piezometric Surface
1´ Unit decline of
piezometric surface
S
Aquiclude
Water table Figure 3.3 Graphical
1´ representation of storage
coefficient. The volume of water
S Artesian Unit decline Unconfined
b aquifer aquifer that a unit decline in head releases
Unit cross- of water table
sectional area from storage in a vertical prism of
Unit cross-sectional area the aquifer of unit cross-sectional
area. (a) Confined aquifer; (b)
Aquiclude Aquiclude unconfined aquifer. Conversion
′
(a) (b) factor: 1 = 1ft = 0.3048 m.