Civil Engineering Reference
In-Depth Information
When water is pumped from a well, the quantity discharged initially is derived
from aquifer storage immediately surrounding the well. As pumping continues, more
water must be derived from storage at greater and greater distances from the well. The
circular-shaped cone of depression must expand so that water can move from greater
distances toward the well. The radius of influence of the well increases as the cone
continues to expand. The drawdown also increases as the cone deepens to provide the
additional head required to move the water from a greater distance. Over time, the
cone expands and deepens at a decreasing rate because with each additional foot of
horizontal expansion, a larger volume of stored water is available than from the pre-
ceding one. The cone will continue to enlarge until aquifer recharge equals the pum-
page.
When the cone has stopped expanding for one or more of the above reasons, a
condition of equilibrium exists. There is no further increase in drawdown with increase
in time of pumping. In some wells, equilibrium occurs within a few hours after pump-
ing begins; in others, it does not occur even though the length of the pumping period
maybe extended for years.
Well discharge formulas for equilibrium conditions are well established.
25
There
are two basic formulas, one for artesian conditions and the other for water-table
conditions. Both assume recharge at the periphery of the cone of depression. Figure
8-20 shows a vertical section of a well constructed in a water-table aquifer. The
formula for the water-table well is:
P
(
H
2
h
)
2
Q
(8-3)
1055 log
R
/
r
where:
Q
well yield or pumping rate, gpm (m
3
/d)
P
permeability of the water-bearing sand, gpd / sq ft (m / d)
H
saturated thickness of the aquifer before pumping ft (m)
h
depth of water in the well while pumping, ft (m)
R
radius of influence, ft (m)
r
radius of the well, ft (m)
1055
constant for English units listed (3.993
constant for metric units listed)
Figure 8-21 is a vertical section of a well pumping from an artesian aquifer. The
formula for a well operating under artesian conditions is:
Pm
(
H
h
)
Q
(8-4)
528 log
R
/
r
where:
m
thickness of aquifer, ft (m)
H
static head at bottom of aquifer, ft (m)
528
constant for English units listed (1.9984
constant for metric units listed)
