TM 5-818-5/AFM 88-5, Chap 6/NAVFAC P-418
will not correspond exactly to that determined for the
(2) Circular and rectangular slots. Equations for
slot due to convergence of flow to the wells. The piezo-
flow and head or drawdown produced by circular and
metric head in the vicinity of the well is a function of
rectangular slots supplied by a circular seepage source
well flow Qw; well spacing a; well penetration W; effec-
are given in figures 4-6 through 4-9. Equations for
tive well radius rw; aquifer thickness D, or gravity head
flow from a circular seepage source assume that the
H; and aquifer permeability k. The equations given in
slot is located in the center of an island of radius R.
figures 4-15 and 4-16 consider these variables.
For many dewatering projects, R is the radius of influ-
(2) Flow to wells from a line source.
ence rather than the radius of an island, and proce-
(a) Equations given in figures 4-17 through
dures for determining the value of R are discussed in
4-19 for flow and drawdown produced by pumping a
a(3) above. Dewatering systems of relatively short
single well or group of fully penetrating wells supplied
length are considered to have a circular source where
from an infinite line source were developed using the
they are far removed from a line source such as a river
method of image wells. The image well (a recharge
or shoreline.
well) is located as the mirror image of the real well
(3) Use of slots for designing well systems. Wells
with respect to the line source and supplies the per-
can be substituted for a slot; and the flow Qw, draw-
vious stratum with the same quantity of water as that
down at the well (H-hw) neglecting hydraulic head
being pumped from the real well.
losses at and in the well, and head midway between
(b) The equations given in figures 4-18 and
4-19 for multiple-well systems supplied by a line
from the equations given in figures 4-20, 4-21, and
source are based on the fact that the drawdown at any
4-22 for a (single) line source for artesian and gravity
point is the summation of drawdowns produced at that
flow for both "fully" and "partially" penetrating wells
point by each well in the system. Consequently, the
where the well spacing a is substituted for the length
drawdown at a point is the sum of the drawdowns pro-
of slot x.
duced by the real wells and the negative drawdowns
(4) Partially penetrating slots. The equations for
produced by the image or recharge wells.
gravity flow topartially penetrating slots are only con-
(c) Equations are given in figures 4-20 through
sidered valid for relatively high-percent penetrations.
4-22 for flow and drawdown produced by pumping an
c. Flow to wells.
infinite line at wells supplied by a (single) line source.
(1) Flow to wells from a circular source.
The equations are based on the equivalent slot assump-
(a) Equations for flow and drawdown produced
tion. Where twice the distance to a single line source
by a single well supplied by a circular source are given
or 2L is greater than the radius of influence R, the
in figures 4-10 through 4-12. It is apparent from fig-
value of R as determined from a pumping test or from
ure 4-11 that considerable computation is required to
figure 4-23 should be used in lieu of L unless the exca-
determine the height of the phreatic surface and re-
vation is quite large or the tunnel is long, in which case
sulting drawdown in the immediate vicinity of a grav-
equations for a line source or a flow-net analysis
ity well (r/h less than 0.3). The drawdown in this zone
should be used.
usually is not of special interest in dewatering systems
(d) Equations for computing the head midway
and seldom needs to be computed. However, it is al-
between wells above that in the wells Ah, are not
ways necessary to compute the water level in the well
given in this manual for two line sources adjacent to a
for the selection and design of the pumping equip-
single line of wells. However, such can be readily de-
ment.
termined from (plan) flow-net analyses.
(b) The general equations for flow and draw-
(3) Limitations on flow to a partially penetrating
down produced by pumping a group of wells supplied
by a circular source are given in figure 4-13. These
ing well (for artesian flow) are approximate relations
equations are based on the fact that the drawdown at
intended to present in a simple form the results of
any point is the summation of drawdowns produced at
more rigorous but tedious computations. The rigorous
that point by each well in the system. The drawdown
computations were made for ratios of R/D = 4.0 and
factors F to be substituted into the general equations
6.7 and a ratio R/rw = 1000. As a consequence, any
in figure 4-13 appear in the equations for both arte-
agreement between experimental and computed
sian and gravity flow conditions. Consequently, the
values cannot be expected except for the cases with
factors given in figure 4-14 for commonly used well
these particular boundary conditions. In model studies
arrays are applicable for either condition.
at the U.S. Army Engineer Waterways Experiment
(c) Flow and drawdown for circular well arrays
Station (WES), Vicksburg, Mississippi, the flow from a
can also be computed, in a relatively simple manner,
partially penetrating well was based on the formula:
by first considering the well system to be a slot, as
shown in figure 4-15 or 4-16. However, the piezo-
(4-2)
Qwp =
metric head in the vicinity of the wells (or wellpoints)
1n(R/rw)
4-28
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