will not correspond exactly to that determined for the

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-

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

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

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.

sidered valid for relatively high-percent penetrations.

4-22 for flow and drawdown produced by pumping an

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-

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

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.

(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

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)

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