2013-07-03_REVISION - M1985112 ‎(3)‎

• Permit No: M1985112
• IBM Index Class Name: REVISION
• Doc Date: 7/3/2013
• Doc Name: TR Submittal
• From: Loloff Construction, Inc.
• To: DRMS
• Type & Sequence: TR1
• Media Type: D
• Archive: No

212
GROUNDWATER AND WELLS
center well
0.2409Dm(1,310 m'/ day) H, =700tt(213
A
�COne 3 57011. (171 m)
CCone 2 R , <00 n
�\ \\ Cone 1 (122 m)
6tt(18m)
0.2 tt (006 m) - \\ 03 11 0
_ (009 )
m)
i
has only extended outward an additional
170 ft (51.8 m) and deepened by an ad-
ditional 0.3 ft (0.09 m). An additional ra-
dial expansion of only 130 ft (39.6 m) and
an increase in depth of only 0.2 ft (0.06 m)
occurs in the next 10 hours. Calculations
of the volume of each of the cones would
show that cone 2 has twice the volume of
cone 1, and cone 3 has three times the vol-
ume of cone 1. This occurs because, at a
constant pumping rate, the same volume
of water is discharged from the well dur-
ing each 10 -hour interval. Thus, the in-
crease in volume of the cone of depres-
Figure 9.7. Changes in radius and depth of cone of sion is constant over time if the well is
depression after equal intervals of time, at constant being pumped at a constant rate and the
pumping rate.
aquifer is homogeneous.
It is evident from this example that after some hours deepening or expansion of the
cone during short intervals of pumping is barely discernible. This often leads observers
to conclude that the cone has stabilized and will not expand or deepen as pumping
continues. The cone of depression will continue to enlarge, however, until one or more
of the following conditions is met:
1. It intercepts enough of the flow in the aquifer to equal the pumping rate.
2. It intercepts a body of surface water from which enough additional water will
enter the aquifer to equal the pumping rate when combined with all the flow toward
the well.
3. Enough vertical recharge from precipitation occurs within the radius of influence
to equal the pumping rate.
4. Sufficient leakage occurs through overlying or underlying formations to equal
the pumping rate.
When the cone has stopped expanding because of one or more of the above con-
ditions, equilibrium exists. There is no further drawdown with continued pumping.
In some wells, equilibrium occurs within a few hours after pumping begins; in others,
it never occurs even though the pumping period may be extended for years.
EQUILIBRIUM WELL EQUATIONS
More than a hundred years ago, engineers began work on adapting Darcy's basic
flow equation to groundwater flow toward a pumping well. The objective was to derive
simple mathematical expressions for describing the flow regime of water in the ground.
Because direct observation of groundwater movement is impossible, mathematical
analysis offers a convenient and reliable way to predict what happens to water in the
ground.
Well discharge equations for equilibrium conditions were derived by various in-
vestigators (Slichter, 1899; Turneaure and Russell, 1901; Thiem, 1906). These equa-
tions relating well discharge to drawdown assumed two- dimensional radial flow to-
ward a well (the vertical component of flow is ignored). There are two basic equations;
one for unconfined conditions and the other for confined conditions. For both equa-