permeability of the soil under a set of operating conditions. Knowing the permeability, the maximum safe yield can be determined. For both nonpressure and
pressure wells, at least one observation well is needed within the zone of influence
of the pumped well. If measurements of water level can be made in the pumped well,
this can serve as the second observation well. If it is not possible to determine the
water level in the pumped well, then a second observation well is needed for the
determination.
For the nonpressure well in the surface aquifer, the relationship between the flow
and the permeability may be determined by the equation:
Q ¼
πK p h
2
1 À h
2
w
À
Á
ln
r 1
r w
ð6:13Þ
The terms of h 1 , h w , r 1 , and r w for the equation are shown in Fig. 6.19, in which
one observation well and the pumped well are used. K p is a coefficient. If two
observation wells are used (see Fig. 6.20), then h 1 and r 1 become the observation well
farther from the pumped well, and h 2 and r 2 for the second observation well closer to
the pumped well may be substituted for h w and r w , respectively.
For pressure wells in a confined aquifer, the equivalent equation is:
Q ¼
2πK p t h 1 À h w
ð
Þ
ln
r 1
r w
ð6:14Þ
The representative parameters for this equation are shown in Fig. 6.20. It may be
seen that, in working with a pressure (artesian) well, the water level in the observation well will rise above the confining layer. This water level represents the piezometric surface or the elevation or pressure head to which the water will rise with no
confinement. In this case, however, there is no actual cone of depression surrounding
the pumped well in the confined aquifer. There is only a reduction in the piezometric
head in the neighborhood of the pumped well.
The previous two equations assume that the zone of influence is circular. Under
actual conditions this may not be true, since there is some horizontal flow in the
aquifer and, therefore, the cone of depression will be lower on the downstream side
of the pumped well. Also, under certain conditions, it may take a long time (up to
10 yr) to establish equilibrium. Thus, other methods for determining the yield of an
aquifer are necessary.
One common method is the Theis method [17]. This considers the fact that an
aquifer is somewhat elastic, so that removing water from it causes a lower pressure in
the area of the pumped well that causes more water to enter into the area. The Theis
method is based upon four assumptions: (a) the soil of the aquifer is homogeneous;
(b) the coefficient of transmissibility, T, is constant; (c) the coefficient of storage, S c ,
is constant, representing the yield of water per unit area of aquifer per unit drop in
hydraulic gradient; and (d) the water is released from the aquifer instantaneously.
270
D. B. Aulenbach et al.
pressure wells, at least one observation well is needed within the zone of influence
of the pumped well. If measurements of water level can be made in the pumped well,
this can serve as the second observation well. If it is not possible to determine the
water level in the pumped well, then a second observation well is needed for the
determination.
For the nonpressure well in the surface aquifer, the relationship between the flow
and the permeability may be determined by the equation:
Q ¼
πK p h
2
1 À h
2
w
À
Á
ln
r 1
r w
ð6:13Þ
The terms of h 1 , h w , r 1 , and r w for the equation are shown in Fig. 6.19, in which
one observation well and the pumped well are used. K p is a coefficient. If two
observation wells are used (see Fig. 6.20), then h 1 and r 1 become the observation well
farther from the pumped well, and h 2 and r 2 for the second observation well closer to
the pumped well may be substituted for h w and r w , respectively.
For pressure wells in a confined aquifer, the equivalent equation is:
Q ¼
2πK p t h 1 À h w
ð
Þ
ln
r 1
r w
ð6:14Þ
The representative parameters for this equation are shown in Fig. 6.20. It may be
seen that, in working with a pressure (artesian) well, the water level in the observation well will rise above the confining layer. This water level represents the piezometric surface or the elevation or pressure head to which the water will rise with no
confinement. In this case, however, there is no actual cone of depression surrounding
the pumped well in the confined aquifer. There is only a reduction in the piezometric
head in the neighborhood of the pumped well.
The previous two equations assume that the zone of influence is circular. Under
actual conditions this may not be true, since there is some horizontal flow in the
aquifer and, therefore, the cone of depression will be lower on the downstream side
of the pumped well. Also, under certain conditions, it may take a long time (up to
10 yr) to establish equilibrium. Thus, other methods for determining the yield of an
aquifer are necessary.
One common method is the Theis method [17]. This considers the fact that an
aquifer is somewhat elastic, so that removing water from it causes a lower pressure in
the area of the pumped well that causes more water to enter into the area. The Theis
method is based upon four assumptions: (a) the soil of the aquifer is homogeneous;
(b) the coefficient of transmissibility, T, is constant; (c) the coefficient of storage, S c ,
is constant, representing the yield of water per unit area of aquifer per unit drop in
hydraulic gradient; and (d) the water is released from the aquifer instantaneously.
270
D. B. Aulenbach et al.