Environmental Engineering FOURTH EDITION

Water Supply 113

L"

Surface area=2arh' I

Figure 6-5. A cylinder with water flowing through its sides toward the center.

the cylinder surface area, the above equation can be integrated

or

r2 (6.7a)

rl

Q In - = nK(hf - h;)

(6.7b)

Note that the integration is between any two arbitrary values of r and h.
These equations can be used to estimate the pumping rate for a given drawdown
any distance away from a well, using the water level measurements in two observation
wells in an unconjned aquifer (where the water table is free to change), as shown in
Fig. 6-6. Also, knowing the diameter of a well, it is possible to estimate the drawdown
at the well, the critical point in the cone of depression. If the drawdown is depressed all
the way to the bottom of the aquifer, the well "goes dry" -it cannot pump water at the
desired rate. Although the derivation of the foregoing equations are for an unconfined
aquifer, the same situation would occur for a confined aquifer, where the pressure
would be measured by observation wells.