Well Hydraulics

The determination of well capacity and flow has great practical significance due to their prevalence in both the private and commercial sector. There has also been great concern over the emergence of contaminants in ground water and knowledge of ground water movement allows us predict the appearance of these contaminants in our water supply. The rate of replenishment in a well is largely a function of soil porosity but is also dependent on the pieziometric head and geologic substrata present.

The basic well equation for an unconfined aquifer with uniform radial flow is:

 Q=(pi*K(h2^2-h1^2)) /ln(r2/r1).  

By converting K to gpd/ft^2, Q to gpm, h and r in ft, and ln to log the equation becomes:

For a well drilled into a confined aquifer a separate equation must be used. This equation takes into account the aquifer thickness, m:

It is also necessary to be able to analyse wells with unsteady flow. Without a computer this is traditionally done by a graphical solution developed by Thiess. His method is used to find the transmissibility and storage coeffecient of the soil. Storage coeffecient is the volume of water an aquifer takes in or releases per unit surface area of aquifer per unit change in head normal to the surface. The method consists of using drawdown, radius, and time measurements from the start of pumping. These are related by the equation:

Next a plot ot the well function W(u), (Viessman, 454), is superimposed on a log-log plot of observed values for r^2/t vs. s, the drawdown. To determine T and S simply place the well function plot over the data plot with the u and r^2/t as the x-axes and move them around until the two match closely yeilding a point with the necessary data. It is then an easy procedure to plug values from this point into the equations:

References

Introduction to Hydrology. Warren Viessman, Jr. et alia. Harper Collins.1989.

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