Rate and Volume of Stream Depletion due to Pumping

The two analytical solutions researched by Theis, and also Glover and Balmer, for the rate of stream depletion are shown to be the same in the mathematical sense by solving the integral appearing in the Theis solution. Expressions for the volume of stream depletion expressed as a fraction of total volume pumped relative to the rate of depletion are obtained for pumping and recovery. The optimum location of a well near the stream and the time to reach equilibrium are suggested.