Modeling Tools for Environmental Engineers and Scientists

water quality standard of 500 mg/L TDS. The proposed pumping rate is 10gpm (20,000 ft 3 /day), while the average aquifer flux is U = 5 ft 2 /day.Stream function and the velocity potential functions developed from thepotential theory can be used in modeling this scenario. A coordinate system,with origin at O, is first chosen, as shown in Figure 9.36.To create a constant potential boundary along the river, an “image” injectionwell is used on the opposite side of the river. Using superposition, thepotential at any point P can be expressed as follows:Q = 0 + Ux + 2 π Qln (r 1 ) – 2 π ln (r 2 )The flow field velocity in the x-direction, Ux, along the river (where x = 0),for various locations of the well can now be found from the following:(U x ) (0,y) = – ∂ ∂x (0,y)Q= –U – 2 π L QL–+2 y + 2 2 π LL 2 + y 2When the above result equals zero, or in other words, U x along the river iszero, all the flow into the well will come from the aquifer. Setting the aboveto zero yields the following condition:2 yL Q = – 1 = – 1πL Uwhich can have one of the following results:Figure 9.36 Problem definition for well location.© 2002 by CRC Press LLC