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r1u 11 u+Lc <br />• 3) qr - qo = Sya dt \ hdx - bLu'+ 5 dt~ Hdx - Ho(Lu+Lc )~ <br />J 0 // Lu <br />where: <br />q is the regional flux, LZ/t; <br />r <br />q is the flux into the pit, L2/t; <br />0 <br />b is the confined aquifer thickness, L; and <br />H is the pressure head above the confining unit in the undisturbed zone. <br />0 <br />Substituting for h, Lu, H, and Lc and carrying out the integrat icon results in the <br />following equation: <br />4) - dt Q 1 s <br />qr-qo= /) <br />0 <br />where: <br />E - CSyaTbZ 5TH 2 5TH b~ <br />5) + o + o <br />6 2 2 <br />• Taking the differential of the right-hand side of equation 4 and rearranging, results in <br />the following equation: <br />6) dt = -E dq <br />3 2 0 <br />qo - grgo <br />Integrating both sides of equation 6 results in the following: <br />7) t qo(t) -E <br />dt 3 2 dqo <br />q q q <br />0 qo(0) =deo r o <br /> q q <br /> ° r <br />8) 1 1 <br /> t=- E + 1n C ~ <br /> q <br />~q 2 q <br /> <br />r <br />o q ° J <br /> r <br /> The total flux of Hater into the open pit as a function of time is represented by the q <br />0 <br /> term in equation 8. Therefore, the flux of water as a function of time can be determined <br /> by solving for the roots of equation 8. The program numerically solves for the roots <br />. through the use of a Newton-5 iteration method. <br />The total volume of flow into the pit is determined by integrating the flux as a function <br />17-7 Revised 04/11/88 <br />