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• d Lu d Lu+Lc <br />3) qr - qo = Sya dt \ hdx - bLu + S dt ` Hdx - Ho(Lu+Lc) <br />J 0 JLu <br />where: <br />q is the regional flux, Lz/t; <br />r <br />q is the flux into the pit, LZ/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 integration results in the <br />following equation: <br />4) tlt~E 1 <br />qr- 90= q /I <br />0 <br />where: <br />S) - (SyaTbz STHoz STHob1 <br />1\ J <br />E 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 />q - q q <br />o r o <br />Integrating both sides of equation 6 results in the following: <br />y) St Qo(t) -E <br />dt = C 3 Z dqo <br />J\ 9 - q q <br />0 qo(0) _~ o r o <br /> q <br />- q <br /> o <br />r1 <br />8) 1 ~ <br /> t_ E + In <br /> <br />9 <br />9 <br />2 / <br />q <br /> r o q o <br /> r <br />The total flux of water 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-S iteration method <br />The total volume of flow into the pit is determined by integrating the flux as a function <br />7 <br />