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• b is the confined aquifer thickness, L; and <br />X 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) d / E <br />qr - qo = - 1\ <br />dt qo <br />where: <br />5) - /SyaT bz 5TH Z 5TH b~ <br />f\ o + o <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) -E <br /> dt - dq <br /> 0 <br /> 3 2 <br /> 9 - q q <br /> o r o <br />• Integrating both sides of equation 6 results in the following: <br />7) 9 (U -E <br />dt 3 _ 2 dqo <br />0 ~ qo qr qo <br />qo(0) = o0 <br /> Ig g <br /> o r <br /> <br />8) <br />t <br />~ ~~ <br /> t = - E + In 1 <br /> g g z 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-g iteration method. <br /> The total volume of flow into the pit is determined by integrating the flux as a function <br /> of time. This is performed numerically in the program by subdividing each day into 100 <br /> equal time increments, calculating [he flux at the fixed time increments, a nd using <br /> gimpson~s rule to numerically integrate the area under the flux versus time cur ve. the <br />• d <br />il <br />t <br />f fl <br />i <br />t <br />it d <br />t The <br />ntial rate ro <br />ram <br /> a <br />y ra <br />e o <br />oe <br />n <br />o an open p ecreases <br />o a . <br />n expone g <br />p <br /> automatically reduces the number of time increments each day is subdivided into when the <br /> change in daily flow rates is less than o ne percent. <br /> 7 Revised 03/24/95 <br />