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<br />GOU j~ <br /> <br />-' <br /> <br />Where radial symmetry prevails, as around a pumped well, the basic <br />differential equation takes the form: <br /> <br />( a2 s <br />a arz <br />\ <br /> <br />+.! as)\ = ~ <br />r or at <br /> <br />. . . (2) <br /> <br />Where <br /> <br />s represents the drawdown from an assumed original stable <br />water table level and <br /> <br />r represents the radius. <br /> <br />In order to estimate the rate of ground water movement in any given case <br />solutions of the above differential equations are needed which conform to the <br />appropriate initial and boundary conditions. A few examples are the following: <br /> <br />(I) For the case of a well pumped at the rate Q drawing water.from <br />storage in an aquifer of unlimited extent which conforms to the <br />conditions <br /> <br />When t = O. <br /> <br />s = O. for r > 0 <br /> <br />A solution of equation 2 is: (2.) (3) <br /> <br /> 0-:, <br /> Q ~ -,' <br />S . e du <br />= <br /> 2.1Tlill ' u <br /> . l' <br /> /4<1t <br /> <br />. . . (3) <br /> <br />The integral Wllich appears here is a form of the exponential integral. A table <br />of values can be found in reference 5. <br /> <br />When a river runs over the surface of an aquifer and is in contact with the <br />ground water in it the stream depletion ql due to a well at a distance x I from <br />the river when pumped at the rate Q can be obtained from this expression in <br />the form: (2.) (9) <br /> <br />ql <br />Q <br /> <br />= I - <br /> <br />2. <br /> <br />XI <br /> <br /> <br />, I'~" " <br /> <br /> <br />~.' 0 <br /> <br />. . . (4) <br /> <br />J--:;( <br /> <br />-3- <br />