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STRAIGHT LINE EOUATION <br />Jacob developed a simplified form of Theis' drawdovn equation by truncating <br />the yell function series after the first two terms. Assuming the truncation, the <br />following equations were developed to analyze drawdown versus time data on semi-log <br />plots and is called the straight-line or Jacob equation: <br />T = 264 Q [log (t2/tl)]/(s2 - sl) <br />T = 264 Q/DELTA s , <br />S = T to/4800 r°2 <br />sl = drawdown, in Feet, at time since pumping started, <br />tl, in min. <br />s2 = drawdown, in feet, at time since pumping started, <br />t2, in min. <br />and t2 '~ tl <br />DELTA s = change in drawdown over one log cycle of time on <br />a semi-log plot, in feet <br />S = storage coefficient <br />to =straight-line intercept of zero drawdown, in min. <br />r = radius of well, in ft <br />A straight line is fitted to the semi-log plot of drawdown versus time (log <br />scale) to obtain transmissivity. Jacob suggested that u values less than 0.01 are <br />~ needed before his straight-line method is useful. However, a plot of W(u) versus <br />1/u on semi-log paper indicates that this method should be applicable for values of <br />• ~ u as large as 0.1. Pages 98-100 of Ferris and others (1962) should be consulted for <br />additional information on Jacob's method. <br />THEIS RECOVERY EQUATION <br />The well functions of the residual-drawdown form of Theis' equation were <br />approximated by using only the first two terms in the well function series. The <br />following equations present the semi-log form of the Theis recovery equation: <br /> T = 264 Q [log (t/t'))/ s' <br />or T = 264 Q/DELTA s' <br />where; t = time since pumping started, in min. <br /> t' = time since pumping stopped, in min. <br /> s' = residual drawdown, in feet <br />and <br />DELTA s' =change in residual drawdown over one log <br /> cycle of t/t' on a semi-log plot, in feet <br />Therefore, when residual drawdown is plotted on an arithmetic scale versus <br />t([' on a logarithmic scale, the above equation can be used for the straight line <br />fit. Pages 100-102 of Ferris and others (1962) should be consulted for a discussion <br />of Theis' recovery method. Theis' recovery equation is for a non-leaky confined <br />aquifer also. <br />i' <br />A-za RE111SED FEB 13'97 <br />