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Discussion of Applicable Equations <br /> PP 9 <br /> Below are stated the equations referred to in Section 4.2 above. We have provided these equations as a review <br /> of possible equations that we will use in this aquifer pumping test investigation. <br /> Equation(1)is the Theis or hon-equilibrium equation. <br /> s=(Q/4irT)j„—e°du/u) (1) <br /> where <br /> u=(r2S/4Tt) (2) <br /> s="drawdown" <br /> u="well function" <br /> Q=constant well discharge <br /> T=transmissivity <br /> S=storage coefficient(for confined aquifers)or specific yield <br /> r (for unconfined aquifers) <br /> ILi t=time since beginning of pumping <br /> r=radius <br /> (Source: Todd, David K., 1980, Groundwater Hydrology, 2nd Edition, John Wiley &Sons,Inc.,New York, p. <br /> 121L However,this basic equation is referred to in most groundwater books.) <br /> r While the non-equilibrium equation deals with drawdown caused by radial flow in aquifers with horizontal water <br /> table or piezometric surface, the following set of equations define the equilibrium radius of influence laterally <br /> (YL),downgradient(XL),and upgradient(2 7r XL)of a pumping well in an aquifer with uniform flow,that is with <br /> a sloping surface. These equations can therefore be used to produce data needed to draw a flow net for the <br /> capture zones in a water extraction system. K is a key parameter in these equations. <br /> -(Y/x)=tan(27rKhoi/Q)y (3) <br /> The finite lateral limit for y is: <br /> YL=±(Q/2Khoi). (4) <br /> The"stagnation point"(flow divide)downgradient is: <br /> XL=-(Q/27[Khoi) (5) <br /> and the upgradient inflow limit at any one time is: <br /> 27EXL (6) <br /> Where: <br /> K=hydraulic conductivity <br /> Q=well discharge <br /> i=natural slope of the water table <br /> ho=uniform saturated aquifer thickness <br /> y=maximum distance of influence laterally from well <br /> x=maximum distance of influence down gradient from well <br /> (Source:as above.) <br /> L <br />