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i <br /> C <br /> . Discussion of Applicable Equations <br /> Below are stated the equations referred to in Section 4.2 above.. We have provided these <br /> equations as a review of possible equations that we will use in this aquifer pumping test <br /> investigation. <br /> f Equation(1)is the Theis or non-equilibrium equation. <br /> s=(Q/4nT)f.—e'"du/u) (1) <br /> i where <br /> i u=(r2S/4Tt) (2) <br /> s= "drawdown" <br /> u= "well function <br /> Q=constant well discharge <br /> T=transmissivity <br /> 4 S=storage coefficient(for confined aquifers)or specific yield <br /> (for unconfined aquifers) <br /> t=time since beginning of pumping <br /> C r=radius <br /> (Source:Todd,David K., 1980,Groundwater Hydrology,2nd Edition,John Wiley&Sons,Inc.,New York,p. <br /> 121f. However,this basic equation is referred to in most groundwater books.) <br /> 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),down gradient(XL),and up gradient(2 n XL)of a pumping well in an aquifer with uniform flow,that is <br /> with a sloping surface. These equations can therefore be used to produce data needed to draw a flow net for the <br /> j capture zones in a water extraction system. K is a key parameter in these equations. <br /> -(y/x)=tan(27<Khoi/Q)y (3) <br /> The finite lateral limit for y is: <br /> YL=±(Q/2Khoi). (4) '1 <br /> The"stagnation,point"(flow divide)down gradient is: <br /> XL=-(Q/2nKhoi) (5) <br /> 1 <br /> and the up gradient inflow limit at any one time is: <br /> �. 27CXL (6) <br /> Where: ; <br /> K=hydraulic conductivity <br /> Q=well discharge s <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 /> fi { � <br /> hd <br />