Laserfiche WebLink
Discussion of Applicable Equations <br /> Below are stated the equations referred to in Section 3.2 above. We have provided these equations <br /> as a review of possible equations that we will use in this aquifer pumping test investigation. <br /> Equation(1) is the Theis or non-equilibrium equation. <br /> r s (Q/4nT)f,,'e°du/u) (1) <br /> where <br /> u=(r'S/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 /> (for unconfined aquifers) <br /> t=time since beginning of pumping <br /> r=radius <br /> (Source: Todd, David K., 1980, Groundwater Hydrology, 2nd Edition, John Wiley & Sons, Inc., <br /> New York,p. 1.21 f. However, this basic equation is referred to in most groundwater books.) <br /> LWhile the non-equilibrium equation deals with drawdown caused by radial flow in aquifers with <br /> horizontal water table or piezometric surface, the following set of equations define the equilibrium <br /> radius of influence laterally (YO, downgradient (XA and upgradient (2 7E XL) of a pumping well in <br /> an aquifer with uniforin flow,that is with a sloping surface. These equations can therefore be used to <br /> produce data needed to draw a flow net for the capture zones in a water extraction system. K is a key <br /> parameter in these equations. <br /> -(y/x) tan (27EKhoi/Q)y (3) <br /> The finite lateral limit for y is: <br /> r YL=f (Q/2Khoi) (4) <br /> The "stagnation point" (flow divide)downgradient is: <br /> XL_- (Q/2nKhoi) (5) <br /> and the upgradient inflow limit at any one time is: <br /> 2nXL <br /> Where: <br /> L' K=hydraulic conductivity <br /> Q=well discharge <br /> i=natural slope of the water table j <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 /> I <br /> I <br /> i <br />