# Well in a Uniform Flow: Groundwater and Well Hydraulics

## Groundwater and Well Hydraulics

### Well in a Uniform Flow

A practical situation is that of a well pumping from an aquifer having a uniform flow field, as indicated by a uniformly sloping piezometric surface or water table. It is apparent that the circular area of influence associated with a radial flow pattern becomes distorted; however, for most relatively flat natural slopes the Dupuit radial flow equation can be applied without appreciable error.

For wells pumping on an area with a sloping hydraulic gradient, the hydraulic conductivity can be determined from the equation by inserting average heads and hydraulic gradients. The resulting expression has the form-

K = 2Q / [r (hu + hd) (iu + id)]

For an unconfined aquifer where Q is the pumping rate, hu and hd are the saturated thickness, and id and iu are the water table slopes at distance r upstream and downstream, respectively, from the well. For a confined aquifer, piezometric slopes replace water table slopes, and (hu + hd) is replaced by 2b where b is the aquifer thickness.

The groundwater divide marking the boundary of the region producing inflow to the well is shown. For a well pumping for an infinite time, the boundary would extend up to the limit of the aquifer. The expression for the boundary of the region producing inflow can be derived by superposition of radial and one-dimensional flow fields to yield

-y/x = tan(Kbiy/Q)

Where b is the aquifer thickness Q is the discharge rate, i is the natural piezometric slope, and K is hydraulic conductivity. The boundary asymptotically approaches the finite limits

yL = (Q/2Kbi)

as x= ∞. The boundary of the contributing area extends downstream to a stagnation point where,

xL = (Q/2Kbi)

It follows that the upstream inflow zone equals 2xL.

An important practical application of these equations concerns determining whether an upstream pollution source will affect a nearby pumping well.

A fully penetrating production well with a radius of 0.5 m pumps at the rate of 15L/s from a 35-m thick confined aquifer with a hydraulic conductivity of 20 m/d. If the distance and the observed piezometric head drop between two observation wells were 1000m and 3m, respectively, before the production well was installed, determine the longitudinal and transverse limits of groundwater entering the well.

First determine the slope of the piezometric surface under natural conditions (i.e. before the production well was installed):

i = Δh/Δx = 3/1000 = 0.003

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