Lecture 19

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Ground-water Flow to Wells


Fetter 7.1-7.3-1


Wells used to extract ground water (or inject)


Cone of depression - area around a discharging well where the hydraulic head

in the aquifer is lowered by pumping.


Want to compute drawdown and T and S.


Unsteady flow - flow in which head changes with time.


(1.) Bottom confining layer
(2.) All geologic units are horizontal and of infinite extent.
(3.) Potentiometric surface is horizontal prior to the start of pumping.
(4.) Potentiometric surface is not changing with time prior to the start of pumping.
(5.) All changes in potentiometric surface position are due to the effect of the pumping well.
(6.) Aquifer is homogeneous and isotropic.
(7.) All flow is radial toward the well.
(8.) Ground-water flow is horizontal.
(9.) Darcy’s Law is valid.
(10.) Ground-water has constant density and viscosity.
(11.) Pumping well and observation wells are fully penetrating.
(12.) Well has an infinitesimal diameter and is 100% efficient.


Unsteady Radial Flow


Assume that the aquifer has a radial symmetry .
Radial flow toward well.
Plan view Cross Section





Use polar coordinates to describe flow.



Therefore, can express flow with-

(1) q value of angle
(2) r Radial distance


If Aquifer is isotropic in horizontal plane. Then Flow is radial.


Equation for confined (radial) -Hantush 1964


r = radial distance from pumping well.


If recharge- leakage through a confining layer


e = rate of vertical leakage (L/T)


Solutions to the equations are extremely useful

Laplace transforms
Fourier transform
Bessel functions
Error function


Use these equations to determine drawdown around a pumping well.


 Aquifer test in a confined aquifer.





Aquifer test in an unconfined aquifer.


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