Lecture 20
Theim Equation
Fetter 7.4.2
Steady-state conditions- when equilibrium has been achieved in an aquifer test.
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More Assumptions
| (1.) Pumping well only screened in tested aquifer. | |
| (2.) All observation wells are only screened in tested aquifers. | |
| (3.) Fully penetrating screens. | |
| (4.) Aquifer is confined top and bottom | |
| (5.) Q is constant | |
| (6.) Equilibrium has been reached. |
At steady state, Q pumped = Rate of Aquifer Transmitting water.
Area providing water to well = 2p rb
Q = (2p rb)K |
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| Q = pumping rate of well L3/T | |
| r = radius of circular section of aquifer (L) | |
| b = thickness (L) | |
| K = hydraulic conductivity (L/T) | |
| = hydraulic gradient |
Simplify Q = 2p rT
Rearrange dh = 
Two observations wells at r1 and r2 with head = h1 and h2
Integrate 
Solutions = h2 -h1 = 
ln 
Thiem Equation (rearrange for T)
T =  |
Under steady-state conditions, no change in storage.
| cannot determine storage with this equation. | |
| s = drawdown (h2-h1) | |
| Not a very practical method. | |
| May take months to achieve steady state. |
Example
| Q = 220 gallons per minute | Well 1 r1 = 26’ | |
| = 42,400 ft3/d | h1 = 29.34’ | |
| Steady state after 1,270 minutes | ||
T =  |
Well 2 r2 = 73’ | |
| h2=32.56’ | ||
| 2,200 ft2/d | ||
Q = (2p rh) K |
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| h - saturated thickness of aquifer |
Rearrange hdh = 
Steady-State Radial Flow (Unconfined Aquifer)
Integrate 
Relation of Porosity to Permeability
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ENV 302 - Lectures
