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**
UNIT 4 -- TRANSIENT ANALYTICAL FLOW MODELING:
Transient analytical solutions provide insight into the
rate of change in a system, that is the length of time required to reach steady
state conditions. This is of value because we may only be interested in the
temporary application of a stress to the ground-water system. For example, the
life of a mine may be 50 years and the response of the system may be slow enough
that we do not even begin to approach steady state during that time frame. The
steady state solution provides the maximum impact of the stress. The impacts
during the transient period while the system is approaching steady state can
only be less than those that prevail under steady state conditions. **

** Some problems do not
have a steady state result. For example if a basin is pumped at a rate greater
than the recharge, eventually the basin will go dry and the pumping cannot continue.
A balanced steady state condition cannot be reached and so a steady state solution
for pumping the basin at that rate does not exist. **

**The OBJECTIVE
of UNIT 4 is for you to:**

** * BECOME
FAMILIAR with some TRANSIENT ANALYTICAL SOLUTIONS**

*** UNDERSTAND the need
for and significance of INITIAL CONDITIONS**

*** LEARN to MANIPULATE
available SOLUTIONS to APPLY them to a somewhat DIFFERENT SITUATION than those
for which they were originally developed **

*** EVALUATE your RESULTS
using COMMON SENSE to FIND YOUR ERRORS **

** DISCUSSION**

** Study
the transient analytical solutions presented on the transient analytical solution
main page. Notice the importance of initial conditions. Think about the parameters
that control the progress of the solution, underlying assumptions, the value
of results obtained using these solutions and the errors that might be introduced
by applying these solutions to a field problem. Then move on to undertake some
interesting (and fun) calculations using these solutions in the exercises of
Unit 4.**

**EXERCISES**

** If you
chose to purchase Applied Ground-water Modeling,
read the sections 7.1 & 7.2
**

** Explore
the stream depletion function and determine
why the stream depletion graph changes as it does for an increase and decrease
of each parameter on the slider bar menu due to pumping near a stream. Explain
why having a slider bar for the discharge from the well is useful. Email me
if you have questions. Also, tell me if you think there is anything wrong
with the behavior of the applet. epoeter@mines.edu
**

** COMMUNICATION**

**Please bring up any concerns you may have about transient analytical modeling and the answers you obtained during the exercises. For example, do you understand why the shape of the graph of stream depletion vs. time changes at early time when all parameters are constant except the maximum time for which the graph is calculated? epoeter@mines.edu**

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