Appendix C. Stella -- More Exercises with the Two Bottles System
| This drawing shows the two bottles system described on page
381 of the book. Before taking on any new exercises, you should complete
exercises #5 and #6 from Appendix C. That is, guess the dynamic behavior
of the two volumes if the bottles start out empty and the inflow remains
constant at 5 cc/sec. Describe your guess in the form of a "pencil
forecast" over an 80 second time period. Then build a model of the
system and compare the simulation results to the pencil forecast. Which do you believe, the pencil results or the simulation results? |
 |
If you have reached Chapter 5, you will recognize the equilibrium
diagram from page 53 of the book. It shows the Stella model along with the
numerical values of each variable when the simulated system reaches dynamic
equilibrium. |
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The exercises below ask you to think of the two bottles
as a system to smooth out variations in flows.
We might have a highly variable flow into the first bottle. We want to learn
if the system will deliver a relatively smooth flow out of the 2nd bottle.
1. Test Case
To test the idea that the bottles can act to smooth the flows, change the
inflow to the first bottle. Rather than a constant 5 cc/sec, we want the
inflow to vary around 5 cc/sec in a cyclical pattern. Let's use Stella's
SINEWAVE function (see Appendix H for information on functions). Set the
inflow to vary around 5 cc/sec with an amplitude of 3 cc/sec and a period
of 10 seconds. The inflow will now range from a low of 2 to a high of 8
cc/sec. Run your model for 80 seconds and document your results with a time
graph of the three flows scaled from 0 to 10 cc/sec. Does the system reduce
the variability in overflow 2 compared to the variability in the inflow?
2. Meet Design Specs
Suppose the design objective is to maintain overflow 2 within the range
from 4 cc/sec to 6 cc/sec even though the inflow is fluctuating as in question
#1. Print a time graph of overflow 2 during the time interval from 60 to
80 seconds in your simulation. Scale the vertical axis from 3 to 7 cc/sec.
Does the system meet the design objective?
3. Let's Try a Different Bottle
If you did the previous exercise correctly, the fluctuations in overflow
2 will not fall within the permissible range. But don't worry, someone said
we can reduce the variability in overflow 2 by simply replacing the 2nd
bottle with a bottle with a different surface area. Unfortunately, he didn't
say whether the surface area should be smaller or larger. What do your instincts
tell you? Should we try a smaller or a larger surface area?
Use your model to experiment with smaller or larger surface
areas for the second bottle. Find a surface area that allows the system
to maintain overflow 2 within the range of 4 cc/sec to 6 cc/sec. Document
your results with a printed time graph of overflow 2 scaled from 3 to 7
cc/sec.
4. Advice on Special Functions
Appendix H concludes with advice on when Stella's special functions should
be used and when they should be avoided. Did our use of the SINEWAVE function
in the previous exercises adhere to this advice?