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Expert: - 3/14/2008


Question

flow loop
I want to calculate flow rate through a filter system where the incoming flow rate is constant and known, but 50% of the outgoing flow is added back to the incoming flow via a feedback loop.

So if X is known, at first .5X leaves the system and .5X goes back and is added to X.  I want to know the flow through the filter at equilibrium assuming constant X.

Answer
Questioner:  Chris
Private: no

flow loopI want to calculate flow rate through a filter system where the incoming flow rate is constant and known, but 50% of the outgoing flow is added back to the incoming flow via a feedback loop.

So if X is known, at first .5X leaves the system and .5X goes back and is added to X.  I want to know the flow through the filter at equilibrium assuming constant X.  
.............................................
Hi, Chris,

First, a little story.  

My wife's doctor decided to send her for a stress test. The tech put her on a treadmill and asked her to walk while he took readings.  After a while, she said "Isn't that enough? I'm getting tired."

"I need two more minutes, Mrs. K."

"No! I can't do two minutes."

"How about one minute? You can do that."

"OK. One minute."

(after a minute)

"How about half a minute more? You can do that, can't you?"

(then)

"How about a quarter of a minute more?"

(etc)

Well, he had to talk very fast, but he got his two minutes.

[See moral of the story at the end.]

........................................

Now I think your output is:

1.  1/2 X  from the original output (feedback 0).
2.  1/4 X from the feedback 1.
3.  1/8 X from the feedback 2.
....
n.  1/2^n X from feedback (n-1)
etc.

And the total is X(1/2 + ... + 1/2^n + ...)

which is an infinite geometric series converging to X(1) = X.

..........................................

Oh, yes, the moral.

You never know when you will need advanced mathematics.

Paul Klarreich

Expertise

I can answer questions in basic to advanced algebra (theory of equations, complex numbers), precalculus (functions, graphs, exponential, logarithmic, and trigonometric functions and identities), basic probability, and finite mathematics, including mathematical induction. I can also try (but not guarantee) to answer questions on Abstract Algebra -- groups, rings, etc. and Analysis -- sequences, limits, continuity. I won't understand specialized engineering or business jargon.

Experience

I taught at a two-year college for 25 years, including all subjects from algebra to third-semester calculus.

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