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# Water flow rate through an opening in a tube

Please see attached file for the illustration.

Tube B (full of air) is sealed on the top and a 16" OD opening on the bottom. B is 104.6' long.
Container E (full of air) is inserted into section H and permanently fixed in place.
B is inserted fully into container C. Water rises 59.6' into B. H is 45' feet of air. See Illustration 1.

E is filled with water (see Illustration 2). E releases water through a 16" OD valve g while venting air through valve f.
E releases water at the rate of 100 gal per second for 8 seconds.

PROBLEM:
When E releases water at 100gal/s will water flow through h at the same rate?
Will the height of W change?

If E is supplied by a constant source of water , releases at a constant flow of 100 gal/s and container C remains at a constant depth will water flow through h at the same rate? Will the length of W remain the same?

#### Solution Preview

I however want to mention this: a couple of quantitative values were given in the question which kind of suggests quantitative answers too, but much more quantitative values are needed if the answers are to be purely quantitative; values like the cross-sectional area or diameter of tube B, the atmospheric pressure at the height were this experiment is performed, the value of acceleration due to gravity at that place, and the densities of water and air will be required to do necessary calculations, but the last statement in the question clearer suggests that a calculative answer is not what is needed.

So, I will help you address this question this way: answer the question in an essay form, giving you all the needed explanations, and presenting the physical & mathematical clues where necessary. (I will try to be as simple as possible). Feel free to neglect the mathematical aspects while making your own solution. I just included them for your savor in case you are interested. I have also marked them in bold so that you can easily see and skip them if you aren't interested.

SOLUTION:
First you will need to understand that since tube B has an open valve at h, the air pressure inside the tube just before it was inserted in the water of container C was equal to the value of the atmospheric pressure at h (that is, the value of atmospheric pressure at the surface of the water contained in container C).

Now, as tube B is inserted completely into container C, the air pressure inside tube B will increase by an amount that is equal to the value of pressure ...

#### Solution Summary

This solution is a concise description of how water/air will flow in a system as described in the question's diagram. It explains whether or not water will flow through certain openings in the diagram depending on how the system is changed, and also at what rate the resulting flow will be.

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