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(Another) manometer question

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Posted by Morris Dovey on February 14, 2011, 3:53 pm
 
A while back Curbie provided this link to manometers

   http://www.efunda.com/formulae/fluids/manometer.cfm

which answered my question of the moment, and I filed the link away as
being helpful.

Now I'm dealing with a similar problem (attempting to use a standpipe
arrangement to maintain a minimum pressure in a heat engine) and find
myself with a severe case of mental indigestion - and what feels like a
dumb question...

What if a U-tube manometer has a different diameter on each side?

I've posted a sketches of two manometers at

   http://www.iedu.com/DeSoto/Misc/Manometers.png

to illustrate. According to the handy-dandy equations describing these
things, applying a given pressure to one side will produce a difference
in height of the fluid that depends only on the pressure, the density of
the fluid, and the gravitational acceleration constant.

I'm comfortable with that for the case where both sides of the U are of
equal diameter, but when they aren't the result looks absurd because it
seems to require a magical change in the volume of the fluid.

The density variable would seem to be telling me that I should be
looking at mass, rather than column height - but none of the articles
I've read seem to want to address mass or tube dimensions.

What am I missing here?

--
Morris Dovey
http://www.iedu.com/DeSoto/
PGP Key ID EBB1E70E


Posted by Jim Wilkins on February 14, 2011, 5:58 pm
 

http://www.grc.nasa.gov/WWW/k-12/WindTunnel/Activities/Pascals_principle.ht=
ml

The fluid in the larger column certainly weighs more, but that weight
is spread across a proportionally larger area so the unit area
pressure at the bottom is the same.

Morph the U tube into a 1" open pipe dipped into a 55 gallon barrel.
Would you expect a different liquid level in the 1" pipe?

jsw


Posted by Morris Dovey on February 14, 2011, 7:02 pm
 On 2/14/2011 11:58 AM, Jim Wilkins wrote:


Thanks! That was exactly what I needed. As usual, I was trying to make a
hard problem out of what should have been an easy one. :-/

--
Morris Dovey
http://www.iedu.com/DeSoto/
PGP Key ID EBB1E70E


Posted by Jim Wilkins on February 15, 2011, 12:42 pm
 
The great minds from Aristotle's to Newton's time did the same.

jsw

Posted by Morris Dovey on February 16, 2011, 12:53 pm
 On 2/15/2011 6:42 AM, Jim Wilkins wrote:

Regrettably, so have all the more ordinary minds - and I think /I/ might
be even better at it than either/both those guys! ;-)

I just can't seem to get quite enough traction to get ahead of the
learning curve - and the hurrier I go, the behinder I get.

The best news is that I seem to be surrounded by folk who've already
acquired knowledge I lack and are willing to help me learn.

--
Morris Dovey
http://www.iedu.com/DeSoto/
PGP Key ID EBB1E70E


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