Ask Tom! Archive: Pre-Selection of Flocculants Using a Separation ::
Welcome to Ask Tom!, a monthly column by our resident water treatment guru, course of centrate height (measured as distance to the center of rotation),
http://www.waterandwastewater.com/www_services/ask_tom_archive/preselecting_flocculants_using_separation_analyzer.htmHOME |
Consider two separate columns of pure water at stp. One column is a
pipe with x-section of .049 inches (.250 diameter). Second column is a
pipe with x-section of 3.1416 (2.000 diameter). Top of pipes closed
off (vacuum). Are water columns equal height when water stream pulls
apart? Would like formulas to figure
mathematically(height,x-section,lbs. vacuum). I think this relates to
how high you can siphon water. Thanks! 3rrotec
The answer is "Yes, they are the same". Do you want the proof of that?
jeremymiles-ga
Hello 3rrotec-ga,
What do you mean by "When water stream
pulls apart?" And, you want a forumula
to compute the height given the x-section
and lbs of the vacuum:
height = f(x-section, vacuum)
Is that right?
dogbite-ga
To Jeremymiles-ga, Yes I would like mathematical proof. You may make
assumptions on barometer, specific gravity of water, and temp.
Interested in mathematical calculations of lbs. absolute in vacuum
chamber when column separates. First of many questions on this
subject. Thanks! Robert Williams 3rrotec Dr. Eng. Mohammed Matouq | Papers | Investigation of The Bubble ::
The effect of gas flow-rate and the height of the whey (liquid holdup) used foam fractionation to recover cellulase from an aerated water solution effectively. Here the separation of protein was conducted in bubble foam column,
http://al-balqa.academia.edu/MohammedMatouq/Papers/73232/Investigation-of-The-Bubble-Foam-Separation-Technique-To-Extract-Protein-VHOME |
Please clarify one thing and answer will be complete. Use answer mode
so I can proceed with more questions. What will be the negative
pressure in the top void chamber if column is say 40" tall? Does the
water vaporize because of the pressure drop thus filling top chamber
with water vapor thus letting the column lower or fall?
Hello Robert,
Since none of the previous interlocutors came back
after your last clarification, I suppose it is OK for
me to answer - and provide any follow-up clarifications.
I am imagining your two tubes to resemble this classical experiment:
http://galileo.imss.firenze.it/multi/torricel/etorat34.html
http://www.royal-met-soc.org.uk/weatherclub/secondary/barometer.html
Commenter leoj-ga is correct pointing out that the
cross-section
of the tube cancels out form the formula (below) so that it is
the density of liquid and atmospheric pressure, which will determine
the height of the column.
The instrument (inverted closed tube) is really first barometer
and as you correctly note, it has to do with maximal height to
which one can 'draw' a liquid:
http://www.newadvent.org/cathen/14784a.htm
Roughly: 760mm of mercury to about 10m of water should be
inverse of density of Hg to density of H2O (about 13)
To this day people measure pressure in mm of Hg (instead of using
SI units and say: Atmospheric pressure is about 100 kPa )
http://www.taftan.com/thermodynamics/PRESSURE.HTM
You are having good physical intuition, noting that some liquid will
evaporate (as nature does abhors vacuum, after all) and for
this reason, early instruments measured combination of both:
pressure and temperature. They nevertheless were useful for weather
prediction.
http://www.zedds.net/WeatherStations/Barometer2.htm
The mathematics:
I was surprised when I did not find a page with calculation ready
made.
Closest was a page with some numbers, like density of Hg and nice
picture:
http://www.du.edu/~jcalvert/phys/mercury.htm#Baro
So, here is the 'original' derivation :
Force= Weight of column = g * Volume * Density = g * Area * height
* Density
Pressure = 100 kPa = Force/Area = g * Density * height
That is the formula for height, D=Density is 1.0 for H2O, 13.5 for
Hg
in g/cc which we need to convert to kg/ m-cubed, as we do use SI
units.
Oh! What about the vapor pressure?
Depending on the temperature and volatility of the liquid
(Hg is good here) it will counterbalance the atmospheric
pressure.
So, in the formula above, you will use as Pressure
Atmospheric Pressure - Vapor Pressure
The tables of the later are on the Internet,
(see search termss below), for example, google
search:
://www.google.com/search?hl=en&ie=ISO-8859-1&q=vapor+pressure%2C+water%2C+mercury
will reveal:
The vapor pressure of water is 20 millimeters of mercury
(room temperature) , so, effect does exist, as a small correction.
But, at the 100 C, it will reach the atmospheric pressure of 760 mm,
(which is the definition of the boiling point)
http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/vappre.html
Search Terms
Torricelli Experiment
History of Barometer
atmospheric pressure, Pa
vapor pressure, water, mercury
This looks like a complete answer to me,
but feel free to ask for clarifications
and please do rate the answer after it is
all clear.
hedgie
 Get Smart About Monitoring Virtual Machines
 Microsoft Gets Ex-Streamly Cozy with U.K.'s MediaWave
|
Height of water column vs. separation