Re: Venturi question

On Thu, 13 Sep 2006, matt271829-news@xxxxxxxxxxx wrote:

matt271829-news@xxxxxxxxxxx wrote:
As you say, various different potential cooling processes have been
mentioned. If expansion of the gas is in some way involved then I'm not
at all sure where this is supposed to occur - you say that the pressure
drop is greatest "at the outlet", but as I understand it the pressure
is lowest in the narrowest part of the tube, which seems to imply that
"expansion" would occur as the gas passes from the inlet into the
narrow part. Is that wrong?

Of course, I'm assuming that lower pressure = lower gas density =
expansion of gas, and higher pressure = higher gas density =
compression of gas. However, I'm starting to wonder about this. Is it
possible that the lower pressure in the narrow part of the venturi tube
is NOT actually associated with a lower gas density there? Don't know.

Richard Perry went through much of this already, but you might like to consider the following anyway:

PV=nRT does suggest that you'll find a lower density (ie n/V) where P is lower. However, it seems odd that as you squeeze the gas into the constriction, the density would decrease rather than increase.

If you put an incompressible fluid (eg, water, approximately) through such a constriction, the velocity must increase. An increase in velocity requires an acceleration, the acceleration requires a force. The force is due to a pressure gradient. Where the fluid accelerates, the pressure must be decreasing. Where the fluid slows down, the pressure must be increasing. Thus, the pressure must be lowest in the constriction.

For a gas, which is compressible, does the same thing happen? If the gas is compressed in the constriction, the increase in velocity will be smaller, and thus the drop in pressure will be smaller. So, the more compression, the smaller the pressure drop. Thus, you do get higher pressures associated with higher densities. So, try this: use Bernoulli's equation to find the pressure in the constriction as a function of the flow velocity. If the cross-sectional areas are A1 outside the constriction and A2 in the constriction, what is the flow velocity in the constriction as a function of the density in the constriction? Finally, use the ideal gas law to find the temperature in the constriction as a function of the density in the constriction.

There's a reason why a venturi tube is usually explained in terms of Bernoulli's equation using an incompressible fluid: simplicity. Bernoulli's equation is all about conservation of energy, and assumes (a) no losses; the fluid is inviscid, and (b) all of the energy is kinetic energy or gravitational potential energy. But it takes work to compress a gas, and an expanding gas can do work, so it becomes quite a bit more complicated. Does this work change the pressure difference above, which just assumed Bernoulli?

--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html

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