Static pressure inside an air conditioner's capillar

[Yuri B.]

Let's a system be as follows (with approximate but, still, real numbers). Compressed refrigerant gas get condensed in a condenser and as liquid with +/- 15 B SP enters a capillary (a "metering device"). It exits the capillary at high speed and enters the pipe leading to the evaporator having there +/- 7 B SP. It evaporates at +/- 4 B SP to be sucked as gas after that by the compressor, and so on.
What +/- SP may it have inside the capillary, according to Bernoulli principle ? (something almost impossible to measure)

 

[jim hardy]

Now you need the services of a good engineer knowledgeable in two phase flow.

I can only tell you that the working fluid enters as a high pressure liquid , and it exits at low pressure gas, perhaps a gas-liquid mix. So now your Bernoulli equation needs to contain energy terms for internal energy of the fluid, and that's thermodynamics.

Both the substantial heat of vaporization and the work of expansion must come out of the fluid's internal energy and that's why it gets so cold - refrigerators work because of phase change.
Two phase flow is a complicated thing to calculate and I only brushed that subject.

Were the pressure not lower at exit end the working fluid would not accelerate toward it.
As the gas turns to vapor its volume increases greatly and so must its velocity.
I once tried to calculate two phase flow of hot water down a pipe and resorted to a graphical approximation on a molier chart. Essentially I admitted defeat.

Here are a couple of scholarly papers that I think will help you.
ASHRAE is another good source of information about refrigeration.
http://docs.lib.purdue.edu/cgi/view...8540,d.b2U#search="ashrae capillary pressure"

Wow what a long url...
You might search for it by title: "Numerical Simulation of Capillary Tubes.
Application to Domestic Refrigeration with
Isobutane"
it's at purdue.edu

here's the other:
http://nptel.iitm.ac.in/courses/Webcourse-contents/IIT%20Kharagpur/Ref%20and%20Air%20Cond/pdf/R&AC%20Lecture%2024.pdf

Sorry I can't help, but two phase flow is simply over my head.

An American humorist, Mark Twain, said:
"It is better to remain silent and be thought a fool than to speak up and remove all doubt."
So i'll not pretend i know how to answer your question.

old jim

 

[Yuri B.]

What I meant rather asking my qwestion :
Can SP be lower upstreem of a point in a closed system consisting of the pipes of different diameters (and no phase change - only incompressible liquid)?
Would not that imply the possibility of the existence of such thing as "negative P drop" ?!

 

[jim hardy]

What I meant rather asking my qwestion :
Can SP be lower upstreem of a point in a closed system consisting of the pipes of different diameters (and no phase change - only incompressible liquid)?

Sure - let's neglect friction and look at venturi effect. That's the most direct application of Bernoulli.

Where velocity is higher dynamic pressure is higher because it's $\frac{1}{2}$V².
Total pressure is sum of dynamic and static pressures and is constant.
Bernouli says we can swap between dynamic and static pressures.
So in larger parts of your pipe the static pressure will be higher and the dynamic pressure lower than in the smaller parts. But their sum will be constant.

A picture of a venturi courtesy of these guys: http://www.lenntech.com/venturi.htm

Observe lower static pressure in mid section, which is upstream of right section.
I think that was your question.

Would not that imply the possibility of the existence of such thing as "negative P drop" ?!

Those words don't sound right to me but it may be a language barrier - I'm old and don't adapt as quick as I used to.

I prefer to think of it this way:

Imagine a tiny cube of water drifting along in that stream above.
If you wish, imagine yourself very tiny and inside that very cube of water wearing a diver's suit.

In order for the flowing stream to pass into the narrow part of the tube it MUST speed up.
That's because the area for flow is smaller.
You see this every day in any river - water moves fast in shallow rapids and slow where the stream is deep.
Now - in order for any mass to speed up it must receive a lateral force.
So your tiny cube of water must see more pressure on its backside than it does on its front side. Else it wouldn't accelerate.
So where it is accelerating, namely in the converging part of the venturi(where it's narrowing), pressure must be decreasing. Else the water could not accelerate for there'd be no lateral force.
Go over that until it makes sense...In the narrow part of the venturi pressure is constant as evidenced by fact the water is neither accelerating nor decelerating.

In the diverging(widening) part of the venturi water is slowing down(decelerating) so it MUST be feeling more pressure from downstream side than upstream.
So pressure in that section is increasing.
With no friction the pressure would come back to same as upstream, in a real venturi it can come very close(better than 99% for a high quality metering venturi).

That imaginary model is what made Bernoulli "click" for me - the fact water can't change velocity without a push.

Some people like me have to see a physical model before we can accept an equation.*

I hope this helps you believe in Bernoulli's principle - it is really useful.
You see it in practical application everywhere.
Those sprayers for your garden hose use a venturi to suck the spray into the water stream
Those drainers for waterbeds use a venturi to suck the water out of the mattress
Every carburetor you'll likely encounter uses a venturi to suck the fuel into the airstream.

(* I read somewhere that this inability to accept pure math without a physical model is characteristic of English speaking people. There are some interesting papers(e.g. Richard Restrak) on how one's native language seems to determine what areas of the brain are used in problem solving - but that's another whole subject.
I mention it only to assure you my earlier remark about language barrier is not in any way a criticism, unless it's of myself.)

Good luck, friends

old jim

 

[Yuri B.]

Thank you very much indeed for your explanation ! I understand the formulas, the physical laws, but still, something make me ask silly qwestions sometimes.
Best regards !
(Proverbially the English are reknown for their Newtonian empiricism in contrast to cartezian rationalism)

 

[jim hardy]

I understand the formulas, the physical laws, but still, something make me ask silly qwestions sometimes.

I don't think they are at all silly.
In my own alleged mind I constantly test ideas that I think I understand. Often it leads me to adjust previously held conceptions. It is better to discuss them with others for in doing so we improve our words hence the thoughts behind them.

When I can explain something to myself(or somebody else) by diverse logical progressions without developing a conflict, I get more confidence my understanding is based on truth.
As you saw above, I had to convince myself that Bernoulli did not conflict with F=MA before I could accept him.
I suspected from your question you were having similar self doubts. I hope this interchange has boosted your confidence.

(Proverbially the English are reknown for their Newtonian empiricism in contrast to cartezian rationalism)

Thank you for that. I just googled "Cartesian Rationalism" and found some interesting reading for tonight. You have introduced me to something of which I was unaware - thank you.


old jim

 

[Yuri B.]

Language-thought is at all the wonder and mystery. Darvin might have originated from an ape but you, Jim, like many others in this world, and, I hope me too, we have not.