# Fluid Mechanics help !

Fluid Mechanics help...plz!

Hello...everyone....

I've come along these lines from "Fluid Mechanics" - by Streeter,Wylie,Bedford

These are the lines:[Quoted]
Section title:[Pg 15-16]
Pressure and a Perfect Gas.
[Lines:]
Liquids normally cannot sustain a tensile (or pulling apart) stress since the liquid would vaporize.Therefore,the absolute pressures used in this book are never negative,since this would imply that the fluid is sustaining a tensile stress.

I just don't understand this....
more specifically "negative absolute pressures"...whats the matter here...can anyone explain it to me..plz??....
Any views are welcome!...

FredGarvin

Negative absolute pressures? Perhaps it is a type-o in which they should have said negative gauge pressures?

The point about negative pressures is that you simply can't have them. (This isnt fully true as surface tension can support tiny tensions)

Pressure is the force/area, and sign convention is that positive pressures are when the material is being compressed (squashed).

Liquids can support loads when they compress, so you canpush on a liquid and it will support you.

Try pulling a liquid, what happens. There is no resistance, this is because they cant support tension loads.

I dont think i've explained that very well, can you break down the question into several smaller questions, specifically stating what you dont understand please?

Ok......
I understand that a liquid would vaporize when subjected to tensile stresses...
but the statement says..."normally"...here
Liquids normally cannot sustain a tensile
Why does "normally" mean..in which cases this doesn't stand true??...

moreover note this part:

this would imply that the fluid is sustaining a tensile stress

I think this shouldn't necessarily hold true for "fluids"...as the statement says...it should say for "Liquids"...am I right??

and also I didn't get this also:
The point about negative pressures is that you simply can't have them. (This isnt fully true as surface tension can support tiny tensions)
I think due to surface tension the fluid surface is in tension...but this tension is in the plane of the surface[I mean the surface remains in tension...because of surface tension..but this all is in the surface's plane]...right??...so I think this tension isn't what the author wants to say about..i.e Tensile stresses...these will be perpendicular to the fluid surface..right....??

plz help me....
..Thanks a lot for all replies....
This statement from the book has taken pretty much of my time ...I utilized for studying today....and still it aint clear to me...so plz help me.......

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Fluids encompass anything that moves, so gases and liquids. Although thte gas is more extreme than a liquid they both act is a similar manner, in that it doesnt support compressive loads very well either.

You misunderstand about the surface tension. The fluid wants to stick together because of intermolecular forces, this is what creastes surface tension.

For the same reason that we have surface tension, the fluid can support a light tension load (giving a negative pressure) because they dont want to be pulled apart. however this is very small when compatred to the compressive load a fluid can withstand so it is ususally just neglected.

A pressure is a force over an area. A positive absolute pressure is a pushing force against an area. In order to have a negative absolute pressure you need to create a pulling force against an area. How can you accomplish this with a fluid?

say in a journal (hrdrodynamic or EHL) bearing, as it rotates the lubrication fluid gets dragged round it creates a pressure profile which is mostly in compression. At the very edges there can be a negative pressure where the fluid is both attached to the inner and outer race. The rotation 'pulls' the fluid.

For the same reason that we have surface tension, the fluid can support a light tension load (giving a negative pressure) because they don't want to be pulled apart. however this is very small when compared to the compressive load a fluid can withstand so it is usually just neglected

Ok...I think I get that..
This is what I understand till now:...
The fluid is capable of withstanding a small amount of -ve pressure[i.e. tensile stress]...because of surface tension...i.e. due to Surface tension which exists because the fluid has resistance to the inward pulling cohesive forces...and this surface in tension resists tensile forces to a small extent...
and also, liquids are considered to be almost incompressible[because of very large bulk modulus]..so thats why they can sustain compressive stresses....

But For gases....[even perfect gas]
They are compressible ... and surface tension is imp here to a even much much lesser extent here..because of lesser magnitude...though the "-ve pressure sustain part" is still applicable here...right??
I would like to know "what can we say for the compressive stresses for gases"...as gases are compressible...
I think for gases we can say that they don't sustain compressive stresses initially..right??..

I think you have explained the "-ve pressure" part really well..thanks...[I wasn't just getting what the author meant by -ve abs pressure..before posting here]
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A pressure is a force over an area. A positive absolute pressure is a pushing force against an area. In order to have a negative absolute pressure you need to create a pulling force against an area. How can you accomplish this with a fluid?

Hi..Topher925..
As fas as I understood what you want to convey...I think your question itself has the answer.....-ve pressure should mean tensile forces..right??

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Fluids seems ok.

To be honest i'm not sure what you'd say for gases due to compressibility, i'd have to read up as i've forgotten a lot of what I used to know. The below may not be fully true.

For gases it depends on the speed of loading, at low speed loading gases dont support compressive loads as the air just moves round the object. Above a certain speeds (Mach 0.3 iirc) compressiblity is a factor and it then begins to support loads.

EDIT: I've just realised a possilbe point of confustion, the speed is only really critical in open flows such as an aeroplane wing and air. In closed systems such as a piston cylinder, the speed of compression doesnt matter, but the resistance will increase the more the gas is compressed.

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Ok......
I will reply as soon as I have understood it properly....

Thanks anyways..I think the 1st statement I posted[very 1st post] ..that wasn't understood by me earlier....is much clearer to me now...
Thanks a lot ...for your help..

Anytime, help is what we are here for.

Hi there... :)
I think I need to go back and understand what "Sustain -ve Pressure(Tensile stress)" means...
Like for Liquids...we say it doesn't sustaiin -ve pressures because it would vaporize.....for compressive stresses(Pressure)...Its almost incompressible...so we say it Sustains Pressures(+ve)"..
..but how does one talk of this for a Gas..on what basis I say that "A gas is able to/(not able to) Sustain a pressure"..

it is simply compressed till the internal pressure becomes equal to the external pressure.(remember gas laws??)

it is simply compressed till the internal pressure becomes equal to the external pressure.(remember gas laws??)
ya...but what is it that makes me say "The Gas sustains Pressure"...especially during the compression...before its pressure is going to be equal to ext pressure.....

I don't get the question.

Anything that has pressure can sustain a 'pressure'.

ya...but what is it that makes me say "The Gas sustains Pressure"...especially during the compression...before its pressure is going to be equal to ext pressure.....

When you talk about incompressible liquid, it doesnt mean they are not compressed at all, there is a small compression even in incompressible fluids, but it is far less then what would it be for a compressible liquid. I forgot what that term is called, i think its bulk modulus, thats pretty high for incompressible fluids.

Lets get to the basics. Imagine a piston in a cylinder containing a compressible fluid & atmospheric pressure on the other side of the piston. In this state, pressure on both sides is equal (assuming mass less piston). Lets say now the piston is pushed with a force of 10N, what happens?? The fluid obeys some freaky law & its pressure is increased. Think of it like, when all particles are pushed closer to each other, they try to repel each other more. So anyways, pressure increases, & volume decreases. This change in pressure & volume continues as long as pressure developed inside the cylinder times the cross sectional area of the piston becomes equal to the applied force, ie. 10N. This is how a fluid sustains pressure(or force).

In case of (so called)incompressible fluids, some other freaky laws are obeyed & change in volume, for the same pressure rise, is negligible.

Hi...ank_gl and Chris....
Last Two replies
In other words the question can be put as follows -
Whether the term "Sustain Pressure" has certain specific requirements so that I say "A fluid is sustaining a pressure{+/-ve} ...
Like consider a liquid first...
On subjecting to +ve pressures it suffers a negligible change in its volume...the effect of pressure is only a negligible change {so almost incompressible} in its volume with corresponding rise in pressure=Ext {+ve pressure}....
On subjecting to -ve pressures it would vaporise {Neglecting small "surface tension"}...here the liquid is undergoing a complete change of phase when subjected to -ve pressure...but no such changes were observed during +ve pressures....

But gases are always compressible{so are liquids but to vvvv small extent}
...The term "Sustain" for gases-does it have certain needs..on the basis of which we say if its able to sustain pressure....
Also ... "Does gas sustain '-ve pressure' ".. I don't think they can...even to the extent the liquids can {because of surface tension}...so does that mean "Sustain" just means that the fluid would resist the ext. pressure{so from above line this pressure has to be +ve...} at some of time as the pressure is applied...
Conclusion:
Fluids generally can't sustain -ve pressures Right..??...

Very bad choice of words by the author indeed. I believe such analogies should be used for self understanding, & should not be published.

Technically speaking(in the world of fluid mechanics), negative pressure is pressure below the atmospheric pressure. Pressure is always(not always) measured relative to atmosphere, ie. P$$_{actual}$$ = P$$_{atm}$$ + P$$_{measured}$$. So if P$$_{actual}$$ is less than the atmospheric pressure, you get negative gauge pressure.
P$$_{actual}$$ can reach 0 ultimately when P$$_{measured}$$ reaches -P$$_{atm}$$. Or in other words, maximum(or minimum??, whatever!!) P$$_{measured}$$ can be -P$$_{atm}$$.

But in no way it means that pressure starts pulling things apart instead of pushing them together.

Solid Mechanics
Imagine a cylindrical bar, if at the ends a force is trying to pull apart the bar, the bar is said to be in tension, or positive pressure, or positive stress.
<------ |||||||||||||||| ------>(positive stress).

If the force tries to push the bar like this,
------> |||||||||||||||| <------
the bar is in compression, or negative pressure, or negative stress.

The author has used the analogy between the two subjects to create a concept, which is super stupid in my view.

Very bad choice of words by the author indeed. I believe such analogies should be used for self understanding, & should not be published.

Technically speaking(in the world of fluid mechanics), negative pressure is pressure below the atmospheric pressure. Pressure is always(not always) measured relative to atmosphere, ie. P$$_{actual}$$ = P$$_{atm}$$ + P$$_{measured}$$. So if P$$_{actual}$$ is less than the atmospheric pressure, you get negative gauge pressure.
P$$_{actual}$$ can reach 0 ultimately when P$$_{measured}$$ reaches -P$$_{atm}$$. Or in other words, maximum(or minimum??, whatever!!) P$$_{measured}$$ can be -P$$_{atm}$$.

But in no way it means that pressure starts pulling things apart instead of pushing them together.

Solid Mechanics
Imagine a cylindrical bar, if at the ends a force is trying to pull apart the bar, the bar is said to be in tension, or positive pressure, or positive stress.
<------ |||||||||||||||| ------>(positive stress).

If the force tries to push the bar like this,
------> |||||||||||||||| <------
the bar is in compression, or negative pressure, or negative stress.

The author has used the analogy between the two subjects to create a concept, which is super stupid in my view.

I think the author was plenty clear in what he meant by that line. I fail to see what was stupid and/or confusing about it. The authors words were perfectly fine. :uhh:

Liquids normally cannot sustain a tensile (or pulling apart) stress since the liquid would vaporize.Therefore,the absolute pressures used in this book are never negative,since this would imply that the fluid is sustaining a tensile stress.

Absolute pressure cannot be negative for a fluid. Even if there are only 2 atoms in the whole galaxy, the pressure would be greater than absolute zero.

Regarding the evaporation of liquids, you need to understand the concept of vapour pressure. At each temperature, there exists a pressure at which the fluid starts boiling. Refer wiki.

As soon as the pressure varies, the fluid condenses or evaporates(vaporizes) to maintain the equilibrium, ie. for evaporating a fluid, negative pressure is not necessary, only a decrease in pressure is.

This is starting to get slightly confusing, as it seems to be mashing together several different concepts.

OP the way you are phrasing the question is also confusing too. Dont try to put it into a context or elaborate. Just state a question.

With fluids you generally talk in gauge pressures.

All 'sustain' means is how much load capacity does it have.

If you had a large (weightless) sheet 1 meter by 1 meter and a gas beneath it at 1 Pa, you would be able to put 1 N of force on the top of the sheet. So the gas can sustain a pressure of 1 Pa. Remember this is gauge pressure, the the acutal pressure of the gas ia atmospheric +1.

If you then compresses the gas to 10 Pa, you would be able to place 10N on the sheet.

Why can a liquid sustain compression (positive pressures)?

High bulk modulus but can flow. The flow is not a problem becuase the container stops it moving. So it basically acts like a solid.

Why can't liquids sustain tensile stresses (negative gauge pressure)?

Although it still has a high bulk modulus, it can flow. There is nothing to contain the movement of the liquid so it flows. However the only think keeping the fluid attached to whatever is pulling it is surface tension.

Liquids will only vapourise if the surrounding pressure is equal to the vapour pressure. However the liquid does not vapourise like you've just boiled it in a kettle (which I assume is what you are thinking). You get cavitation.

Why can't gases sustain a positive pressure (compression) at first?

Low bulk modulus and can flow, however as the gas is compresses its pressure rises. This compression then allows higher pressures to be 'sustained'. Basically it can hold more up. The closer you can get the molecules together the higher the pressure and the more resistance it will give to further compression.

Why can't gases sustain negative pressure?

Same reason a liquids, only more so.

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I think the author was plenty clear in what he meant by that line. I fail to see what was stupid and/or confusing about it. The authors words were perfectly fine. :uhh:

Yes they make sense when you are through with the subject. They don't when one is trying to understand the concept. Anyways, it is one's own perception

This is starting to get slightly confusing, as it seems to be mashing together several different concepts.

OP the way you are phrasing the question is also confusing too. Dont try to put it into a context or elaborate. Just state a question.

With fluids you generally talk in gauge pressures.

All 'sustain' means is how much load capacity does it have.

If you had a large (weightless) sheet 1 meter by 1 meter and a gas beneath it at 1 Pa, you would be able to put 1 N of force on the top of the sheet. So the gas can sustain a pressure of 1 Pa. Remember this is gauge pressure, the the acutal pressure of the gas ia atmospheric +1.

If you then compresses the gas to 10 Pa, you would be able to place 10N on the sheet.

Why can a liquid sustain compression (positive pressures)?

High bulk modulus but can flow. The flow is not a problem becuase the container stops it moving. So it basically acts like a solid.

Why can't liquids sustain tensile stresses (negative gauge pressure)?

Although it still has a high bulk modulus, it can flow. There is nothing to contain the movement of the liquid so it flows. However the only think keeping the fluid attached to whatever is pulling it is surface tension.

Liquids will only vapourise if the surrounding pressure is equal to the vapour pressure. However the liquid does not vapourise like you've just boiled it in a kettle (which I assume is what you are thinking). You get cavitation.

Why can't gases sustain a positive pressure (compression) at first?

Low bulk modulus and can flow, however as the gas is compresses its pressure rises. This compression then allows higher pressures to be 'sustained'. Basically it can hold more up. The closer you can get the molecules together the higher the pressure and the more resistance it will give to further compression.

Why can't gases sustain negative pressure?

Same reason a liquids, only more so
.

Wow...that answers all my earlier questions!{1 question still down there..}....[PLAIN]http://www.frendz4m.com/forum/images/ohmy.gif...Thanks...:smile:[/URL] [Broken]

Liquids will only vapourise if the surrounding pressure is equal to the vapour pressure. However the liquid does not vapourise like you've just boiled it in a kettle (which I assume is what you are thinking). You get cavitation.
Ya...I was aware of the relationship between Saturation Pressure and Saturation Temperature...

But...one statement I wanna get cleared of in your last reply is this : [The underlined part of this statement]
Why can't liquids sustain tensile stresses (negative gauge pressure)?
That pressure need not be -ve gauge pressure...its possible to just speak of -ve pressure...what is that "gauge" term doing there...
because..Pressure is defined to be positive towards the Center of Mass of the surface it acts upon[The same author specifies this in 2nd chapter]...
That completely defines that -ve pressure we are talking of here is external pressure taken to be +ve/-ve with respect to fluid mass of our interest...right????

Originally posted by ank_gl
Yes they make sense when you are through with the subject. They don't when one is trying to understand the concept. Anyways, it is one's own perception
Ya..I think I agree with you on this point..the author should have added the page number/small note referring to what -ve pressure means...it would have been of great use to noobs like me...

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Gauge pressure is exactly what itsays on the tin. Its the pressure read from a gauge. It's what the pressure is ABOVE atmospheric (or surrounding pressure).

When talking about fluid mechanics we ALWAYS talk in terms of gauge pressure. Which is why the distinction from 'absolute' pressure usually doesnt need to be made and we can just say 'pressure'. However for clarity in the post I specifically said gauge pressure becuase I suspected you werent making that link.

You cannot have negative absolute pressure.

Gauge pressure is exactly what itsays on the tin. Its the pressure read from a gauge. It's what the pressure is ABOVE atmospheric (or surrounding pressure).

When talking about fluid mechanics we ALWAYS talk in terms of gauge pressure. Which is why the distinction from 'absolute' pressure usually doesnt need to be made and we can just say 'pressure'. However for clarity in the post I specifically said gauge pressure becuase I suspected you werent making that link.

You cannot have negative absolute pressure.

Ya...You are right ...
I'm not getting the Link between why you used "-ve gauge pressure there specifically"...
Going a little back from the discussion at this point of time...
The liquid when subjected to -ve pressure....would expand continuously....... as soon as the pressure it is subjected to becomes less than the Saturation pressure at corresponding temperature....
but this pressure can be above the atmospheric pressure...the liquids would start evaporating depending on its temperature and corresponding saturation pressure...and then the applied pressure comes into picture which if -ve(* ){away from CM of liquid}{what I'm trying to say its directed away from the mass of fluid we are currently studying...thats why we say its -ve}....
Taking into consideration our current topic of discussion...we aren't really concerned as to when the liquid would evaporate...but whats important is that it would evaporate at some point of time when subjected to -ve pressure...and so they don't 'Sustain' -ve pressures{as this would cause them to flow continuously ... and then all that evaporating stuff and what not...}

(*) For the time being just visualize this pressure as being applied by some force directed away from fluid mass of interest}...and then other cases

Right????...For me this is getting confusing now....