I Does gas flow from low to high pressure?

[Baluncore]

Again, no argument, this uphill flowing can be explained in simple physics terms of trading body's KE for PE.

On a bicycle, the lower the road is where you are, the faster you are rolling.
That is the same with the water in the pipe. If it flows faster, it must have a lower pressure.

 

[Sailor Al]

I was going to point out a more trivial example of water flowing "uphill":
[actually, I first looked for firefighting videos but didn't quickly find a good one.]

OK, OK already!

 

[Sailor Al]

On a bicycle, the lower the road is where you are, the faster you are rolling.

WOAH! It's not the altitude ("..the lower the road...") of the road that provides the potential gradient that allows you to trade KE for PE as you roll uphill, it's the gradient of the road.

 

[russ_watters]

WOAH! It's not the altitude ("..the lower the road...") of the road that provides the potential gradient that allows you to trade KE for PE as you roll uphill, it's the gradient of the road.

No. You're misunderstanding here also speaks to part of your apparent issue with Bernoulli I (and several others) mentioned above). How "low" a particular stretch of road is with respect to a baseline speaks to the speed in that stretch. The slope determines the acceleration between "high' and "low" sections.

 

[Arjan82]

I'm still looking for a similarly simple physics explanation of how a gas flows from low to high pressure. I know it does, I just can't quite work out how.

Well, several posts in this thread are devoted to answering this question in the simplest of terms. Apparently that still doesn't explain it for you. I personally wouldn't know how to provide a better answer for you. If you want a better answer, you need to be very specific about what you don't understand about the explanations you already got. Then we can build from there.

 

[Arjan82]

And in the video, the air does flow from the low pressure of chamber B to the high pressure of chamber C.
I guess the problem lies in the word "flow".

Please explain? Flow is a very well defined term.

I don't think the answers will come from quoting Bernoulli or linking to Wikipedia articles,

Why wouldn't that work? Linking to wikipedia articles provides more background information which presumably might help you. If it doesn't, you can always ignore it. Please be more specific in what constitutes an answer to you.

nor will it come from using conversationally non-physics terms such as inertia (the tendency for an object to resist motion!).

Calling 'inertia' a non-physics term is silly to me. It does have a clear definition, you even quoted it (but actually, it is the resistance to changes in velocity, i.e. you need a force to change its velocity -> Newton's first and second law). But it does not have a unit, nor does it have to. It is a concept. But if this is not the answer you want, then what is?

Or indeed from considering a gas other than the continuum of an "Ideal gas". Any venture down the path of molecules will end poorly. Air doesn't behave like a stream of ping-pong balls!

So how do you think the kinetic theory of gases works? It essentially treats the gas as ping-pong balls in a statistical fashion. This theory can explain a lot of things about a gas (but of course has its limitations).

So this is my attempt to explain what I don't get about what you want in an answer. Please clarify yourself.

 

[Herman Trivilino]

Classical Physics states that a gas will only flow from a region of high to one of low pressure and, like water, won't run uphill.

Neither of those claims is valid. Do you have a reference?

 

[jack action]

Again, no argument, this uphill flowing can be explained in simple physics terms of trading body's KE for PE.
[...] I'm still looking for a similarly simple physics explanation of how a gas flows from low to high pressure. I know it does, I just can't quite work out how.

So the water particle flows at the bottom of the hill at velocity $v_1$ and thus has $KE_1 = \frac{1}{2}mv_1^2$. It also has some potential energy, $PE_1 = mgh_1$. The total energy is $KE_1 + PE_1$. And you understand that it will go uphill while decelerating, i.e. $KE_1 + PE_1 = KE_2 + PE_2$, or:
$$\frac{1}{2}(v_1^2 - v_2^2) = g(h_2-h_1)$$

But a particle also has internal energy $U = PV$, where $P$ is the pressure and $V$ is the volume occupied by the particle.

Ignoring $PE$ change for the moment, we get $KE_1 + U_1 = KE_2 + U_2$, thus (assuming an incompressible fluid or $V_1 = V_2 = V$):
$$\frac{1}{2}\frac{m}{V}(v_1^2 - v_2^2) = (P_2-P_1)$$
Where $\frac{m}{V}$ is the density $\rho$ of the fluid. That is the Bernoulli equation. If we assume that $v_1 > v_2$, we can see that $P_2 > P_1$ or the pressure increases as the velocity decreases; Just like the height of a particle must increase as the velocity decrease when it goes uphill. The energy must be conserved.

The only difference with a compressible fluid is that $V_1 \ne V_2$ and thus the change in pressure is not that simple. A relation must be determined between pressure and volume. (And that relation is usually the ideal gas equation.)

 

[Sailor Al]

Neither of those claims is valid. Do you have a reference?

In my post #23 I have conceded that water does indeed flow uphill.
And the video clearly shows that in the Venturi tube, gas does indeed flow from low to high pressure.

 

[Sailor Al]

Please explain? Flow is a very well defined term.

Could you please provide a reference to a definition of "flow" - preferably from a physics textbook or published paper. Encyclopaedias, dictionaries and Wikipedia are fine for conversational explanations but are not reliable sources.

Calling 'inertia' a non-physics term is silly to me. It does have a clear definition, you even quoted it (but actually, it is the resistance to changes in velocity, i.e. you need a force to change its velocity -> Newton's first and second law). But it does not have a unit, nor does it have to. It is a concept. But if this is not the answer you want, then what is?

Once again, could I request a physics definition of inertia. I have accessed digital copies of a dozen modern, in-print, physics and mechanics textbooks and performed a text search over thousands of pages but can find no definition for "inertia".
Since this is one of the "Physics Forums", shouldn't we stick to physics?

So how do you think the kinetic theory of gases works? It essentially treats the gas as ping-pong balls in a statistical fashion. This theory can explain a lot of things about a gas (but of course has its limitations).

Yes, and it is precisely these limitation that make it unsuitable for explaining the fluid/continuum nature of gas.

 

[Frabjous]

Once again, could I request a physics definition of inertia. I have accessed digital copies of a dozen modern, in-print, physics and mechanics textbooks and performed a text search over thousands of pages but can find no definition for "inertia".
Since this is one of the "Physics Forums", shouldn't we stick to physics?

If you want better quality answers, stop being so hostile. Newton’s first law is also known as the law of inertia.

 

[Sailor Al]

If you want better quality answers, stop being so hostile. Newton’s first law is also known as the law of inertia.

Please, can we play the ball, not the player?
I don't think that politely requesting a physics definition for a term being used in a physics discussion qualifies as "hostile".

 

[Frabjous]

Please, can we play the ball, not the player?
I don't think that politely requesting a physics definition for a term being used in a physics discussion qualifies as "hostile".

If you honestly believe that your responses come across as polite, I would suggest having a friend review them.

 

[Sailor Al]

If you honestly believe that your responses come across as polite, I would suggest having a friend review them.

If my bluntness comes across as impolite, then I apologise. I am an old dog and am struggling to find the correct tone of voice.
Could you help me rephrase the request for a definition of "inertia" that is applicable to a serious scientific discussion please?

 

[jack action]

Once again, could I request a physics definition of inertia.

From Philosophiæ Naturalis Principia Mathematica by Isaac Newton:

DEFINITION III.

The vis insita, or innate force of matter, is a power of resisting, by which every body, as much as in it lies, endeavours to persevere in its present state, whether it be of rest, or of moving uniformly forward in a right line.

This force is ever proportional to the body whose force it is; and differs nothing from the inactivity of the mass, but in our manner of conceiving it. A body, from the inactivity of matter, is not without difficulty put out of its state of rest or motion. Upon which account, this vis insita, may, by a most significant name, be called vis inertiæ, or force of inactivity. But a body exerts this force only, when another force, impressed upon it, endeavours to change its condition; and the exercise of this force may be considered both as resistance and impulse; it is resistance, in so far as the body, for maintaining its present state, withstands the force impressed; it is impulse, in so far as the body, by not easily giving way to the impressed force of another, endeavours to change the state of that other. Resistance is usually ascribed to bodies at rest, and impulse to those in motion; but motion and rest, as commonly conceived, are only relatively distinguished; nor are those bodies always truly at rest, which commonly are taken to be so.

As for the definition of flow, it appears to be a mathematical concept, not a physics one:

In mathematics, a flow formalizes the idea of the motion of particles in a fluid. Flows are ubiquitous in science, including engineering and physics. The notion of flow is basic to the study of ordinary differential equations. Informally, a flow may be viewed as a continuous motion of points over time. More formally, a flow is a group action of the real numbers on a set.

I know this one comes from Wikipedia, but it does go deeper into the more formal mathematical definitions that I find are not really helpful unless you understand all the advanced mathematical concepts. There are also references in the article pointing to the Encyclopedia of Mathematics, which are even more difficult to understand.

 

[russ_watters]

If my bluntness comes across as impolite, then I apologise. I am an old dog and am struggling to find the correct tone of voice.
Could you help me rephrase the request for a definition of "inertia" that is applicable to a serious scientific discussion please?

It's not your tone of voice, it's the request/your approach itself. This subject is high school level and Wikipedia is perfectly fine for learning it. Questioning simple concepts while demanding formal and higher level sources is incongruous and disrespectful of the help you are being given.

 

[Arjan82]

Yes, and it is precisely these limitation that make it unsuitable for explaining the fluid/continuum nature of gas.

Which limitations do you mean exactly? It sounds like you know already what the kinetic theory of gasses entails. If you do, why do you ask us? If you don't, what are you trying to do here?

 

[PeterDonis]

inertia (the tendency for an object to resist motion!).

No, inertia is the tendency for an object to resist changes in its motion. If the object is at rest, its inertia will resist it being put in motion. If the object is in motion, its inertia will resist its velocity being changed.

 

[PeterDonis]

The explanation of how water flows upstream in a syphon is answered with simple mechanics: as long as the pressure in the water on the rising side is greater than its vapour pressure, the water will remain a liquid and gets pushed by air pressure over the hump. If the rise is more than 32 feet, then at the top of the hump the water will change form a liquid to a gas the water velocity will reduce to zero.

Where are you getting this from? It doesn't look like any explanation for a siphon that I've seen.

 

[Frabjous]

If my bluntness comes across as impolite, then I apologise. I am an old dog and am struggling to find the correct tone of voice.
Could you help me rephrase the request for a definition of "inertia" that is applicable to a serious scientific discussion please?

Newton's first law is also know as the law of inertia. Here is an excerpt from Halliday and Resnick (3rd edition). He gives two formulations of the law. Inertia is the concept used in the first definition. In modern practice, knowledge of mass and and conservation of momentum handles most of this. The concept of inertial reference frames proves to be very important.

 

[Sailor Al]

Newton's first law is also know as the law of inertia. Here is an excerpt from Halliday and Resnick (3rd edition). He gives two formulations of the law. Inertia is the concept used in the first definition. In modern practice, knowledge of mass and and conservation of momentum handles most of this. The concept of inertial reference frames proves to be very important.

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But at risk of further castigation for impoliteness, I have to point out that the term "inertia" that appears in your reference in the context of: "is sometimes called the law of inertia" really doesn't qualify as a scientific definition of inertia. There is no definition or indication of its physics [MLT] dimensions.
I have no issue with the phrase "inertial reference frames" to describe a non-accelerating, non-rotating frame of reference not subject to a gravitation field.

 

[PeterDonis]

There is no definition or indication of its physics [MLT] dimensions.

In terms of mechanics, inertia has the dimensions of mass (M), since it is mass; the mass of an object is its inertia, its resistance to having its motion changed.

 

[Sailor Al]

In terms of mechanics, inertia has the dimensions of mass (M), since it is mass; the mass of an object is its inertia, its resistance to having its motion changed.

So are mass and inertia interchangeable terms?

 

[PeterDonis]

So are mass and inertia interchangeable terms?

In mechanics, yes, at least for the inertia aspect of mass, i.e., the $m$ that appears in $F = ma$. Sometimes the term "inertial mass" is used to make it clear what aspect of mass is being described.

 

[Sailor Al]

In mechanics, yes, at least for the inertia aspect of mass, i.e., the $m$ that appears in $F = ma$. Sometimes the term "inertial mass" is used to make it clear what aspect of mass is being described.

So could the explanation provided by @boneh3ad at post #5:

Gas has inertia like any mass. Pressure gradient provides a force, so moving from low to high pressure will slow it down and moving from high to low will speed it up.

have been written as:
"Gas has mass like any mass." or "Gas has inertia like any inertia."?

I suspect inertia is being presented as having a wider connotation than just mass.

 

[Frabjous]

I suspect inertia is being presented as having a wider connotation than just mass

Mass is a quantified measure of inertia. So they are frequently interchangeable, but not always.

 

[PeterDonis]

So could the explanation provided by @boneh3ad at post #5:

have been written as:
"Gas has mass like any mass." or "Gas has inertia like any inertia."?

Yes. But since his point was to emphasize the inertia aspect of mass, he wrote it like he wrote it.

I suspect inertia is being presented as having a wider connotation than just mass.

No, you have it backwards. The term "mass" has more meanings in physics than just "inertia". That is why I phrased my statements in post #54 in a very specific way.

 

[Sailor Al]

No, you have it backwards. The term "mass" has more meanings in physics than just "inertia". That is why I phrased my statements in post #54 in a very specific way.

Could you please help me understand, in classical physics or mechanics, how inertia differs from mass? Young and Freedman 's University Physics states :
"The tendency of an object to keep moving once it is set in motion is called inertia. You use inertia when you try to get ketchup out of a bottle by shaking it. First you start the bottle (and the ketchup inside) moving forward; when you jerk the bottle back, the ketchup tends to keep moving forward and, you hope, ends up on your burger. Inertia is also the tendency of an object at rest to remain at rest. You may have seen a tablecloth yanked out from under a table setting without breaking anything. The force on the table setting isn’t great enough to make it move appreciably during the short time it takes to pull the table- cloth away."
and
"Mass is a quantitative measure of inertia"
It seems to me that they are interchangeable and neither has more meaning than the other.

 

[PeterDonis]

Could you please help me understand, in classical physics or mechanics, how inertia differs from mass?

It doesn't. More precisely, it doesn't differ from inertial mass. The term "inertia" in the various quotes you have given from physics textbooks seems to be used when a qualitative description is being given, while the term "mass" (or more specifically "inertial mass") would be used when a more quantitative description is being given, for example using the equation $F = ma$ that I have already referenced.

None of this is at all abstruse or controversial.

 

[hutchphd]

Could you please help me understand, in classical physics or mechanics, how inertia differs from mass?

I think you are perhaps not appreciating the historical context. Aristotle had posited that the natural state for an object is to be at rest and if you don't push on an object, it will stop moving. Newton's notion was so radical that he sort of said it twice, once in words and once quantitatively. Only in the quantitative statement was the mass strictly defined and so that carries an unambiguous dimension. The notion of inertia is a little bit more fuzzy.
Thanks for a good question. As another old dog, I think you did occasionally snarl inappropriately.