Register to reply

Fluids mechanics is also gas mechanics?

by Femme_physics
Tags: fluids mechanics, mechanics
Share this thread:
cjl
#19
Jul14-11, 12:33 PM
P: 1,008
Quote Quote by Andy Resnick View Post
Liquids and gases are both considered "fluids", as has been pointed out. The relevant parameter in your question is the Knudsen number:

http://en.wikipedia.org/wiki/Knudsen_number

For Kn >>1, the continuum approximation breaks down and we instead model the fluid as a dilute gas using statistical methods.
Oh dear.

The Knudsen number has absolutely nothing to do with any of the concepts discussed in this thread. The Knudsen number describes whether a gas is sufficiently rarefied such that individual molecular effects must be taken into consideration when modeling the flow. It comes into play when modeling either very low density flows (such as satellite drag or reentry) or very small scale flows (such as the flow around a hard disk drive's head, or flows around some MEMS and NEMS devices). While the Knudsen number is tremendously useful in some cases, it's completely irrelevant for this discussion.


Quote Quote by Andy Resnick View Post
Gases are not inviscid! In fact, accounting for the difference in density (the kinematic viscosity, measured in Stokes ), air is as viscous as water. Fluids don't "stick" to walls (exempting adhesion/bonding/chemical interactions)- the no-slip condition arises simply by demanding the divergence of the stress tensor be finite.
True, gases are not inviscid. However, their viscosity is small enough that in some cases, the viscosity can be ignored and useful solutions still arise (which is actually true for some liquids as well). As for air vs water viscosity? Kinematic viscosity isn't really the relevant parameter - dynamic viscosity is the much more common parameter, and using that measurement, air is far less viscous than water (as would be expected).

As for the no-slip condition? No, it does not arise from the need for the divergence of the stress tensor to be finite. It arises from the tendency of the flow to stick to the surface. At a molecular level, individual surface reflections tend to be diffuse, which means that the outgoing angle of an individual molecule after impacting the surface tends to be independent of the incoming angle, and statistically distributed. When averaged over large numbers of molecules, this means that the reflected fluid is stationary with respect to the surface, aside from the velocity away from the surface (that comes from the fact that we are only considering reflected molecules). These reflected molecules then interact with incoming molecules, and the net result is that the fluid adjacent to the surface is stationary for any flow in which the molecular interaction length scale is substantially smaller than the object's length scale (such that the reflected molecules can interact with and slow down the incoming molecules).
cjl
#20
Jul14-11, 12:37 PM
P: 1,008
Quote Quote by timthereaper View Post
Fluids aren't really inviscid. I guess you can think of it as "sticking" to the wall if it helps you, but I think Resnick answered the question very succinctly. We assume inviscid flow a lot of times to simplify the equation when we know (or think) that viscosity doesn't play a large part in the problem we're trying to solve. However, when dealing with certain types of problems (like in aerodynamics), you can't assume inviscid flow.

Hope that helps.
Actually, in aerodynamics, inviscid flow is frequently assumed, as inviscid flow plus a couple of small corrections (the biggest one for aerodynamics is the Kutta condition) can give surprisingly accurate results for high Reynolds number flow. You do need viscosity to correctly model the skin friction drag and boundary layer behavior, but induced drag and lift don't really need viscosity to determine an accurate solution.
timthereaper
#21
Jul14-11, 02:11 PM
P: 343
The point I was making was more about the ability/inability to assume inviscid flow. I knew that there were certain problems in aerodynamics that you could assume inviscid flow, but I know there are certain ones you can't. I couldn't come up with another case in other areas of fluids where you could assume inviscid flow off the top of my head.
Andy Resnick
#22
Jul14-11, 04:12 PM
Sci Advisor
P: 5,510
Quote Quote by Femme_physics View Post
The quote said "fluid" which can also mean liquid! As you probably already know.
Eh? The quote within your quote mentioned 'gases":

Quote Quote by Femme_physics View Post
<snip>

Can anyone though answer me for what I asked before

[Similarly, it can sometimes be assumed that the viscosity of the fluid is zero (the fluid is inviscid). Gases can often be assumed to be inviscid. If a fluid is viscous, and its flow contained in some way (e.g. in a pipe), then the flow at the boundary must have zero velocity]

This is because the fluid sticks to the walls, right?
klimatos
#23
Jul14-11, 05:32 PM
P: 409
Quote Quote by I like Serena View Post
The air fills the entire container and in time the blue gas will mix more thoroughly with the air, filling the container completely as well.
You may see this as a quibble, but I should like to take issue with this statement. In kinetic gas theory and statistical mechanics it is considered a matter of some importance that most gases do NOT completely fill their container.

For instance, a container of air at NTP is 99.9% nothingness and only 0.1% gas molecules. The air is a long, long way from "filling" the container. I prefer to say that the probability of a gas molecule being in any volume of that container is the same for any similarly-sized volume. The actual number of molecules in any given volume will vary considerably from volume to volume an any given instant; and will vary from instant to instant for any given volume. It's all a matter of probability.

I believe the "filling" language is a holdover from the days when gas molecules were believed to be able to expand indefinitely in size so as to "fill" a container.
Studiot
#24
Jul14-11, 06:06 PM
P: 5,462
You may see this as a quibble, but I should like to take issue with this statement. In kinetic gas theory and statistical mechanics it is considered a matter of some importance that most gases do NOT completely fill their container.
I don't think that is quite what is meant by filling the container or taking on the shape as mentioned earlier.

Take a container.

The difference in behaviour as regards 'filling' between a gas and a liquid is simple here.

For a gas there is no part of the volume that is not available to the gas molecules to occupy.
Yes there is only a finite probability of finding a gas molecule in any given region at any given time, and yes the distribution will be uneven and vary with time, but unlike a liquid, there is no boundary or surface.

A liquid on the other hand has a surface. All the liquid molecules occupy space on one side of the surface only.
Yes there may be vapour molecules escaped from the surface in the rest of the container, but these are no longer liquid.

go well
Femme_physics
#25
Jul14-11, 09:36 PM
PF Gold
Femme_physics's Avatar
P: 2,551
Quote Quote by Andy Resnick View Post
Eh? The quote within your quote mentioned 'gases":
Then in that case you have an argument to pick against wiki, not me!
Femme_physics
#26
Jul15-11, 12:49 AM
PF Gold
Femme_physics's Avatar
P: 2,551
I'm trying to understand this lever principle of fluid based on this:




Does that mean that I can apply a really small force on the right side and lifts a huge heavy car with it?


If so, it's incredible, and reminds me of the pulley lever!
Studiot
#27
Jul15-11, 02:21 AM
P: 5,462
That diagram and others like it are a tad misleading.

Your force formulae are correct but the diagram suggest the piston moves the same distance as the plate under the car.

Of course the volume change is the same on both sides so

ALdL = ARdR

where d is the distance moved

So if the area of the plate under the car is 10 times the area of the piston the piston moves 10 times as far!

go well
I like Serena
#28
Jul15-11, 02:50 AM
HW Helper
I like Serena's Avatar
P: 6,187
Cool huh!

Although if you put a small pressure on the right side, it will become even harder to lift the heavy car!
Femme_physics
#29
Jul15-11, 03:03 AM
PF Gold
Femme_physics's Avatar
P: 2,551
Quote Quote by Studiot View Post
That diagram and others like it are a tad misleading.

Your force formulae are correct but the diagram suggest the piston moves the same distance as the plate under the car.

Of course the volume change is the same on both sides so

ALdL = ARdR

where d is the distance moved

So if the area of the plate under the car is 10 times the area of the piston the piston moves 10 times as far!

go well
I see. So not as useful as I thought, but still pretty useful!



Quote Quote by I like Serena View Post
Cool huh!

Although if you put a small pressure on the right side, it will become even harder to lift the heavy car!

Noted!
xxChrisxx
#30
Jul15-11, 06:48 AM
P: 2,043
Quote Quote by Femme_physics View Post
I'm trying to understand this lever principle of fluid based on this:

Does that mean that I can apply a really small force on the right side and lifts a huge heavy car with it?
That's how hydraulic jacks work, so yes.
It's also how brakes work.
Studiot
#31
Jul15-11, 12:32 PM
P: 5,462
It is not fashionable to teach basic mechanics quantities these days but here are some that are applicable to this hydraulic lift and other purely mechanical things like levers and pulleys.

[tex]{\rm{VelocityRatio = VR = }}\frac{{{\rm{distance}}\,{\rm{moved}}\,{\rm{byload}}}}{{{\rm{distance} }\,{\rm{moved}}\,{\rm{byeffort}}}}[/tex]

[tex]{\rm{MechanicalAdvantge = MA = }}\frac{{{\rm{load}}}}{{\,{\rm{effort}}}}[/tex]

[tex]{\rm{Efficiency = }}\frac{{{\rm{MA}}}}{{{\rm{VR}}}}[/tex]

and finally what is really the law of conservation of energy

[tex]{\rm{load*distance}}\,{\rm{moved}}\,{\rm{by load = effort*distance}}\,{\rm{moved}}\,{\rm{by}}\,{\rm{effort}}[/tex]

Which you can see equals MA * VR
I like Serena
#32
Jul15-11, 05:15 PM
HW Helper
I like Serena's Avatar
P: 6,187
Similarly, it can sometimes be assumed that the viscosity of the fluid is zero (the fluid is inviscid). Gases can often be assumed to be inviscid. If a fluid is viscous, and its flow contained in some way (e.g. in a pipe), then the flow at the boundary must have zero velocity
This is because the fluid sticks to the walls, right?
Perhaps a bit late, but I'd like to answer this question anyway.

I'll stick my neck out and say: yes, it is because the fluid sticks to the walls.
Or rather, the friction between the fluid and the wall makes it stand still where it makes contact with the wall (in modelling).


Register to reply

Related Discussions
Basic exercise for finding a Lagrangian from the Landau's Mechanics Advanced Physics Homework 1
The book Introduction to tensor calculus and continuum mechanics Calculus & Beyond Homework 5
Any comments on Mathematical Foundations of Quantum Mechanics by Parthasarathy Math & Science Software 0
Any comments on Mathematical Foundations of Quantum Mechanics by Parthasarathy Math & Science Software 0
Introduction to Quantum Mechanics - Third Edition, by Richard Liboff General Physics 12