
#19
Jul1411, 12:33 PM

P: 975

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. As for the noslip 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). 



#20
Jul1411, 12:37 PM

P: 975





#21
Jul1411, 02:11 PM

P: 341

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.




#22
Jul1411, 04:12 PM

Sci Advisor
P: 5,468





#23
Jul1411, 05:32 PM

P: 403

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 similarlysized 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. 



#24
Jul1411, 06:06 PM

P: 5,462

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 



#25
Jul1411, 09:36 PM

PF Gold
P: 2,551





#26
Jul1511, 12:49 AM

PF Gold
P: 2,551




#27
Jul1511, 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 A_{L}d_{L} = A_{R}d_{R} 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 



#28
Jul1511, 02:50 AM

HW Helper
P: 6,189

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



#29
Jul1511, 03:03 AM

PF Gold
P: 2,551

Noted! 



#30
Jul1511, 06:48 AM

P: 2,032

It's also how brakes work. 



#31
Jul1511, 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 



#32
Jul1511, 05:15 PM

HW Helper
P: 6,189

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). 


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