I Why in the steady flow of a fluid, the fluid cannot move through the wall....?

[fxdung]

Because of temperature, molecules of fluid have chaos movements.So I do not understand why in steady flow,the molecules of fluid can not move through the wall of flow tube?I think two layers of fluid exchange molecules while they move.How do we understand when saying: fluid can not move through the wall flow tube(made of flow lines) as every textbook saying?

 

[BvU]

Because of temperature, molecules of fluid have chaos movements

It's the other way around.

in steady flow
...
as every textbook saying

I suppose you refer to laminar flow of a continuous medium (*) in a cylindrical tube ?
If so, then:
From symmetry considerations there can not be flow in radial direction

(*) this term means you don't look at the individual molecules​

 

[fxdung]

I think we must consider at the individual molecules,because if we dye(making color) some layers, then the color does not spread from one layer to another layer when they flow?Then it seem that two layers do not exchange the molecules.But it is impossible because molecules have chaos movement.

 

[BvU]

What is it you want to ask ?
Can you post a passage from your 'every textbook' that is confusing to you?

Mixing up molecular descriptions and continuous media descriptions might to be your hangup: of course they are linked, but properties like viscosity and diffusion constants are specifically meant for the latter.
And: yes, the origin of these phenomena is molecular.

 

[fxdung]

Now owe you I can clarify between the two descriptions.But please explain to me why the color of two layers of fluid do not mix while they still exchange molecules if they(two layers)move relative each other.

 

[Chestermiller]

Now owe you I can clarify between the two descriptions.But please explain to me why the color of two layers of fluid do not mix while they still exchange molecules if they(two layers)move relative each other.

Who says they can’t and don’t?

 

[fxdung]

I see in figure in the textbook that they flow separately,and the color don't mix?E.g fig 12.19, fig 12.20 page 379, University Physics of Young and Freedman ,14ed.
Is that correct that in short time we neglect the exchange molecules between layers comparing with the macro flowing?

 

[Chestermiller]

I see in figure in the textbook that they flow separately,and the color don't mix?E.g fig 12.19, fig 12.20 page 379, University Physics of Young and Freedman ,14ed.
Is that correct that in short time we neglect the exchange molecules between layers comparing with the macro flowing?

Well, it takes time/distance for the diffusion to occur. But, it will occur.

 

[BvU]

I see in figure in the textbook that they flow separately,and the color don't mix?E.g fig 12.19, fig 12.20 page 379, University Physics of Young and Freedman ,14ed.
Is that correct that in short time we neglect the exchange molecules between layers comparing with the macro flowing?

Ah, found your flow tube fig 12.18. And as the author says:

​

The flow lines passing through the edge of an imaginary element of area, such​

as area A in Fig. 12.18, form a tube called a flow tube. From the definition of a​

flow line, in steady flow no fluid can cross the side walls of a given flow tube.​

​

So it's by definition. Thinking about a flow tube on a molecular scale seems pointless to me ( I grant you the authors of this book do not emphasize the difference between continuous media and 'ensembles of many molecules' -- they more or less bypass it, e.g. when discussing pressure).

Re diffusion: diffusion constants are usually very small. From school, I vividly remember a demo with a measuring cylinder filled with water with a lump of CuSO₄ thrown in. It would take many days for the blue to move upwards in the cylinder.

So yes, it's correct we can neglect... as you say.
But, as Chet writes and you suspect, diffusion does take place...

 

[anorlunda]

You can see a more intuitive demo in this screenshot of an artist's technique. Of course the paint colors mix due to diffusion, but the paint dries before the mixing becomes visible.

 

[jbriggs444]

If we are talking about lateral pressure between adjacent flow tubes then any diffusion across the boundary is irrelevant. The same momentum is transferred whether the molecules in the two flow tubes bounce off one another, pass silently past one another or bounce off an imaginary boundary between the tubes. Regardless of which description is used, the effect is that of a simple pressure between the tubes. One may as well adopt the simple, albeit non-physical, model of strict separation.

However, if the flows are at different velocities one wants to include the resulting shear force then the rate of diffusion enters in as viscosity.

 

[boneh3ad]

A typical undergraduate textbook covering fluid mechanics is not generally considering flows of multiple fluids, i.e. they ignore diffusion. The question about dye here is effectively becoming more complicated due to this fact.

In a continuous medium, we ignore the action of individual molecules. This means that a fluid particle (which is not true physical particles but an abstraction that allows us to work with a continuum) cannot cross a streamline. By definition, a streamline is everywhere parallel to the velocity vector. This works because we ignore individual molecular motion. Those molecules can and do cross streamlines, but on average, the same number will be crossing in the opposite direction, so the continuum properties of the fluid particles don't change and we see no difference at that level of abstraction.

Now if you throw the dye part of the question into the mix, you need to consider whether diffusion is important. Food coloring in water is a diffusion-dominated problem, so you either have to consider the molecules (less common) or model that process based on a two-fluid continuum process (more common). On the other hand, if you have something like food coloring in corn syrup, diffusion is a much slower process and could often be ignored in most contexts. For example, see the video below where diffusion is so slow that the food coloring effectively stays in place and can be "unmixed."