Is shear stress at the pipe wall the same for turbulent and laminar flows?

[lost captain]

TL;DR Summary

Is the shear stress at the walls of the pipe basically the same for turbulent and laminar flow?

Hello everyone ,
I know that shear stress in turbulent flow is a lot larger from shear stress in laminar flow. My question is about the shear stress at the walls of the pipe.

So i was watching a video about shear stress in turbulent flow and the narrator pointed out that the shear stress in turbulent flow consists of shear stress laminar plus shear stress turbulent. BUT as we go closer to the pipe walls the laminar shear stress dominates.
So i wanted to ask is the shear stress at the walls of the pipe basically the same for turbulent and laminar flow?

 

[Chestermiller]

In both laminar and turbulent flow, the shear stress at the wall is equal to the product of shear rate and viscosity. However, for the same flow rate, in turbulent flow, the velocity gradient near the wall is much higher than in laminar flow.

 

[lost captain]

In both laminar and turbulent flow, the shear stress at the wall is equal to the product of shear rate and viscosity. However, for the same flow rate, in turbulent flow, the velocity gradient near the wall is much higher than in laminar flow.

But shear rate is equal to the velocity gradient... isn't it?
So shear stress at the walls of the pipe, in turbulent flow isn't equal to the shear stress in laminar flow

If for example i have the same fluid in 2 different pipes, in the first pipe it flows with small velocity and we have laminar flow, in the second pipe it has higher velocity and so turbulent flow. The shear stress at the wall is the same?

 

[lost captain]

In both laminar and turbulent flow, the shear stress at the wall is equal to the product of shear rate and viscosity. However, for the same flow rate, in turbulent flow, the velocity gradient near the wall is much higher than in laminar flow.

And when we defined the friction factor "f", was the shear stress(τ) in the nominator between the laminar layer and the pipe walls or was the shear stress between the laminar layer and the inner turbulent main layer?

 

[Arjan82]

So i was watching a video about shear stress in turbulent flow and the narrator pointed out that the shear stress in turbulent flow consists of shear stress laminar plus shear stress turbulent.

Well, I'm not sure that is a very helpful way of looking at it. A laminar flow gets its name from the fact that the instantaneous flow direction is always parallel to the surface and thus the fluid flows in 'laminates' or layers. The only interaction between these layers is the viscosity.

Turbulent flow on the other hand has 'eddies'. These eddies are, roughly, swirling motions of the flow but then of all possible sizes and at the same time, in other words the flow is chaotic. The instantaneous flow direction is thus also chaotic in nature, potentially in all directions. Of course continuity is still to be adhered to so on average it is still parallel to the wall.

So to call the shear stress a sum of laminar and turbulent flow misses the mark for me. If there is turbulent flow, there is simply no laminar flow and thus the shear stress has nothing to do with that of laminar flow.

What the narrator may be confused with is how such a flow is often modeled on a computer. When you want to do computations it very, VERY expensive to compute the flow in all its detail including these eddies. So, the solution is to compute the mean flow and model the effect of turbulence on this mean flow. If you think about it, the turbulence has an effect of redistributing the momentum of the flow, much like viscosity does. So, a very simple way of modelling turbulence is by coming up with a 'turbulent viscosity' (often called 'eddy viscosity') based on mean flow parameters (e.g. the mean velocity gradients) that does the same thing as viscosity: redistribution of momentum.

So in this modeling sense you can call the shear stress at some location as a sum of shear stress caused by viscosity (or 'laminar shear stress', but please don't ever use this term...) and eddy viscosity (turbulent shear stress), since this is indeed how you would compute it. I however still think that also in this case it is very confusing to talk about 'laminar shear stress', it has nothing to do with laminar flow...

Some notes:
- Note that 'eddy viscosity' is a property of the flow, not of the fluid. It differs from location to location.
- Eddy viscosity is a model, not an actual physical quantity. But since this is a very common model, and since actual computations of fully fledged turbulent flow is very rare (even today), the model is often confused for reality, or at least the distinction is often sloppy.
- You can come up with an eddy viscosity ratio, which is the eddy viscosity divided by the fluid viscosity. Values of 1000 or more are very common here. In other words: turbulence is way more effective in redistributing momentum than viscosity is.
- The shear stress in actual flow is only caused by viscosity and nothing else. But in turbulent flow the instantaneous shear stress is in all directions because of the eddies in the flow. It is very costly to compute this shear stress distribution, so we revert to modelling the averages.

BUT as we go closer to the pipe walls the laminar shear stress dominates.

So, based on the previous discussion, let's replace this sentence with 'Closer to the pipe walls the viscosity dominates over the eddy viscosity', this is actually true, although 'closer' is not capturing what's really going on, see below.

Think now for a moment that turbulent flow just consists of eddies and simplify those as circular motions of fluid parcels. If you are in the middle of the pipe, the diameter of such a circular motion can be close to the pipe's diameter. But the closer you approach the wall, the smaller these circular motions need to be because there is a wall in the way. At some distance to the wall the motions become so small that they are damped again by viscosity. This is what happens in the viscous sublayer (not to be confused with a viscous boundary layer!). There, no eddies can exist and the flow is strictly laminar again.

To get a feel of the size of this viscous sublayer, consider a pipe of 2cm diameter (I guess about a typical pipe diameter going to your faucet) in which there is an average flow velocity of 2m/s. In this case the viscous sublayer is only about 25 microns (25e-6m) thick! So to say 'closer to the wall ...' doesn't really cut it...

So i wanted to ask is the shear stress at the walls of the pipe basically the same for turbulent and laminar flow?

Well, yes and no I guess. Yes in the sense as @Chestermiller already described: the wall shear stress is always equal to the velocity gradient (shear rate actually) times the viscosity.
But no in the sense that the shear rate of a turbulent boundary layer is always way higher. Also, the way to compute this shear rate is very different: you can compute the flow in the pipe in case of laminar flow exactly, but in case of turbulent flow it requires a model for the turbulence, or a heck of a lot of computational effort. If you are able to keep the flow in the pipe laminar, the pressure drop will be much less than for a turbulent flow with the same volume flow.

I've got to learn to write shorter answers.....

 

[Arjan82]

And when we defined the friction factor "f", was the shear stress(τ) in the nominator between the laminar layer and the pipe walls or was the shear stress between the laminar layer and the inner turbulent main layer?View attachment 347050

As an aside: a fraction consists of a numerator and a denominator. A 'nominator' is not a thing ;).

The f (and thus also the $\tau_w$ ) is between the fluid and the pipe wall.

 

[Arjan82]

But shear rate is equal to the velocity gradient... isn't it?

Not in general. The shear rate actually looks like this:
$$
\dot{\gamma}_{ij} = \frac{\partial v_i}{\partial x_j} + \frac{\partial v_j}{\partial x_i}
$$

In here you can substitute x-y-z for i and j, so $\dot{\gamma}_{xy}$ has i = x, and j = y. And it is the stress on a plane at a right angle with the x-direction directed along the y-axis (or the other way around..., this always messes me up...). For a flow in a pipe, there is only a $dv/dr$ term ($r$ in radial direction) and there you can say that the gradient is equal to the shear stress (but there is a factor of two in there as well I believe... that's the other thing that always messes me up....)

So shear stress at the walls of the pipe, in turbulent flow isn't equal to the shear stress in laminar flow

The definition for both is exactly equal. The value usually is very different.

If for example i have the same fluid in 2 different pipes, in the first pipe it flows with small velocity and we have laminar flow, in the second pipe it has higher velocity and so turbulent flow. The shear stress at the wall is the same?

Not in value. But it already isn't the same if for both velocities the flow was laminar. But also not in friction factor.

A better comparison would be this:
compare the friction factor for a laminar flow and a turbulent flow in a pipe where the volume flow is equal
^*). In that case the friction (factor) is much higher for the turbulent case.

*) note that this is perfectly well possible. You can delay transition to turbulence by using very smooth pipes, making the flow into the pipe free of disturbances, use very pure water, minimize vibrations etc. etc. Normally transition occurs at a Reynolds number of about 2000, but it can be delayed up to about 40 000, according to wikipedia...

 

[lost captain]

Well, I'm not sure that is a very helpful way of looking at it. A laminar flow gets its name from the fact that the instantaneous flow direction is always parallel to the surface and thus the fluid flows in 'laminates' or layers. The only interaction between these layers is the viscosity.

Turbulent flow on the other hand has 'eddies'. These eddies are, roughly, swirling motions of the flow but then of all possible sizes and at the same time, in other words the flow is chaotic. The instantaneous flow direction is thus also chaotic in nature, potentially in all directions. Of course continuity is still to be adhered to so on average it is still parallel to the wall.

So to call the shear stress a sum of laminar and turbulent flow misses the mark for me. If there is turbulent flow, there is simply no laminar flow and thus the shear stress has nothing to do with that of laminar flow.

What the narrator may be confused with is how such a flow is often modeled on a computer. When you want to do computations it very, VERY expensive to compute the flow in all its detail including these eddies. So, the solution is to compute the mean flow and model the effect of turbulence on this mean flow. If you think about it, the turbulence has an effect of redistributing the momentum of the flow, much like viscosity does. So, a very simple way of modelling turbulence is by coming up with a 'turbulent viscosity' (often called 'eddy viscosity') based on mean flow parameters (e.g. the mean velocity gradients) that does the same thing as viscosity: redistribution of momentum.

So in this modeling sense you can call the shear stress at some location as a sum of shear stress caused by viscosity (or 'laminar shear stress', but please don't ever use this term...) and eddy viscosity (turbulent shear stress), since this is indeed how you would compute it. I however still think that also in this case it is very confusing to talk about 'laminar shear stress', it has nothing to do with laminar flow...

Some notes:
- Note that 'eddy viscosity' is a property of the flow, not of the fluid. It differs from location to location.
- Eddy viscosity is a model, not an actual physical quantity. But since this is a very common model, and since actual computations of fully fledged turbulent flow is very rare (even today), the model is often confused for reality, or at least the distinction is often sloppy.
- You can come up with an eddy viscosity ratio, which is the eddy viscosity divided by the fluid viscosity. Values of 1000 or more are very common here. In other words: turbulence is way more effective in redistributing momentum than viscosity is.
- The shear stress in actual flow is only caused by viscosity and nothing else. But in turbulent flow the instantaneous shear stress is in all directions because of the eddies in the flow. It is very costly to compute this shear stress distribution, so we revert to modelling the averages.



So, based on the previous discussion, let's replace this sentence with 'Closer to the pipe walls the viscosity dominates over the eddy viscosity', this is actually true, although 'closer' is not capturing what's really going on, see below.

Think now for a moment that turbulent flow just consists of eddies and simplify those as circular motions of fluid parcels. If you are in the middle of the pipe, the diameter of such a circular motion can be close to the pipe's diameter. But the closer you approach the wall, the smaller these circular motions need to be because there is a wall in the way. At some distance to the wall the motions become so small that they are damped again by viscosity. This is what happens in the viscous sublayer (not to be confused with a viscous boundary layer!). There, no eddies can exist and the flow is strictly laminar again.

To get a feel of the size of this viscous sublayer, consider a pipe of 2cm diameter (I guess about a typical pipe diameter going to your faucet) in which there is an average flow velocity of 2m/s. In this case the viscous sublayer is only about 25 microns (25e-6m) thick! So to say 'closer to the wall ...' doesn't really cut it...



Well, yes and no I guess. Yes in the sense as @Chestermiller already described: the wall shear stress is always equal to the velocity gradient (shear rate actually) times the viscosity.
But no in the sense that the shear rate of a turbulent boundary layer is always way higher. Also, the way to compute this shear rate is very different: you can compute the flow in the pipe in case of laminar flow exactly, but in case of turbulent flow it requires a model for the turbulence, or a heck of a lot of computational effort. If you are able to keep the flow in the pipe laminar, the pressure drop will be much less than for a turbulent flow with the same volume flow.

I've got to learn to write shorter answers.....

Please no, i really appreciate your answers, they are detailed and make physics easy, i was actually hoping to get a reply especially from you. Thank you
So

So to call the shear stress a sum of laminar and turbulent flow misses the mark for me. If there is turbulent flow, there is simply no laminar flow and thus the shear stress has nothing to do with that of laminar flow.

The fact that there is a very thin viscous sublayer that's moving with laminar flow, is this actually true or is this some type of model to help us with the computations in turbulent flow?
If it is true or even if it's just the way we describe the turbulent flow at the walls of the pipe, doesn't this viscous sublayer with laminar flow, change the way we think about shear stress and friction?
How is the shear stress between the turbulent fluid flow and the walls since between them exists this layer of laminar flow? And the same goes with friction.

According to @Chestermiller the wall shear stress is always equal to the velocity gradient times the viscosity no matter the type of flow. This made me think that the shear stress is actually between the wall and the laminar sublayer.
If that's not the case then the shear stress is between the viscous sublayer and the turbulent one, but again how come they both have the same formula?

-Wall Shear stress in laminar flow: between a stationary wall and a moving fluid in laminar flow
-Wall Shear stress in turbulent flow: between
(a) between a stationary wall and a moving fluid, viscous sublayer, laminar flow
OR
(b)between two moving fluids a viscous sublayer, laminar flow and a turbulent layer

And both of these 2 wall shear stress are calculated using the same formula

So thats why i thought the (a) case was probably what was going on.
How exactly is this shear stress applied between the walls and the turbulent layer when there's a laminar layer between them?

 

[lost captain]

As an aside: a fraction consists of a numerator and a denominator. A 'nominator' is not a thing ;).

The f (and thus also the $\tau_w$ ) is between the fluid and the pipe wall.

Yeah sorry about that, english isn't my first language, it's kinda obvious i guess

 

[Arjan82]

The fact that there is a very thin viscous sublayer that's moving with laminar flow, is this actually true or is this some type of model to help us with the computations in turbulent flow?

No, it is really there in reality. It exists because very close to the wall turbulence cannot exist. The fluid has no room to fluctuate at some point close to the wall. But note that this layer is tiny! For a 2m/s flow of water through a 20mm diameter pipe this viscous sublayer is only about 0.025mm thick!

If it is true or even if it's just the way we describe the turbulent flow at the walls of the pipe, doesn't this viscous sublayer with laminar flow, change the way we think about shear stress and friction?

No, why would it? Friction with the wall was, is and always will be equal to the viscosity times the shear rate at the wall. For both laminar and turbulent boundary layers.

How is the shear stress between the turbulent fluid flow and the walls since between them exists this layer of laminar flow? And the same goes with friction.

Note first that what we call 'friction' is the shear stress at the boundary of the flow with the wall...

The name 'turbulent boundary layer' is for the whole thing, this includes the viscous sublayer, the buffer layer and the log layer. You seem to insist that the friction of a turbulent boundary layer needs to be between a turbulent part and the wall. But turbulence can simply not exist very close to the wall. However, the viscous sublayer is itself heavily influenced by the turbulence a bit further out (its gradient and its thickness). So the viscous sublayer is as much a part of the turbulent boundary layer as the log layer is.

According to @Chestermiller the wall shear stress is always equal to the velocity gradient times the viscosity no matter the type of flow.

He said 'shear rate', not gradient. And I agree with him on that.

This made me think that the shear stress is actually between the wall and the laminar sublayer.

The shear stress is defined everywhere, this means both everywhere inside of the flow as well as at its boundaries with the wall of the pipe. But if you are talking about the friction 'in a pipe', you mean the shear stress at the boundary between the fluid and the pipe. And it is indeed the viscous sublayer that is in contact with the wall.

If that's not the case then the shear stress is between the viscous sublayer and the turbulent one, but again how come they both have the same formula?

Why would there be a different formula? Shear stress is only one thing, so you need only one formula.

-Wall Shear stress in laminar flow: between a stationary wall and a moving fluid in laminar flow
-Wall Shear stress in turbulent flow: between
(a) between a stationary wall and a moving fluid, viscous sublayer, laminar flow
OR
(b)between two moving fluids a viscous sublayer, laminar flow and a turbulent layer

And both of these 2 wall shear stress are calculated using the same formula

So thats why i thought the (a) case was probably what was going on.

It is (a) indeed.

How exactly is this shear stress applied between the walls and the turbulent layer when there's a laminar layer between them?

There is no connection between the wall and the turbulent part of the turbulent boundary layer, so you cannot define a shear stress between them.

 

[lost captain]

It's all clear to me now, THANK YOU
My confusion was coming from the fact that in laminar flow the thin layer that's not moving(no slip condition) on the walls of the pipe is being considered as part of the walls and not the flow. So i falsely assumed that the very very thin layer that's laminar flow, that is very close to the pipe, in turbulent flow is also considered as part of the pipe.

So just to be clear, when we talk about shear stress at the walls of a pipe in turbulent flow, that shear stress is applied at the viscous laminar sublayer. It's between the wall and the viscous sublayer.
And the same holds true for friction in the pipe walls, it is between the viscous laminar sublayer and the wall.
Of course this shear stress and the friction affect the whole flow, the whole turbulent boundary layer, but they do it through the viscous laminar layer.

And one last thing, the no slip condition applies also to turbulent flow? There is also a non moving layer at the walls of the pipe? I guess this layer is being considered as part of the wall, i mean it must be very very very thin, way thinner than it is in laminar flow.

The no slip, not moving layer doesn't belong to the laminar layer in laminar flow, right? So i guess it doesn't belong to the turbulent layer either, in turbulent flow.

 

[Arjan82]

It's all clear to me now, THANK YOU
My confusion was coming from the fact that in laminar flow the thin layer that's not moving(no slip condition) on the walls of the pipe is being considered as part of the walls and not the flow.

... no.... Please read my posts at your other topic again.

There is no separate layer in laminar flow that is stationary to the wall. The part of the flow that is stationary is a infinitesimally thin layer, i.e. a 2D surface without any thickness whatsoever at the wall (which is much MUCH thinner than even a viscous sublayer)

So i falsely assumed that the very very thin layer that's laminar flow, that is very close to the pipe, in turbulent flow is also considered as part of the pipe.

Very very thin as the laminar sublayer may be, it is way way bigger than the infinitesimally thin layer that is stationary at the wall. Because the infinitesimally thin layer has, by definition, no thickness at all.

You first say:

when we talk about shear stress at the walls of a pipe in turbulent flow, that shear stress is applied at the viscous laminar sublayer. It's between the wall and the viscous sublayer.

Then you say:

for friction in the pipe walls, it is between the viscous laminar sublayer and the wall.

I want to stress that these two remarks mean EXACLTY the same thing. Not almost, exactly! The shear stress at the wall IS the friction!

And one last thing, the no slip condition applies also to turbulent flow?

There is nothing special about turbulent flow. It has random motion on top of the mean flow, but otherwise it is also just normal flow. So of course the no-slip condition applies here as well!

There is also a non moving layer at the walls of the pipe?

That layer is infinitesimally thin, that means: it has no thickness at all, it is the boundary of the fluid domain, do not think about it as a separate layer, a layer has thickness, this no-slip condition has no thickness.

I guess this layer is being considered as part of the wall,

NO!!!

i mean it must be very very very thin, way thinner than it is in laminar flow.

It is infinitesimally thin, this means it has no thickness at all, none! No thickness whatsoever!

The no slip, not moving layer doesn't belong to the laminar layer in laminar flow, right? So i guess it doesn't belong to the turbulent layer either, in turbulent flow.

It is not a layer, it has no thickness...

Ok, I hope we've got that settled now... Please start dreaming about it, ask someone around you to wake you up in the middle of the night asking "what about the no-slip layer at the wall?" you just shout: "It is not a separate layer, it has no thickness! I shouldn't think about it that way! The no-slip condition is at the boundary of the flow!"

 

[lost captain]

NO!!!

We discussed about this in an other thread, about the no slip condition in laminar flow, and you agreed when i said the following: we think the non moving fluid as part of the wall.
I'm sorry, did i misunderstood you?

 

[lost captain]

It is not a layer, it has no thickness...

If it had no thickness then friction in laminar flow whould also depend on the pipe roughness, but it doesn't. The non moving fluid at the pipe wall is thick enough as a layer to make laminar flow independent from pipe roughness.

 

[lost captain]

Here did you agree with me that the friction at the pipe walls, in laminar flow is actually between the no slip stationary fluid and the moving one?

 

[Chestermiller]

Well, I'm not sure that is a very helpful way of looking at it. A laminar flow gets its name from the fact that the instantaneous flow direction is always parallel to the surface and thus the fluid flows in 'laminates' or layers. The only interaction between these layers is the viscosity.

Turbulent flow on the other hand has 'eddies'. These eddies are, roughly, swirling motions of the flow but then of all possible sizes and at the same time, in other words the flow is chaotic. The instantaneous flow direction is thus also chaotic in nature, potentially in all directions. Of course continuity is still to be adhered to so on average it is still parallel to the wall.

So to call the shear stress a sum of laminar and turbulent flow misses the mark for me. If there is turbulent flow, there is simply no laminar flow and thus the shear stress has nothing to do with that of laminar flow.

What the narrator may be confused with is how such a flow is often modeled on a computer. When you want to do computations it very, VERY expensive to compute the flow in all its detail including these eddies. So, the solution is to compute the mean flow and model the effect of turbulence on this mean flow. If you think about it, the turbulence has an effect of redistributing the momentum of the flow, much like viscosity does. So, a very simple way of modelling turbulence is by coming up with a 'turbulent viscosity' (often called 'eddy viscosity') based on mean flow parameters (e.g. the mean velocity gradients) that does the same thing as viscosity: redistribution of momentum.

So in this modeling sense you can call the shear stress at some location as a sum of shear stress caused by viscosity (or 'laminar shear stress', but please don't ever use this term...) and eddy viscosity (turbulent shear stress), since this is indeed how you would compute it. I however still think that also in this case it is very confusing to talk about 'laminar shear stress', it has nothing to do with laminar flow...

Some notes:
- Note that 'eddy viscosity' is a property of the flow, not of the fluid. It differs from location to location.
- Eddy viscosity is a model, not an actual physical quantity. But since this is a very common model, and since actual computations of fully fledged turbulent flow is very rare (even today), the model is often confused for reality, or at least the distinction is often sloppy.
- You can come up with an eddy viscosity ratio, which is the eddy viscosity divided by the fluid viscosity. Values of 1000 or more are very common here. In other words: turbulence is way more effective in redistributing momentum than viscosity is.
- The shear stress in actual flow is only caused by viscosity and nothing else. But in turbulent flow the instantaneous shear stress is in all directions because of the eddies in the flow. It is very costly to compute this shear stress distribution, so we revert to modelling the averages.



So, based on the previous discussion, let's replace this sentence with 'Closer to the pipe walls the viscosity dominates over the eddy viscosity', this is actually true, although 'closer' is not capturing what's really going on, see below.

Think now for a moment that turbulent flow just consists of eddies and simplify those as circular motions of fluid parcels. If you are in the middle of the pipe, the diameter of such a circular motion can be close to the pipe's diameter. But the closer you approach the wall, the smaller these circular motions need to be because there is a wall in the way. At some distance to the wall the motions become so small that they are damped again by viscosity. This is what happens in the viscous sublayer (not to be confused with a viscous boundary layer!). There, no eddies can exist and the flow is strictly laminar again.

To get a feel of the size of this viscous sublayer, consider a pipe of 2cm diameter (I guess about a typical pipe diameter going to your faucet) in which there is an average flow velocity of 2m/s. In this case the viscous sublayer is only about 25 microns (25e-6m) thick! So to say 'closer to the wall ...' doesn't really cut it...



Well, yes and no I guess. Yes in the sense as @Chestermiller already described: the wall shear stress is always equal to the velocity gradient (shear rate actually) times the viscosity.
But no in the sense that the shear rate of a turbulent boundary layer is always way higher. Also, the way to compute this shear rate is very different: you can compute the flow in the pipe in case of laminar flow exactly, but in case of turbulent flow it requires a model for the turbulence, or a heck of a lot of computational effort. If you are able to keep the flow in the pipe laminar, the pressure drop will be much less than for a turbulent flow with the same volume flow.

I've got to learn to write shorter answers.....

The turbulence in pipe flow is not mostly the effects of circular eddies. The key feature of turbulence in pipe flow (and most other turbulent flows) is a velocity field that fluctuates with time (all 3 velocity vector components), and all 9 components of the stress tensor being non-zero (not just the r-z shear stress).

In computational fluid dynamics, they often use so called $k-\epsilon$ theory (a two parameter. approach) to model turbulent flow.

 

[Arjan82]

This is what I'm referring to:

I find it a bit unhelpful, maybe even confusing, to make a distinction between
1) The fluid friction between the stagnant part of the fluid at the wall and the fluid right next to it
and
2) The friction between that same stagnant fluid and the wall.
This is because in fluid dynamics (and actually also in solid mechanics) you make the assumption of a continnuum for a fluid. This model makes this stagnant fluid layer infinitesimally thin. So you can not really identify it as a 'layer' and distinguish it from the rest. So for me they are kind of the same thing. For me there is just friction between the fluid and the wall, and from that point on there is only friction that is internal to the fluid which changes continuously through the fluid domain (if it changes, which it usually does).

 

[Arjan82]

The turbulence in pipe flow is not mostly the effects of circular eddies. The key feature of turbulence in pipe flow (and most other turbulent flows) is a velocity field that fluctuates with time (all 3 velocity vector components), and all 9 components of the stress tensor being non-zero (not just the r-z shear stress).

Of course it is... I'm trying to make a simplified picture to convey a message. The eddy 'analogy' is just a way to think about it, it is often depicted like this:

In computational fluid dynamics, they often use so called $k-\epsilon$ theory (a two parameter. approach) to model turbulent flow.

In the industry actually most often the $k-\omega$-SST model is used.

 

[lost captain]

This is what I'm referring to:

️This is because in fluid dynamics (and actually also in solid mechanics) you make the assumption of a continnuum for a fluid. This model makes this stagnant fluid layer infinitesimally thin. So you can not really identify it as a 'layer' and distinguish it from the rest.️

Because of the assumption of continuum we can't distinguish this very thin stagnant layer from the rest moving layer....okay.. but when we need to understand the friction and why it's independent of the pipe roughness in laminar flow, we need to distinguish them. When i am trying to think what is actually going on at the walls of the pipe, i need to make that distinction .

 

[Arjan82]

Because of the assumption of continuum we can't distinguish this very thin stagnant layer from the rest moving layer....okey.. but when we need to understand the friction and why it's independent of the pipe roughness in laminar flow, we need to distinguish them. When i am trying to think what is actually going on at the walls of the pipe, i need to make that distinction .

Then I cannot help you

 

[lost captain]

This is what I'm referring to:

️This is because in fluid dynamics (and actually also in solid mechanics) you make the assumption of a continnuum for a fluid. This model makes this stagnant fluid layer infinitesimally thin. So you can not really identify it as a 'layer' and distinguish it from the rest.️
Because of the assumption of continuum we can't distinguish this very thin stagnant layer from the rest moving layer....okey.. but when we need to understand the friction and why it's independent of the pipe roughness in laminar flow, we need to distinguish them. When i am trying to think what is actually going on at the walls of the pipe, i need to make that distinction

Then I cannot help you

I'm sorry if i offended you, and thank you for trying so hard to make me understand. I am trying to understand what's really happening at the pipe walls but maybe im not thinking in "a fluid dynamics way."

i was also searching on other sites to understand how am i supposed to think about friction at the walls of the pipe

 

[Arjan82]

I'm sorry if i offended you, and thank you for trying so hard to make me understand. I am trying to understand what's really happening at the pipe walls but maybe im not thinking in "a fluid dynamics way."

You are asking about details at pretty much the molecular scale, maybe a bit larger. I don't know what happens at that level. It is usually ignored by applying the continuum hypothesis, then you simply have no roughness and no stagnant layer of finite thickness. And, most importantly, it agrees very well with measurements.

View attachment 347077

I disagree with this. Laminar flow is not an idealization. Usually turbulent flow computations are an idealization, not laminar flow. If you have true laminar flow you can solve the Navier-Stokes equations exactly.

Also, I disagree with the statement 'Therefore, within this model, it makes no difference whether the surface is smooth or somewhat rough'. This is because also for cases where you do need to take roughness into account, you still apply the no-slip condition. This condition is not discriminatory for laminar flow, turbulent flow which is hydrodynamically smooth and turbulent flow with roughness. For all cases no-slip is applied (and actually present in real cases).

Lastly, he explains why a 'model' does not feel roughness, not why real laminar flow does not feel roughness...

For turbulent flow with roughness this is somewhat of an idealization. Because the surface with roughness is usually modeled as a smooth surface where extra turbulence is generated at the inner most layers (but still outside of the viscous sublayer) of the boundary layer.

 

[lost captain]

Ok just to make one thing clear

(That no slip stagnat part of the fluid is the end of the laminar boundary layer)
I just want to know where is this pipe friction applied

 

[Lnewqban]

These links may help understand interdependence of friction losses in piped fluids and pipe wall roughness (which is also material dependent):

https://en.m.wikipedia.org/wiki/Darcy_friction_factor_formulae

https://en.m.wikipedia.org/wiki/Moody_chart

Moving from the microscopic to the macroscopic point of view:
Turbulent flow costs energy and money.

In practical engineering terms, what is important is to estimate how much pumping is needed to make a liquid flow at certain rate, comparing that cost with the cost of pipe’s bigger diameters (which always reduce friction losses in pipes) or/and alternative materials.

Laminar flow is more economic to pump, but it is seldom achievable in industrial applications.
The P-51 Mustang fighter of WW2 was faster and reached farther because the flow over its wings was mainly laminar.

Please, see:
http://www.aviation-history.com/theory/lam-flow.htm

 

[Arjan82]

Ok just to make one thing clearView attachment 347081
(That no slip stagnat part of the fluid is the end of the laminar boundary layer)
I just want to know where is this pipe friction applied

In reality: neither, it is at the actual surface, so the rough line between (a) and (b).

In computations:
The part between (a) and (b) is not modeled in any usual fluid dynamical computation except the most highly advanced research based computations of people doing research on roughness itself. This is way to hard to do for any normal computation. So the distance between layer (a) and (b) is 0, the thickness of that layer is zero and thus (a) and (b) collapse.

 

[lost captain]

In reality: neither, it is at the actual surface, so the rough line between (a) and (b).

In computations:
The part between (a) and (b) is not modeled in any usual fluid dynamical computation except the most highly advanced research based computations of people doing research on roughness itself. This is way to hard to do for any normal computation. So the distance between layer (a) and (b) is 0, the thickness of that layer is zero and thus (a) and (b) collapse.

The thickness of the no slip" layer " is zero both for laminar and turbulent flow, right? At least for our basic computations

How do you interpret the fact that laminar flow isn't affected by pipe roughness? Considering that the no slip boundary has no thickness, can it play any role preventing the pipe roughness to influence the laminar flow?

Do you agree with this approach?

 

[Arjan82]

The thickness of the no slip" layer " is zero both for laminar and turbulent flow, right? At least for our basic computations

Yes, the no-slip condition (not a layer, never was, never will be) is a boundary condition to the flow, it applies to the boundary of a flow, laminar or turbulent. And not just for the basic computations, also for very advanced computations. Modelling roughness elements themselves is extremely rare and pretty much exclusively for research purposes. For engineering it is simply never done, and those engineering computations can become quite advanced, even without explicitly taking into account roughness elements.

How do you interpret the fact that laminar flow isn't affected by pipe roughness?

It has to do with disturbance propagation (or hydrodynamic stability). In laminar flow a small disturbance is damped and dies out, and thus it influence is only very locally (i.e. directly around the roughness element). In turbulent flow a small disturbance becomes larger and larger, it grows way beyond the original disturbance and thus has a more global effect.

What does roughness do? It increases friction with the wall, how? By increasing the shear rate at the wall. How does it do that? By stronger mixing of momentum (axial velocity) towards the wall, i.e. higher velocities are transported closer to the wall and thus the gradient/shear rate increases. This turbulent mixing increases because the disturbances caused by the roughness elements spread, cause chaotic flow and thereby cause much more transport of momentum closer to the wall.

Considering that the no slip boundary has no thickness, can it play any role preventing the pipe roughness to influence the laminar flow?

I don't know what you mean here. But for roughness to influence laminar flow it has to make the flow become hydrodynamically instable, this would then 'trip' the boundary layer towards turbulent flow. This indeed happens if the roughness elements get large enough.

View attachment 347087

What you underline here is what would need to be done to compute the influence of roughness elements explicitly. This is very VERY expensive (computationally and money wise) to do so it is never done in normal engineering.

View attachment 347088
Do you agree with this approach?

If by 'approach' you mean: use the Moody Diagram, yes, of course, by all means.

If by 'approach' you mean, model the full roughness explicitly, well, then you better be a billionaire...

 

[lost captain]

Ok just to make one thing clear

Yes, the no-slip condition (not a layer, never was, never will be) is a boundary condition to the flow, it applies to the boundary of a flow, laminar or turbulent.

Ok, is the no slip condition visible macroscopically, do i see this not moving fluid with my naked eye? Yes
If it has no thickness to be considered a layer how come i observe this so easily?

In reality: neither, it is at the actual surface, so the rough line between (a) and (b).

In computations:
The part between (a) and (b) is not modeled in any usual fluid dynamical computation except the most highly advanced research based computations of people doing research on roughness itself. This is way to hard to do for any normal computation. So the distance between layer (a) and (b) is 0, the thickness of that layer is zero and thus (a) and (b) collapse.

Is this correct? Also the layer (a) has velocity right?

 

[Arjan82]

Ok, I've tried... You clearly don't believe me. That's a 2sec demonstration with a bit of manual messing around with some die, if that convinces you more than the precision measurements and computations that are behind all the statements I made than I cannot help you...

About the second thing, I'm not going to repeat myself again.... We are going in circles over and over again.

I would recommend you to go to a university and read some good books about fluid dynamics and math.

 

[lost captain]

Ok, I've tried... You clearly don't believe me. That's a 2sec demonstration with a bit of manual messing around with some die, if that convinces you more than the precision measurements and computations that are behind all the statements I made than I cannot help you...

About the second thing, I'm not going to repeat myself again.... We are going in circles over and over again.

I would recommend you to go to a university and read some good books about fluid dynamics and math.

You said that
In reality: neither, it is at the actual surface, so the rough line between (a) and (b). And that in our computations a and b colapse since there is no layer. So that leaves us with the lowest slowest moving layer, which is layer (a). Thats why i said the friction is at (a). I concluded that based on the answers you gave me. I dont view this as going in circles either way, im sorry

 

[A.T.]

do i see this not moving fluid with my naked eye? Yes

Compare the position of the right tip of the dyed fluid between 0.09 and 0.18. It very slowly moves left. You need longer experiments than just a few seconds.

If it has no thickness to be considered a layer how come i observe this so easily?

"No thickness" applies to the mathematical continuum model. In reality you have particles and surface irregularities of finite size.

 

[lost captain]

Compare the position of the right tip of the dyed fluid between 0.09 and 0.18. It very slowly moves left. You need longer experiments than just a few seconds.


"No thickness" applies to the mathematical continuum model. In reality you have particles and surface irregularities of finite size.

Okay thank you very much. Could you also answer me this: is the friction at the walls of the pipe applied at the moving layer on top of the no slip condition?