Relationship between viscosity and velocity in fluid mechanics

[samy4408]

hello, I read in a lecture paper about fluid mechanics that velocity is not related to viscosity, i found this odd and i think it is an error , can someone confirm that?

 

[jbriggs444]

hello, I read in a lecture paper about fluid mechanics that velocity is not related to viscosity, i found this odd and i think it is an error , can someone confirm that?

The viscous force within a fluid will depend on the velocity gradient (aka shear rate) within the fluid. That does not mean that the viscosity is a function of velocity.

Viscosity is the ratio between the viscous force and the shear rate. As long as viscous force and shear rate have a linear relationship, viscosity will have a single fixed value.

As I understand it, the idea is that one is considering laminar flow. No turbulence. We imagine the fluid to be made up of a stack of thin layers, sliding across one another. For instance, a vertical stack of layers with one at rest on the bottom and one at the highest speed moving along the top.

Diffusion between layers means that mass is flowing (think of molecules if you must) both up and down through the stack. This moving mass carries momentum between the layers. Upward mass flow tends to exert a retarding force on the layer above since it must bring that new mass up to speed. Downward mass flow tends to exert a forward force on the layer below since it must slow that new mass down. In equilibrium, the upward and downward mass flows must be in balance.

This force between moving layers arrising from diffusion is the viscous force. If diffusion takes place at a fixed rate, this force will scale proportionately with the velocity gradient. The constant of proportion is what we call "viscosity".

 

[Arjan82]

hello, I read in a lecture paper about fluid mechanics that velocity is not related to viscosity, i found this odd and i think it is an error , can someone confirm that?

Can you explain why you think that is odd?

 

[Chestermiller]

The viscous force within a fluid will depend on the velocity gradient (aka shear rate) within the fluid. That does not mean that the viscosity is a function of velocity.

Viscosity is the ratio between the viscous force and the shear rate. As long as viscous force and shear rate have a linear relationship, viscosity will have a single fixed value.

As I understand it, the idea is that one is considering laminar flow. No turbulence. We imagine the fluid to be made up of a stack of thin layers, sliding across one another. For instance, a vertical stack of layers with one at rest on the bottom and one at the highest speed moving along the top.

Diffusion between layers means that mass is flowing (think of molecules if you must) both up and down through the stack. This moving mass carries momentum between the layers. Upward mass flow tends to exert a retarding force on the layer above since it must bring that new mass up to speed. Downward mass flow tends to exert a forward force on the layer below since it must slow that new mass down. In equilibrium, the upward and downward mass flows must be in balance.

This force between moving layers arrising from diffusion is the viscous force. If diffusion takes place at a fixed rate, this force will scale proportionately with the velocity gradient. The constant of proportion is what we call "viscosity".

It’s not mass that’s flowing. It’s momentum transfer due to molecular collisions.

 

[jbriggs444]

It’s not mass that’s flowing. It’s momentum transfer due to molecular collisions.

The net effect is momentum transfer, certainly. Whether one explains this by imagining molecules from one layer bouncing preferentially in one direction when colliding with molecules from the adjoining layer or by imagining molecules from each layer penetrating into the next and carrying their momentum with them does not matter. Either way momentum is transferred.

 

[boneh3ad]

As I understand it, the idea is that one is considering laminar flow. No turbulence. We imagine the fluid to be made up of a stack of thin layers, sliding across one another. For instance, a vertical stack of layers with one at rest on the bottom and one at the highest speed moving along the top.

Laminar versus turbulent flow has nothing to do with the original question here. Viscosity is an intrinsic property of the fluid whether the flow is laminar or turbulent.

Diffusion between layers means that mass is flowing (think of molecules if you must) both up and down through the stack. This moving mass carries momentum between the layers. Upward mass flow tends to exert a retarding force on the layer above since it must bring that new mass up to speed. Downward mass flow tends to exert a forward force on the layer below since it must slow that new mass down. In equilibrium, the upward and downward mass flows must be in balance.

This force between moving layers arrising from diffusion is the viscous force. If diffusion takes place at a fixed rate, this force will scale proportionately with the velocity gradient. The constant of proportion is what we call "viscosity".

The net effect is momentum transfer, certainly. Whether one explains this by imagining molecules from one layer bouncing preferentially in one direction when colliding with molecules from the adjoining layer or by imagining molecules from each layer penetrating into the next and carrying their momentum with them does not matter. Either way momentum is transferred.

Why is this an either-or thing? You also have to be careful in how you think about molecules moving vertically to transfer momentum because it can occur both diffusively and convectively. This is where the distinction between laminar and turbulent flows is important.

 

[anorlunda]

Viscosity is an intrinsic property of the fluid whether the flow is laminar or turbulent.

Or indeed no flow at all.

 

[vanhees71]

Sure, in hydrostatics viscosity doesn't play any role.

 

[anorlunda]

Sure, in hydrostatics viscosity doesn't play any role.

Yes. And then we have the borderline cases.

 

[vanhees71]

This is not statics, although for our human timescales it seems to be ;-).

 

[boneh3ad]

It turns out viscosity plays no role in hydrostatics, a huge role in very, very slow flows, and an increasingly small role as you get faster (or more precisely, as $Re$ increases).

 

[samy4408]

Laminar versus turbulent flow has nothing to do with the original question here. Viscosity is an intrinsic property of the fluid whether the flow is laminar or turbulent.

so the final answer is that viscosity is the same for a given fluid at any velocity .

 

[jbriggs444]

so the final answer is that viscosity is the same for a given fluid at any velocity .

Yes. It is independent of shear rate. It is also independent of the rate at which the fluid is moving past your chosen coordinate system.

 

[samy4408]

Yes. It is independent of shear rate.

The viscous force within a fluid will depend on the velocity gradient (aka shear rate) within the fluid.

??

 

[jbriggs444]

??

I am trying to say that if we look at fluid in a pipe, viscosity will not depend on whether the fluid is flowing.

Also, if we look at fluid in a river, viscosity will not depend on whether we measure fluid velocity relative to the shore, relative to a boat at rest on the river or relative to a speed boat roaring upstream.

It was not clear whether by "velocity" you meant "velocity gradient" (shear rate) or ordinary frame-relative "velocity".

 

[samy4408]

I am trying to say that if we look at fluid in a pipe, viscosity will not depend on whether the fluid is flowing.

Also, if we look at fluid in a river, viscosity will not depend on whether we measure fluid velocity relative to the shore, relative to a boat at rest on the river or relative to a speed boat roaring upstream.

It was not clear whether by "velocity" you meant "velocity gradient" (shear rate) or ordinary frame-relative "velocity".

ok , thanks a lot !

 

[Arjan82]

??

Please note that viscous force is not the same as viscosity. The viscous force will depend on the velocity gradient, but the viscosity is exactly what you can use to compute the viscous force given a velocity gradient. So, as @jbriggs444 already pointed out, viscosity is the ratio between the two (actually, the ratio between shearstress and strainrate is viscosity, to go to shear force you need an area of application).

Also note that we are talking about Newtonian fluids here, which are the most common types of fluids like water, air etc. But there are kinds of fluids that are, well, non-Newtonian. So either shear thickening (like cornstarch with water) or shear thinning (ketchup, paint, blood apparently...).

Also, viscosity can be a strong function of temperature, for example for oil (the higher the temperature, the lower the viscosity).