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.samy4408 said: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?samy4408 said: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?
It’s not mass that’s flowing. It’s momentum transfer due to molecular collisions.jbriggs444 said: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".
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.Chestermiller said:It’s not mass that’s flowing. It’s momentum transfer due to molecular collisions.
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.jbriggs444 said: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.
jbriggs444 said: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".
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.jbriggs444 said: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.
Or indeed no flow at all.boneh3ad said:Viscosity is an intrinsic property of the fluid whether the flow is laminar or turbulent.
Yes. And then we have the borderline cases.vanhees71 said:Sure, in hydrostatics viscosity doesn't play any role.
so the final answer is that viscosity is the same for a given fluid at any velocity .boneh3ad said: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.
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 said:so the final answer is that viscosity is the same for a given fluid at any velocity .
jbriggs444 said:Yes. It is independent of shear rate.
??jbriggs444 said:The viscous force within a fluid will depend on the velocity gradient (aka shear rate) within the fluid.
I am trying to say that if we look at fluid in a pipe, viscosity will not depend on whether the fluid is flowing.samy4408 said:??
ok , thanks a lot !jbriggs444 said: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".
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).samy4408 said:??
The relationship between viscosity and velocity in fluid mechanics is known as the viscosity-velocity relationship. It states that the viscosity of a fluid is directly proportional to the velocity of the fluid. This means that as the velocity of the fluid increases, the viscosity also increases.
Viscosity affects the flow of a fluid by creating resistance to the movement of the fluid. The higher the viscosity, the more resistance there is to flow. This results in a slower flow rate and a thicker, more viscous fluid.
The viscosity-velocity relationship can be influenced by several factors such as temperature, pressure, and the type of fluid. Generally, an increase in temperature will decrease the viscosity of a fluid, while an increase in pressure will increase the viscosity. The type of fluid also plays a role, as different fluids have different viscosities at the same temperature and pressure.
The viscosity-velocity relationship is used in many real-world applications, including the design of pumps, turbines, and other fluid-based systems. It is also important in industries such as oil and gas, where the viscosity of crude oil can affect its flow through pipelines. Additionally, the relationship is used in the study of weather patterns and ocean currents.
Understanding the viscosity-velocity relationship is crucial in the field of fluid mechanics as it helps engineers and scientists predict and control the behavior of fluids in various applications. It also allows for the optimization of designs and processes, leading to more efficient and effective systems. Furthermore, understanding this relationship can provide insights into natural phenomena and aid in the development of new technologies.