Some questions about Friction in fluid flow

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Friction in fluid flow

Main Question or Discussion Point

I have few conceptual doubts in fluid mechanics. Here is the one I will ask first.

I want to understand the force direction acting on the solid liq interface during fluid flow, Lets say a fluid is flowing in a pipe. Now the fluid applies a shear stress at the walls of pipe in the direction of flow, from newtons third law the wall will apply a backward force on the fluid which will be equal in magnitude to the shear stress times surface area. Is this reaction force applied by the wall is the same due to friction of surface of wall? I mean to say ,like when we push a solid block on a floor we have a friction force resisting the motion, In our fluid flow case , is the reaction force from wall same as the resistive force due to pipe wall friction, are they both same?
 

Answers and Replies

  • #2
anuttarasammyak
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They are same. Newton's 3rd law applies for fluid and the wall.
 
  • #3
jrmichler
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Simple answer is yes, friction against a surface is a force on the surface. And a force is a force.

Longer answer: Trying to make an analogy between fluid flow along a surface, and a block sliding on a surface, is not a good idea because the processes are different, which results in confusion. In both cases, there is a shear stress and an area. In both cases, the shear stress times the area is a force. In both cases, that force is applied to the surface.

In the fluid case, the shear stress is the result of a velocity gradient and viscosity. The fluid velocity at the surface is zero. The work to maintain the velocity gradient comes from a pressure difference in the direction of flow.

In the block case, the shear stress is the result of a force applied to the block. The block has a velocity relative to the surface on which it is sliding.

I suggest studying the first part of the Wikipedia article on viscosity. It's a good discussion and might help.
 
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  • #4
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... I want to understand the force direction acting on the solid liq interface during fluid flow, Lets say a fluid is flowing in a pipe... Is this reaction force applied by the wall is the same due to friction of surface of wall?...
The explanation about the Darcy–Weisbach equation could give you an idea of how complex the response to your excellent question can be.
Please, see:
https://en.m.wikipedia.org/wiki/Darcy–Weisbach_equation

:cool:
 
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  • #5
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The physical mechanism for viscous drag force on the fluid by the pipe wall is not the same as in dry friction. In the dry kinetic friction case, there is mechanical interference between the austerities in the wall surface and the the block surface. In the fluid flow case, the velocity of the fluid at the wall is zero. This is the so-called non-slip boundary condition. The zero velocity at the wall results in a velocity gradient that allows for momentum transfer between the fluid molecules at different distances from the wall, causing axial momentum to be transferred radially within the fluid. This is the mechanistic cause of the viscous wall drag.
 
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  • #6
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Thanks everyone for the response, I need one confirmation . As Sir Chet said the mechanism of mechanical friction and fluid friction are different , when we study pressure drop in a pipe flow. We have friction factor term , which depends on pipe characteristics .Both friction factor and wall shear stress are related .

Friction factor= (Wall shear stress)/( Kinetic Energy Density)

The wall shear stress determined from above relation is the reaction force of the wall on the fluid and the action force is the stress on the pipe wall by fluid . Am I right? Also both are actually same .

Here is the second problem I wanted to ask,
In a laminar flow in pipe, we have a parabolic velocity profile. If we have to determine stress at a plane lets say AB which is at a location r, we will differentiate the velocity profile to determine the velocity gradient,then we will put it in newton law of viscosity to determine stress at that point.
If we see the stress at above and below the plane , we see two stresses acting in opposite direction.
So is the stress obtained from Newton law via velocity gradient which was obtained from differentiation of velocity profile is equal to the net of the stress we have above and below the plane which in infinitesimal in thickness.
P_20200701_171607.jpg
 
  • #7
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Thanks everyone for the response, I need one confirmation . As Sir Chet said the mechanism of mechanical friction and fluid friction are different , when we study pressure drop in a pipe flow. We have friction factor term , which depends on pipe characteristics .Both friction factor and wall shear stress are related .

Friction factor= (Wall shear stress)/( Kinetic Energy Density)

The wall shear stress determined from above relation is the reaction force of the wall on the fluid and the action force is the stress on the pipe wall by fluid . Am I right? Also both are actually same .

Here is the second problem I wanted to ask,
In a laminar flow in pipe, we have a parabolic velocity profile. If we have to determine stress at a plane lets say AB which is at a location r, we will differentiate the velocity profile to determine the velocity gradient,then we will put it in newton law of viscosity to determine stress at that point.
If we see the stress at above and below the plane , we see two stresses acting in opposite direction.
So is the stress obtained from Newton law via velocity gradient which was obtained from differentiation of velocity profile is equal to the net of the stress we have above and below the plane which in infinitesimal in thickness.View attachment 265612
The shear stress components of the stress tensor are the same on both sides of the plane, and determined by Newton's law of viscosity. The traction vectors on the two sides of the plane constitute and action-reaction pair, and are equal in magnitude and opposite in direction. So, of course, the net force on the (massless) plane is zero.
 
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  • #8
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Thanks sir, things are much clearer now.
Here is another one.
In a double pipe, talking about flow in the annulus region we get stress profile something like this. What does the negative and positive in stress profile means?
P_20200701_202258.jpg
 
  • #9
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In the inner region, the fluid at ##r^-## is pulling backwards on the fluid at ##r^+##. In the outer region, the fluid at ##r^-## is pulling forwards on the fluid at ##r^+##.
 

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