B How Does Viscosity and Turbulence Affect Fluid Flow Between Plates?

[Sbee]

TL;DR Summary

Why does internal friction cause the fluid to move in direction of applied force? In this derivation, a plate is placed on a fluid and then a force is applied to the plate, causing the plate to move at a certain velocity. If there is a friction force between the plate and the fluid pointing in the opposite direction, why would the fluid move in the same direction as the plate? What is the force that causes the fluid and the plate to stick together, if the friction is pulling the fluid backwards?

https://openstax.org/books/university-physics-volume-1/pages/14-7-viscosity-and-turbulence
I am trying to understand the derivation from Figure 14.36 which starts with " The fluid to be measured is placed between two parallel plates. The bottom plate is held fixed, while the top plate is moved to the right, dragging fluid with it. " Why does it drag the fluid with it if there is a force of friction?

 

[Dale]

It is a basic assumption of fluid mechanics that the fluid immediately adjacent to a solid body (the boundary layer) has the same velocity as the solid body. The "friction" is the force applied to the boundary layer of the fluid that keeps the boundary layer "attached" to the solid body. Basically, the boundary layer is considered to have negligible mass, so it is easy for even the slightest friction to hold it in place.

 

[Sbee]

It is a basic assumption of fluid mechanics that the fluid immediately adjacent to a solid body (the boundary layer) has the same velocity as the solid body. The "friction" is the force applied to the boundary layer of the fluid that keeps the boundary layer "attached" to the solid body. Basically, the boundary layer is considered to have negligible mass, so it is easy for even the slightest friction to hold it in place.

Thank you. Okay so maybe I'm not understanding friction correctly. The friction force that is allowing the fluid underneath the boundary layer to slide with the boundary layer, is that static friction? I'm sorry if that's dumb I am teaching myself physics.

 

[Dale]

Yes, it is static friction. Remember that static friction acts to prevent slipping, or in other words to prevent relative motion between the object and the boundary layer. So the fact that the boundary layer moves with the object is essentially a given, and then the force is whatever is required for that to happen. Since the boundary layer has negligible mass, $F=ma$ is not useful here, and instead the force is usually determined by the interaction of the boundary layer with the bulk fluid, i.e. viscosity.

 

[Sbee]

Since the boundary layer has negligible mass, $F=ma$ is not useful here, and instead the force is usually determined by the interaction of the boundary layer with the bulk fluid, i.e. viscosity.

So the negligible mass is important because the force of static friction = uFn, and Fn = mass of boundary layer * g. So because there is small amount of mass, there is a small normal force and a small amount of static friction keeping it from slipping, Is that right?

 

[Dale]

So the negligible mass is important because the force of static friction = uFn, and Fn = mass of boundary layer * g. So because there is small amount of mass, there is a small normal force and a small amount of static friction keeping it from slipping, Is that right?

Almost. The normal force is the pressure, which can be large. The reason that it is important is that with $F=ma$ if $m$ is very small then $a$ can be very large even if $F$ is very small. So we don’t need to worry if there is enough friction force to keep the boundary layer in place.

 

[Chestermiller]

It really shouldn't be thought of in terms of static friction. No matter how high the shear stress at the upper plate is, the fluid at the surface still travels with the speed of the plate. This is called the "no slip" boundary condition. Also, after a short while, the velocity of the plate has affected the fluid velocities over the entire gap between the plates, such that it varies linearly from zero at the lower plate to the upper plate velocity at the upper plate. So, very soon, there is typically no boundary layer adjacent to the upper plate. The velocity profile encompasses the entire gap.

The real question, Mr. OP, is what do you think the mechanism is for frictional momentum transfer between the fluid layers?