Shearing Force Direction in Fluid Mechanics

[goldfish9776]

Homework Statement

why the shearing force acting on the object in the first diagram is in different direction , while in the second photo , it's in same direction ?

Homework Equations

The Attempt at a Solution

in my opinion , it should be in different direction , because the shearing force must be applied in 2 different direction , so that the object will be 'teared' . Which is correct?

 

[Chestermiller]

Of the four shear force vectors shown in your figures, when specific ones do you think are drawn correctly (if any), which specific ones do you think are drawn incorrectly (if any), and why.

 

[goldfish9776]

Of the four shear force vectors shown in your figures, when specific ones do you think are drawn correctly (if any), which specific ones do you think are drawn incorrectly (if any), and why.

i think the first one is correct , because the shearing force must be applied in 2 different direction , so that the object will be 'teared' . i think the second 1 is incorrect

 

[haruspex]

i think the first one is correct , because the shearing force must be applied in 2 different direction , so that the object will be 'teared' . i think the second 1 is incorrect

Yes, shear force requires opposing forces, but in the second diagram there are four forces, and one of them goes the other way. Both diagrams are correct.

 

[Chestermiller]

I agree with haruspex. The directions of all 4 shear forces are drawn correctly in the diagrams.

In the first diagram, you are doing a shell (control volume) force balance on the fluid within the cylindrical shell between r and r + Δr. The fluid at radii greater than r + Δr is traveling more slowly than the fluid within the shell, so it is dragging the fluid in the control volume backwards (to the left). The fluid at radii less than r is traveling more rapidly than the fluid within the shell, so it is dragging the fluid in the control volume forwards (to the right).

In the second diagram, the arrow at the bottom and the arrow at the top actually represent the exact same shear force exerted by the wall on fluid filling the tube (or channel). Since the wall is stationary and the fluid is moving to the right, the wall exerts a drag force on the fluid to the left.

Chet