Understanding Viscosity: Solving a Fluid Mechanics Problem

[Chestermiller]

Yes I understand the mathematical concept torque= from but when I find force it is 0 so how is this physically possible?

Suppose you have two parallel forces acting on a rigid body. The forces are equal in magnitude, but opposite in direction. What is the net force acting on the body?

Even through the two parallel forces are equal in magnitude and opposite in direction, they do not have the same line of action. If the magnitudes of each of the two forces is F and the perpendicular distance between their lines of action is d, what is the net torque on the body?

 

[fayan77]

A couple system?

 

[Chestermiller]

A couple system?

Yes. Please answer my questions.

 

[fayan77]

Net force is 0 and net torque is Fd

 

[Chestermiller]

Net force is 0 and net torque is Fd

Correct. Now, in our problem, for each differential element of area on the disk, there is a corresponding differential area element located 180 degrees away in which the force per unit area is parallel and opposite in direction. Do you see that?

 

[fayan77]

Yes, so instead of integrating df (force) I should integrate dam (moment).

 

[Chestermiller]

Yes, so instead of integrating df (force) I should integrate dam (moment).

Well, you already showed by integrating that the net force is equal to zero. Of course, we expected that from the symmetry of the system.

To get the moment, integrating is required.

 

[fayan77]

Oh ok! now I don't care about direction since all the vectors are all tangential so we just integrate radius so I can can pull out 2pi out of integral?

 

[Chestermiller]

Oh ok! now I don't care about direction since all the vectors are all tangential so we just integrate radius so I can can pull out 2pi out of integral?

Yes. You just integrate the equation in post 49, pulling out the 2pi.

 

[fayan77]

Thank you so much! I can honestly say I fully understand this problem!