Drag torque of rotating cylinder

[FishJaws]

Hey folks,

New to the forum and eager to tap the resources of all your brilliant minds.

Here's the problem. I'm modeling a system as a cylinder rotating on its end. Under a dynamic equilibrium situation with an applied force of a known value, I know its angular acceleration and instantaneous velocity.

How would one find the drag torque acting on the cylinder? I know the drag coefficient, area, and angular velocity of course, but need to apply it all to this drag force equation, Fd=-(1/2)*Cd*A*p*v^2,

where Cd is the drag coefficient, p the density of the medium (water in this case), and v the linear velocity.

Do you'll have a differential and derivative you can pull out of the air, something that accounts for the moment arm?

Many thanks!

 

[RandomGuy88]

Hey folks,

New to the forum and eager to tap the resources of all your brilliant minds.

Here's the problem. I'm modeling a system as a cylinder rotating on its end. Under a dynamic equilibrium situation with an applied force of a known value, I know its angular acceleration and instantaneous velocity.

How would one find the drag torque acting on the cylinder? I know the drag coefficient, area, and angular velocity of course, but need to apply it all to this drag force equation, Fd=-(1/2)*Cd*A*p*v^2,

where Cd is the drag coefficient, p the density of the medium (water in this case), and v the linear velocity.

Do you'll have a differential and derivative you can pull out of the air, something that accounts for the moment arm?

Many thanks!

The equation you have written for drag is the drag parallel to the flow. That drag force will not cause the cylinder to rotate about its axis nor will it oppose that motion. To determine that force you would need to calculate the shear force acting on the surface of cylinder. So you would need information about the boundary layer around the circumference.

 

[FishJaws]

Thanks, Random. Would the same be the case if I modeled the system as a flat plate rotating on end?

I was sure that I could integrate area along the moment arm based on my original equation using the appropriate Cd for the shape. Bummer.

Thanks again.

 

[RandomGuy88]

Thanks, Random. Would the same be the case if I modeled the system as a flat plate rotating on end?

I was sure that I could integrate area along the moment arm based on my original equation using the appropriate Cd for the shape. Bummer.

Thanks again.

Let me first make sure I am understanding you. Do you mean the cylinder will be rotating about its cylindrical axis? Because that what I was referring to in my first post. What exactly do you mean rotating on end?

 

[FishJaws]

Thanks again, Random.

The cylinder is rotating on it's perpendicular axis. See this: http://hyperphysics.phy-astr.gsu.edu/hbase/icyl.html#icyl4. (description of I of a cylinder under the same conditions).

It'll be like a swinging bat or pipe.

Thanks for the help.

 

[RandomGuy88]

Ok, so you disregard my previous comments.

I have an idea of how to solve this hopefully it is correct. Basically I calculated the force on a differential element of length dr and then integrated over the length of the cylinder. I have attached my solution. Hopefully it makes sense.

 

[FishJaws]

Random, you're a life life saver. This does indeed make sense. Lots of thanks for the help!

 

[GT1]

Usually when calculating impeller power/torque due to drag forces, the torque/power is proportional to the fifth power of the impeller diameter.
see thishttp://books.google.com/books?id=s4...al mixing&hl=iw&pg=PA360#v=onepage&q&f=false" for example