# Drag torque of rotating cylinder

1. Jun 28, 2010

### 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!

2. Jun 29, 2010

### RandomGuy88

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.

3. Jun 29, 2010

### 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.

4. Jun 29, 2010

### RandomGuy88

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?

5. Jun 29, 2010

### 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.

6. Jun 29, 2010

### 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.

Last edited: Jul 19, 2011
7. Jun 30, 2010

### FishJaws

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

8. Jul 2, 2010

### GT1

Last edited by a moderator: Apr 25, 2017