Drag torque of rotating cylinder

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Discussion Overview

The discussion revolves around calculating the drag torque acting on a rotating cylinder, specifically under conditions of dynamic equilibrium with known applied forces, angular acceleration, and instantaneous velocity. Participants explore the application of drag force equations and the implications of different geometrical models, such as a cylinder versus a flat plate.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant seeks to find the drag torque using the drag force equation, expressing uncertainty about how to incorporate the moment arm into their calculations.
  • Another participant points out that the drag force described does not cause rotation about the cylinder's axis and suggests calculating the shear force acting on the cylinder's surface instead.
  • A participant questions whether the same considerations apply if the system is modeled as a flat plate rotating on its end, indicating a potential misunderstanding of the original setup.
  • Clarification is sought regarding the axis of rotation, with one participant confirming that the cylinder rotates about its perpendicular axis.
  • One participant proposes a method involving the calculation of forces on differential elements along the cylinder's length, indicating they have developed a solution based on integration.
  • A later reply expresses gratitude for the assistance received, indicating that the proposed solution makes sense to them.
  • Another participant mentions that torque and power calculations for impellers due to drag forces are typically proportional to the fifth power of the impeller diameter, referencing external literature.

Areas of Agreement / Disagreement

Participants express differing views on how to approach the calculation of drag torque, with no consensus reached on the best method or model to use. The discussion remains unresolved regarding the implications of different geometrical shapes on the drag torque calculations.

Contextual Notes

Participants have not fully resolved the assumptions regarding the boundary layer effects or the specific conditions under which the drag force operates. The discussion also highlights the need for clarity on the axis of rotation and the implications of modeling choices.

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

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