Hydrodynamic drag of a rotating paddle wheel

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Discussion Overview

The discussion revolves around the hydrodynamic drag experienced by a rotating paddle wheel submerged in water. Participants explore the forces exerted on the wheel and the torque required for its rotation, considering the application of the drag equation in a rotational context. The conversation includes elements of calculus and engineering estimates.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related
  • Debate/contested

Main Points Raised

  • One participant expresses difficulty in calculating the drag force and torque on a rotating paddle wheel, noting the complexity due to varying speeds at different radial locations.
  • Another participant questions whether the original inquiry is a homework problem, indicating a concern about the nature of the request.
  • A participant clarifies that the problem is not homework but rather a practical engineering question aimed at reducing drag on a rotating object.
  • One participant proposes using the average speed at the midpoint of the paddle wheel to estimate drag and torque, providing a calculation based on this assumption.
  • Another participant suggests setting up a differential drag equation and integrating to find the total moment, indicating a potential approach to the problem.
  • A participant acknowledges the calculus aspect of the problem and considers replacing variables in the drag equation to set up a differential equation for torque calculation.
  • Another participant reiterates the suggestion to calculate the force on a differential length and integrate to determine the total moment, implying a straightforward approach to the problem.

Areas of Agreement / Disagreement

Participants express varying approaches to the problem, with some suggesting integration methods while others focus on average speed calculations. There is no consensus on a single method or solution, and the discussion remains open-ended.

Contextual Notes

Participants have not resolved the mathematical steps involved in applying the drag equation to a rotating paddle wheel, and assumptions regarding speed and force distribution remain unclarified.

erlend
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Hello, i have a problem that look's easy to solve but really is not.

It involves a rotating paddle wheel submerged in water and i want to know the force exerted on the wheels and the torque required to rotate it. I have made a simple drawing to illustrate the problem below. I want to use the Drag equation to solve it, even though it is for linear motion, we can convert rotational motion to linear. But since the diameter changes the speed at any radial location and the force is based on a square function i can't get an exact solution for the problem.
1581264977590.png


Can you help me with this problem?
 
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:welcome:
This sounds like homework. Is it?
 
Hi anorlunda.

Actually this is not a homework problem.

I want to reduce the drag of something that is rotating in water and want to know the exact solution to it, i already have a rough estimate that would suffice for basic engineering. Just curious i quess :)
 
My current solution:
I assume the average speed to be in the middle of the paddle wheel. That point is located at Ø135 or r=0.0675M

v= r x RPM x rad/s
v =0.0675m x 1500rpm x 0.10472 = 10.6 meter / second

Drag equation using the speed:
1581269703732.png

So the combined torque for both sides of the paddle wheel would be:
Nm= 60 Newton * 0,0675M = 4.1 Nm
 
Last edited:
Why not set up the differential drag on a differential[ length and then integrate? But isn't the thing you want actually the total moment?
 
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Hi Dr.D.

Yes i think you are correct that this is a calculus problem. If i replace v with r x RPM x rad/s in the drag equation, i could maybe setup an differential equation? The total moment is what I am after, i need to know the torque for selecting an electric motor.
 
erlend said:
Hi Dr.D.

Yes i think you are correct that this is a calculus problem. If i replace v with r x RPM x rad/s in the drag equation, i could maybe setup an differential equation? The total moment is what I am after, i need to know the torque for selecting an electric motor.
Let's see your attempt to do this.
 
Its not hard. Just look at the force on a differential length, calculate the moment of that force, and then integrate to get the total moment.
 

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