Hydrodynamic drag of a rotating paddle wheel

In summary: I think you would get the same answer as if you used the equation for total moment.In summary, the problem involves rotating a paddle wheel submerged in water. The drag equation can be used to calculate the torque needed to rotate the wheel.
  • #1
erlend
4
0
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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  • #2
:welcome:
This sounds like homework. Is it?
 
  • #3
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 :)
 
  • #4
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:
  • #5
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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Likes Chestermiller
  • #6
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.
 
  • #7
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.
 
  • #8
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.
 

1. What is hydrodynamic drag?

Hydrodynamic drag is a force that resists the motion of an object through a fluid, such as air or water. It is caused by the friction between the object and the fluid it is moving through.

2. How does the rotation of a paddle wheel affect hydrodynamic drag?

The rotation of a paddle wheel can increase or decrease the hydrodynamic drag depending on the direction and speed of rotation. When the paddle wheel is rotating in the same direction as the fluid flow, it can reduce drag by creating a smoother flow. However, when rotating in the opposite direction, it can increase drag by creating turbulence.

3. What factors affect the hydrodynamic drag of a rotating paddle wheel?

The main factors that affect the hydrodynamic drag of a rotating paddle wheel are the speed of rotation, the shape and size of the paddle blades, and the viscosity of the fluid. Other factors such as the angle of the paddle blades and the density of the fluid can also have an impact.

4. How can the hydrodynamic drag of a rotating paddle wheel be reduced?

To reduce the hydrodynamic drag of a rotating paddle wheel, the speed of rotation can be adjusted to match the fluid flow, the shape and size of the paddle blades can be optimized for smooth flow, and the viscosity of the fluid can be decreased. Additionally, using a streamlined design and reducing the angle of the paddle blades can also help reduce drag.

5. What are some real-world applications of studying the hydrodynamic drag of rotating paddle wheels?

Studying the hydrodynamic drag of rotating paddle wheels can have various applications, such as in the design of efficient propellers for boats and ships, wind turbines for renewable energy, and cooling systems for industrial processes. It can also be useful in understanding the movement of aquatic animals and developing more efficient swimming techniques for athletes.

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