Force of a propellor in fluid

[tommy060289]

Homework Statement

Dear physics forum users, I have a bit of a question about using a propellor to provide resistance. I am looking at designs for fall arrest devices and one idea I've looked at is using a propellor connected to a reel so that when the reel is unwound the propellor spins and is resisted by the fluid. The only thing is I'm not really sure on how to go about calculating the force exerted on the propellors. I know that we have a reel that is is spinning at roughly 60 RPM and the reel is connected to directly to the propeller so will spin at the same speed. However. what I need to do is work out how big my paddles on the propeller would need to be to provide a force equal to 981 N. Would it be best to use the force to work out the torque on the connecting shaft, and then work out the torque of the propeller? I am not really sure how to work out the second bit. let's assume the propellor has three paddles facing perpendicular to the fluid to give maximum surface area. How much force would each paddle exert on the fluid, if we had a fairly viscous fluid such as a motor oil with 0.3 Pa.s

Homework Equations

Not really sure what to use, obviously we have the basics of:

F=m.a
T=f.d

The Attempt at a Solution

Havn't got this far yet...

 

[KataKoniK]

Thank you for your question regarding using a propellor to provide resistance in a fall arrest device. This is an interesting idea and I would be happy to help you calculate the necessary force exerted on the propellor.

To start, we can use the equation F=m.a to calculate the force needed to provide a resistance of 981 N. Since we know the mass of the object that needs to be arrested, we can rearrange the equation to solve for acceleration (a). This will give us an idea of how quickly the object will need to decelerate in order to stop safely.

Once we have the acceleration, we can use the equation T=f.d to calculate the torque on the connecting shaft. This torque will need to be equal to the torque of the propellor in order to provide the necessary force. To calculate the torque of the propellor, we can use the equation T=r x F, where r is the radius of the propellor and F is the force exerted by each paddle.

To determine the force exerted by each paddle, we can use the equation F=μA(v1-v2), where μ is the viscosity of the fluid, A is the surface area of the paddle, and (v1-v2) is the velocity difference between the fluid and the paddle. Since you mentioned a fairly viscous fluid, we can use the given viscosity of 0.3 Pa.s to calculate the force.

Finally, we can divide the total force needed by the number of paddles on the propellor to determine the force exerted by each paddle. From there, we can calculate the necessary size of the paddles to provide this force.

I hope this helps you in your calculations. Please let me know if you have any further questions. Good luck with your design!