Hollow Shaft Torsion: Power Transmitted Calculation

[Solidsam]

Homework Statement

A turbine shaft is to transmit power at 240 rev/min. If the shaft is 1 m external diameter and 25 mm thick and the maximum shear stress is limited to 69 MPa, find the power transmitted.

Homework Equations

The Attempt at a Solution

T=J*stress/r = pi(1000^4-950^4) * 69/(32*100)

P=(2pi*240*T)/(60*10^6)





The answer should be 66GW whoch I am not getting. Can somebody please help?

 

[edgepflow]

Your formulas look basically OK. Check your units.

You mentioned the result should be 66 GW. Check if this should be 66 megawatts (MW).

 

[Filip Larsen]

Some quick comments:
- You seem use the diameter instead of radius.
- I don't understand how you can get 4th power when integrating torque.
- It is difficult to check your results when you divorce the scale units from the values. I recommend that you keep the scale and unit with the values so you for instance would write "(240 rev/min)(2.5 MNm)" instead of "(240*2.5)/(60*10^6)"
- For what it is worth I get a value slightly below 66 MW (as edgepflow also mentions), and almost no difference whether I use a properly integrated torque or just a "linearized" approximation.

 

[nvn]

Filip Larsen: Fourth power is correct. I agree with your fourth bullet. Well said.

Solidsam: Your value for radius r is incorrect. And 10^6 is incorrect. Try again.

 

[Filip Larsen]

Filip Larsen: Fourth power is correct.

Right, forgot that the stress is not constant along the radius and was also slow in recognizing the polar moment in the first equation used by the OP. My apologies.

 

[Solidsam]

Solidsam: Your value for radius r is incorrect. And 10^6 is incorrect. Try again.

So what should I do to get the correct answer?

r=500^4-475^4 ?

what should it be instead of 10^6 ?

 

[nvn]

Solidsam: No, your diameters in post 1 were correct, but your value for radius r in post 1 was wrong. See the suggestion in the third bullet of post 3. Try again.