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## Homework Statement

__Question__

Assuming the torque and maximum shear stress values to be the same for both shafts, determine the size of a suitable soild shaft which could be used instead of the hollow shaft.

__Information/Data Known__

Firstly, a previous question - A ship's propellar shaft transmits 7.5MW at 440rev/min. The shaft has an external diameter of 230mm. Calculate the maximum permissable bore diameter if the shearing stress in the shaft is limeted to 150MN/m^2. The modulus of rigidity for the shaft material is 79GN/m^2

Ok, the following is known:

Bore Diameter = 108mm = 0.108m

DH = Hollow shaft External Diameter = 0.23m

touH = touS

TH=TS

## Homework Equations

T/J = tou/r = Gθ/l

We're using T/J = tou/r

J=pi(D^4-d^4)/32 [Hollow Shaft]

J=pi(D^4)/32 [Soid Shaft]

## The Attempt at a Solution

Ok so to show understanding, the question says that the torque and stress values are the same for both shafts therefore:

touH = touS

TH=TS

Which means we need to find JS, rS, JH and rH

JS/rS = JH/rH

We can find our H values but not our solid so:

JH = pi(DH^4 - dH^4)/32

DH = 0.23m

dH = 0.108m

JH = 2.6138x10^-4m^4

rH = D/2 = 0.115m

JS = pi/32 [because we can only assume DS atm is equal to 1]

JS = 0.0982m^4

rS = D/2 = 0.5Dm

Back to the equation: JS/rS = JH/rH

Muliply over:

JH(rS)/JS(rH)

Which looks like so:

(2.6138x10^4)x0.5 / 0.0982 x 0.115 = d^3 = 11.5727x10^-3

to get the diamter, we cube route the answer:

(cube root)11.5727x10^-3 = D

D = 0.226m

Therefore the diameter of the solid shaft use to replace the hollow shaft is: 226mm

What i'm asking for here is clarification that what i've just done here is correct. I've been told by my collegues that i may have gotten the bore diamter wrong, someone said they got 198mm instead of 108mm.

So from the second question i have typed out p above, could you find the time to check if i have the correct or incorrect bore diamter and the second request is simply to read the above (my workings out) to see if it looks / is valid.

Thankyou for your time, i really do appreciate your help even if it's a simple word.