Answer to Question #151939 in Mechanical Engineering for Banda

Question

A propeller shaft has external and internal diameter 25cm and 15cm, what power can be transmitted at 110 revs/minute with a maximum shearing stress of 75 MN/m^3 and what will be twist in degrees on a 10 meter length of the shaft?.

Answer 1

The polar second moment of area or the torsion constant of the cross- section about an axis through the centre

$J=\frac{\pi}{2}(r_2^4-r_1^4)=\frac{3.14}{2}(0.125^4-0.075^4)=0.334\cdot10^{-3}(m^4)$

$\tau=75(MN/m^3)$

$T=\frac{J\tau}{r_2}=\frac{0.334\cdot10^{-3}\cdot 75\cdot10^{6}}{0.125}=200400(N)$

The power generated is

$P=T\cdot\omega=200400\cdot(2\cdot3.14\cdot\frac{110}{60})=2.31\cdot10^6(W)$

The angle of twist is

$\theta=\frac{TL}{GJ}=\frac{200400\cdot10}{80\cdot10^9\cdot0.334\cdot10^{-3}}=0.075(rad)=4.3°$