Answer to Question #151939 in Mechanical Engineering for Banda

Question #151939
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?.
1
Expert's answer
2020-12-22T05:07:20-0500

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\u00b0"






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