Question

A hollow shaft of 1 m length is designed to transmit a power of 30 kW at 700 rpm. The maximum permissible angle of twist in the shaft is $1^0$. The inner diameter of the shaft is 0.7 times the outer diameter. The modulus of rigidity is 80 GPa. The outside diameter (in mm) of the shaft is

• A. 44.5212

Answer 1

The correct option is A 44.5212
Given data: P = 30 kW, N = 700 rpm

$\frac{2\pi NT}{60}=30\times {10}^3=P$

or T = 409.25 Nm

$\theta =\frac{TL}{GJ}\left(\theta inradian\right)\therefore \frac{1\times \pi }{180}=\frac{409.25\times {10}^3\times {10}^3\times 32}{\pi \times \left(d_0{)}^4\right(1-{0.7}^4)\times 80\times {10}^3}$

or $d_0=44.5212mm$