309 Finding the Diameter of a Propeller Shaft Transmitting a Power

$T = \dfrac{P}{2\pi f} = \dfrac{4.5(1\,000\,000)}{2\pi(3)}$

$T = 238\,732.41 \, \text{N}\cdot\text{m}$
 

Based on maximum allowable shearing stress:
$\tau_{max} = \dfrac{16T}{\pi d^3}$

$50 = \dfrac{16(238\,732.41)(1000)}{\pi d^3}$

$d = 289.71 \, \text{mm}$
 

Based on maximum allowable angle of twist:
$\theta = \dfrac{TL}{JG}$

$1^\circ \left( \dfrac{\pi}{180^\circ} \right) = \dfrac{238\,732.41(26d)(1000)}{\frac{1}{32}\pi d^4 (83\,000)}$

$d = 352.08 \, \text{mm}$
 

Use the larger diameter, thus, d = 352 mm.           answer