Respuesta :
The question is incomplete. The complete question is :
The hydrofoil boat has an A-36 steel propeller shaft that is 100 ft long. It is connected to an in-line diesel engine that delivers a maximum power of 2590 hp and causes the shaft to rotate at 1700 rpm . If the outer diameter of the shaft is 8 in. and the wall thickness is [tex]$\frac{3}{8}$[/tex] in.
A) Determine the maximum shear stress developed in the shaft.
[tex]$\tau_{max}$[/tex] = ?
B) Also, what is the "wind up," or angle of twist in the shaft at full power?
[tex]$ \phi $[/tex] = ?
Solution :
Given :
Angular speed, ω = 1700 rpm
[tex]$ = 1700 \frac{\text{rev}}{\text{min}}\left(\frac{2 \pi \text{ rad}}{\text{rev}}\right) \frac{1 \text{ min}}{60 \ \text{s}}$[/tex]
[tex]$= 56.67 \pi \text{ rad/s}$[/tex]
Power [tex]$= 2590 \text{ hp} \left( \frac{550 \text{ ft. lb/s}}{1 \text{ hp}}\right)$[/tex]
= 1424500 ft. lb/s
Torque, [tex]$T = \frac{P}{\omega}$[/tex]
[tex]$=\frac{1424500}{56.67 \pi}$[/tex]
= 8001.27 lb.ft
A). Therefore, maximum shear stress is given by :
Applying the torsion formula
[tex]$\tau_{max} = \frac{T_c}{J}$[/tex]
[tex]$=\frac{8001.27 \times 12 \times 4}{\frac{\pi}{2}\left(4^2 - 3.625^4 \right)}$[/tex]
= 2.93 ksi
B). Angle of twist :
[tex]$\phi = \frac{TL}{JG}$[/tex]
[tex]$=\frac{8001.27 \times 12 \times 100 \times 12}{\frac{\pi}{2}\left(4^4 - 3.625^4\right) \times 11 \times 10^3}$[/tex]
= 0.08002 rad
= 4.58°
