Question

The drilling pipe on an oil rig is made from steel pipe which having thickness of 5-mm and an outside diameter of 90-mm. Calculate the maximum shear stress occur in the pipe if the pipe is turning at 650 rev/min while being powered using 12kW motor.

Answer 1

`\tau_(max)= 3.28 \ MPa`

Step-by-step explanation:

outside diameter = 90 mm

inside diameter = 90- 2× t= 90- 2× 5 = 80mm

where t is thickness of pipe.

power (P) = 12 kW

Revolution (N)= 650 rev/min

we

Power = torque × angular velocity

P= T× ω

ω =
`(2 \pi N)/(60)`

`P=T * (2\pi N)/(60)\\12 * 10^3=T* (2\pi * 650)/(60)`

T= 176.3 Nm

for maximum shear stress

`(\tau_(max))/(y_(max))=(T)/(I_p)`

where ymax is maximum distance from neutral axis.

`y_(max)=(d_0)/(2)= (90)/(2)`= 45 mm

`I_p`= polar moment area

=
`(\pi)/(32) (d_o^4-d_i^4)=(\pi)/(32) (90^4-80^4)`

= 2,420,008 mm⁴

`(\tau_(max))/(45)=(176.3 * 10^3)/(2,420,008)`

`\tau_(max)= 3.28 \ MPa`