Question 12.2: A cylindrical tank holding oxygen at 2000 kPa pressure has a...
A cylindrical tank holding oxygen at 2000 kPa pressure has an outside diameter of 450 mm and a wall thickness of 10 mm. Compute the hoop stress and the longitudinal stress in the wall of the cylinder.
Objective Compute the hoop stress and the longitudinal stress in the wall of the cylinder.
Given p = 2000 kPa; D_{o} = 450 mm;t= 10 mm
Analysis We must first determine if the cylinder can be considered to be thin walled by computing the ratio of the mean diameter to the wall thickness.
D_{m} = D_{o} – t = 450 mm – 10 mm = 440 mm
D_{m} /t = 440 mm/10 mm = 44
Because this is far greater than the lower limit of 20, the cylinder is thin. Then Equation (12–20) should be used to compute the hoop stress and Equation (12-16) should be used to compute the longitudinal stress. The hoop stress is computed first.
\sigma = \frac{F_{R}}{A_{w}} = \frac{pD_{m}L}{2tL} = \frac{pD_{m}}{2t} (12-20)
\sigma = \frac{F_{R}}{A_{w}} = \frac{p( \pi D_{m}^{2}/4)}{ \pi D_{m} t} = \frac{pD_{m}}{4t} (12-16)
Results
\sigma = \frac{pD_{m}}{2t} = \frac{(2000 \times 10^{3} Pa)(440 mm)}{2(10 mm)} = 44.0 MPa
The longitudinal stress, from Equation (12–12), is recognized to be ½ of the hoop stress.
\sigma = \frac{pD_{m}}{4t} = 22.0 MPa