Question 12.1: Compute the stress in the wall of a sphere having an inside ...
Compute the stress in the wall of a sphere having an inside diameter of 300 mm and a wall thickness of 1.50 mm when carrying nitrogen gas at 3500 kPa internal pressure.
Objective Compute the stress in the wall of the sphere.
Given p = 3500 KPa: D_{i} = 300 mm; t= 1.50 mm
Analysis We must first determine if the sphere can be considered to be thin walled by computing the ratio of the mean diameter to the wall thickness.
D_{m} = D_{i} + t = 300 mm + 1.50 mm = 301.5 mm
D_{m} /t = 301.5 mm/1.50 mm = 201
Because this is far greater than the lower limit of 20, the sphere is thin. Then Equation (12–12) should be used to compute the stress.
\sigma = \frac{p( \pi D_{m}^{2} /4)}{ \pi D_{m}t} = \frac{pD_{m}}{4t}
Results
\sigma = \frac{pD_{m}}{4t} = \frac{(3500 \times 10^{3} Pa)(301.5 mm)}{4(1.50 mm)}
\sigma = 175.9 \times 10^{6} Pa = 175.9 MPa