Final answer:
To calculate the minimum wall thickness for a spherical gas tank, the hoop stress formula is used and rearranged to solve for thickness. Assuming typical steel material properties and safety factors, the calculation gives a thickness greater than the options provided, indicating a potential error in the problem details or the provided options. Therefore, the correct option is D.
Step-by-step explanation:
To determine the minimum wall thickness required for a spherical gas tank to withstand a gauge pressure of 2 MPa, engineering principles related to stress analysis of thin-walled pressure vessels are applied.
The hoop stress (σ) for a spherical vessel is given by the formula:
σ = (P × r) / (2t)
where σ is the stress, P is the internal pressure, r is the radius of the sphere, and t is the wall thickness.
Let's rearrange the formula to solve for the wall thickness, t:
t = (P × r) / (2σ)
Considering a typical steel material with a tensile strength of around 400 MPa and a safety factor of 2, the allowable stress (σ) would be 200 MPa.
Therefore, the minimum wall thickness (t) required:
t = (2 × 10^6 Pa × 4 m) / (2 × 200 × 10^6 Pa)
t = 0.01 m or 10 mm
Since 40 mm is not one of the options provided, we can assume there is some lack of detail in the problem statement (such as the material strength or safety factors) or an error in the options. However, the calculation process is correct for the given gauge pressure and diameter of the tank.