Question

A spherical pressure vessel has an outer diameter of 3.8 m and a wall thickness of 12 mm. For the steel used, σall = 80 MPa, E = 200 GPa, and ν = 0.29.

Determine the allowable gage pressure. (Round the final answer to three decimal places.)

Answer 1

The allowable gage pressure for the spherical steel pressure vessel is calculated using the hoop stress formula for thin-walled pressure vessels, considering the given dimensions and mechanical properties of the steel.

Step-by-step explanation:

The question asks for the calculation of the allowable gage pressure for a spherical pressure vessel made of steel with given dimensions and material properties. To solve for the allowable gage pressure, we use the formula derived from the thin-wall pressure vessel theory, which is suitable for vessels where the wall thickness is small compared to the diameter, and thus, this approximation is reasonable in this case.

The hoop stress (σ) for a thin-walled spherical pressure vessel under internal pressure (P) is given by σ = P × r / (2 × t), where 'r' is the internal radius of the vessel and 't' is the wall thickness. The allowable gage pressure can thus be calculated by rearranging the formula: P = (2 × σall × t) / r.

Given that the outer diameter is 3.8 m, the inner diameter 'd' is 3.8 m - 2*0.012 m, hence the internal radius is 'r' = d / 2. Now, substituting σall = 80 MPa, 't' = 12 mm, and 'r' into the formula will yield the allowable gage pressure.