Which formula is used to calculate longitudinal stress in a pressure vessel?

The formula used to calculate longitudinal stress in a pressure vessel is based on the internal pressure, the diameter of the vessel, and the thickness of the vessel wall. The correct formula expresses how longitudinal stress, which is the stress experienced along the length of a cylindrical vessel, is determined by the internal pressure and geometry of the vessel.

In the correct formula, the term ( p ) represents the internal pressure exerted on the walls of the vessel, ( d ) is the diameter of the vessel, and ( T ) is the wall thickness. The division by ( 2T ) indicates that the stress distribution is influenced by the thickness of the vessel wall, accounting for how the material resists this internal pressure.

This formula is derived from basic principles of mechanics and provides an essential understanding of how pressure vessels need to be designed to withstand the stresses they encounter during operation. It reflects that longitudinal stress is directly proportional to the pressure and diameter, and inversely proportional to the wall thickness, which is critical for the safety and integrity of the pressure vessel.

In contrast, the other options either misrepresent the relationship between these variables or do not reflect the correct derivation of stress in a cylindrical vessel, leading to incorrect interpretations for calculating the necessary structural