In a pressure vessel, such as a cylindrical tank or a pipe designed to contain pressurized fluids or gases, the circumferential stress is generally greater than the longitudinal stress due to the geometry and mechanics of the vessel.
When a pressure vessel is pressurized, the internal pressure exerts forces on the walls of the vessel. These forces lead to stresses, which are distributed over the cross-section of the vessel's walls. The two primary stress components that occur are circumferential stress (also known as hoop stress) and longitudinal stress (also known as axial stress).
- Circumferential Stress (Hoop Stress): Circumferential stress is the stress that acts tangentially to the circumference of the pressure vessel. In a cylindrical pressure vessel, this stress is generated due to the tendency of the pressurized fluid or gas to expand outward in all directions. As a result, the circumferential stress is at its maximum at the inner surface of the vessel (closest to the pressurized contents) and gradually decreases toward the outer surface.
The formula for circumferential stress in a cylindrical pressure vessel is given by: σ_c = (P * r) / t Where: σ_c = Circumferential stress P = Internal pressure r = Internal radius of the vessel t = Wall thickness of the vessel
As you can see from the formula, the circumferential stress is directly proportional to the internal pressure and the internal radius of the vessel, and inversely proportional to the wall thickness.
- Longitudinal Stress (Axial Stress): Longitudinal stress is the stress that acts along the length (axis) of the pressure vessel. In a cylindrical pressure vessel, the longitudinal stress is generated because of the tendency of the pressurized fluid or gas to elongate or shorten the vessel along its length.
The formula for longitudinal stress in a cylindrical pressure vessel is given by: σ_l = (P * r) / (2 * t)
As you can see from the formula, the longitudinal stress is also directly proportional to the internal pressure and the internal radius of the vessel but is halved compared to the circumferential stress due to the denominator "2" in the equation.
Since the circumferential stress depends only on the wall thickness, it is typically greater than the longitudinal stress. As a result, in practical design considerations for pressure vessels, engineers pay more attention to the circumferential stress as it plays a critical role in determining the overall strength and structural integrity of the vessel.