Stresses Due to Internal Pressure in Pipes and Vessels
Liquids and gases exert pressure on the walls of a pipe or vessel. This pressure acts equally in all directions and is primarily influenced by the fluid's weight and gravitational force. The fluid molecules continuously move in random directions, creating an internal pressure within the pipe or vessel.
When a pipe or pressure vessel is subjected to internal pressure, stresses are developed in its walls. These stresses are important considerations during the design of piping systems and pressure vessels.
The two most important stresses caused by internal pressure are:
- Circumferential Stress (Hoop Stress)
- Longitudinal Stress (Axial Stress)
1. Circumferential Stress (Hoop Stress)
Circumferential stress acts around the circumference of the pipe or vessel. This stress tends to split the pipe longitudinally and is therefore considered the most critical stress in thin-walled pressure vessels.
The formula for circumferential stress is:
σc = (P × D) / (2 × t)
Where:
- σc = Circumferential Stress
- P = Internal Pressure
- D = Internal Diameter of Pipe/Vessel
- t = Wall Thickness
Since hoop stress has the highest magnitude, it plays a major role in determining the required wall thickness of pipes and pressure vessels.
2. Longitudinal Stress
Longitudinal stress acts along the length of the pipe or vessel. It is generated due to the force acting on the end caps or closed ends of a pressure vessel.
The formula for longitudinal stress is:
σL = (P × D) / (4 × t)
Where:
- σL = Longitudinal Stress
- P = Internal Pressure
- D = Internal Diameter
- t = Wall Thickness
Comparing both equations, it can be seen that longitudinal stress is only half of the circumferential stress:
σL = 0.5 × Ïƒh
Therefore, in many piping applications, longitudinal stress due to internal pressure is relatively small compared to hoop stress and may sometimes be neglected. However, in pressure vessel design, both circumferential and longitudinal stresses must be carefully evaluated to ensure safe operation.
Conclusion
Internal pressure creates two primary stresses in pipes and pressure vessels: circumferential stress and longitudinal stress. Among these, circumferential stress is the governing stress because it is twice the magnitude of longitudinal stress. Understanding these stresses is essential for the safe and efficient design of piping systems and pressure vessels.