Discuss the difference between open ended and closed cylinder of a thin walled pressure vessel
The correct answer and explanation is:
Correct Answer:
The key difference between an open-ended and a closed-ended thin-walled pressure vessel lies in the presence of axial stress (also called longitudinal stress). An open-ended cylinder has no axial stress, while a closed-ended cylinder experiences both hoop and axial stresses due to internal pressure.
Explanation (300 Words):
Thin-walled pressure vessels are commonly used in engineering applications such as pipelines, gas tanks, and boilers. These vessels are called “thin-walled” when the wall thickness is small compared to the internal radius (typically, thickness t<110t < \frac{1}{10} of the radius rr).
Two common configurations of cylindrical thin-walled pressure vessels are open-ended and closed-ended:
1. Open-Ended Cylinders:
These cylinders are typically open at one or both ends and are often used in situations like pipelines, where fluid flows continuously. When pressurized internally, the main stress developed is the hoop stress (circumferential stress). This stress tries to burst the cylinder outward and is calculated by: σhoop=p⋅rt\sigma_{hoop} = \frac{p \cdot r}{t}
Where:
- pp = internal pressure
- rr = inner radius
- tt = wall thickness
There is no axial stress because the ends are open, and the internal pressure doesn’t act on end caps to induce a force in the axial direction.
2. Closed-Ended Cylinders:
These cylinders are sealed at both ends. In this case, the internal pressure acts not only on the cylinder wall (creating hoop stress) but also on the end caps. This introduces an axial stress along with the hoop stress:
- Hoop stress remains the same as for open-ended.
- Axial stress is given by:
σaxial=p⋅r2t\sigma_{axial} = \frac{p \cdot r}{2t}
The axial stress is typically half the magnitude of the hoop stress in a thin-walled vessel. The presence of this additional stress in closed-ended vessels makes their design more complex and critical compared to open-ended ones.
In summary, the main difference is the additional axial stress in closed-ended cylinders, which must be considered for safe and accurate structural design.