Thin-Walled Pressure Vessels Examples

Problem: A cylindrical steel water tank has an internal diameter of $4.00 \text{ m}$ and a wall thickness of $12.0 \text{ mm}$. If the tank is pressurized to $1.50 \text{ MPa}$, determine the tangential and longitudinal stresses.

Problem: A spherical gas tank is designed to hold gas at a pressure of $3.00 \text{ MPa}$. The tank will have an inner diameter of $3.00 \text{ m}$. If the allowable tensile stress of the material is $120 \text{ MPa}$ and the joint efficiency is $80.0\%$, determine the required wall thickness.

Problem: A cylindrical tank with a diameter of $1.50 \text{ m}$ is subjected to an internal pressure of $2.00 \text{ MPa}$. The material has an allowable stress of $140 \text{ MPa}$. The longitudinal joint efficiency is $75.0\%$ ($\eta_l$) and the circumferential joint efficiency is $85.0\%$ ($\eta_c$). Determine the required wall thickness.

Problem: A seamless steel pipe has an internal diameter of $500 \text{ mm}$ and a wall thickness of $15.0 \text{ mm}$. If the allowable tensile stress is $160 \text{ MPa}$, what is the maximum internal pressure it can safely carry?

Problem: A closed cylindrical tank is $2.00 \text{ m}$ in diameter and has walls $10.0 \text{ mm}$ thick. If the internal pressure is $1.20 \text{ MPa}$, calculate the total longitudinal force acting on the end caps.

Problem: A pipe has an inner radius of $100 \text{ mm}$ and an outer radius of $120 \text{ mm}$. It is subjected to an internal pressure of $10.0 \text{ MPa}$. Calculate the maximum tangential stress using both the thin-walled assumption and Lame's thick-walled equation. What is the percentage error of the thin-walled approximation?

Problem: A thick-walled steel pipe has an inner radius of $200 \text{ mm}$ and an outer radius of $300 \text{ mm}$. It is subjected to an internal fluid pressure of $40.0 \text{ MPa}$ and zero external pressure. Determine the maximum tangential (hoop) stress and the maximum radial stress in the pipe wall.

Problem: A thin-walled cylindrical vessel has a hoop stress of $150 \text{ MPa}$ and a longitudinal stress of $75.0 \text{ MPa}$. The material has a yield strength of $250 \text{ MPa}$. Calculate the factor of safety according to both the Maximum Shear Stress Theory (Tresca) and the Distortion Energy Theory (Von Mises).

Problem: Explain why a hot dog boiled in water usually splits lengthwise rather than splitting crosswise, using principles of thin-walled pressure vessels.

Problem: In the 19th century, catastrophic boiler explosions on steamboats were common. Often, these failures initiated at longitudinal riveted joints. Why were longitudinal seams much more critical than circumferential seams?

Problem: A cannon barrel experiences extreme transient internal pressures during firing. If designed using simple elastic thick-walled theory, the barrel would be unmanageably heavy. How does autofrettage solve this problem?

Problem: Deep-sea submersibles like Alvin or the Titan operate under immense external hydrostatic pressure. What is the fundamental difference in the structural behavior and failure modes of vessels subjected to external pressure compared to internal pressure?