Thin Cylinders Problem 3

TL;DR

A comprehensive explanation of how to calculate the internal pressure and hoop stress in a thin cylinder filled with an incompressible fluid.

Transcript

let us take the third question on thin cylinders let's read what is given here a cylindrical shell of 900 mm long 200 mm internal diameter and 8 mm thickness is filled with an incompressible fluid at atmospheric pressure if additional 20 centimeter cube fluid is pumped into the cylinder comma find pressure exerted by the fluid on the cylinder the f... Read More

Key Insights

• 🤭 The problem involves calculating the internal pressure and hoop stress in a thin cylinder filled with an incompressible fluid.
• ❓ Volumetric strain is used to determine the internal pressure, and an empirical formula relates the two.
• 🤭 The formula for hoop stress is different and only requires the internal pressure, diameter, and thickness of the cylinder.
• 🥳 Assumptions are made for the values of Young's modulus and Poisson's ratio in the calculations.

Questions & Answers

Q: How do you calculate the volumetric strain in a thin cylinder filled with an incompressible fluid?

The volumetric strain can be found by dividing the change in volume (additional volume pumped in) by the original volume of the cylinder. In this case, it is 20 cm³ divided by the original volume calculated using the diameter and length of the cylinder.

Q: What is the empirical formula to relate volumetric strain and internal pressure in a thin cylinder?

The empirical formula is volumetric strain = (P * d) / (4 * t * E * (5 - 4μ)), where P is the internal pressure, d is the diameter, t is the thickness, E is the Young's modulus, and μ is Poisson's ratio.

Q: How do you calculate the internal pressure in a thin cylinder using the empirical formula?

Plug in the values for volumetric strain, diameter, thickness, Young's modulus, and Poisson's ratio into the formula. Calculate the internal pressure by rearranging the formula accordingly.

Q: What is the formula to calculate hoop stress in a thin cylinder?

The formula for hoop stress is hoop stress = (P * d) / (2 * t), where P is the internal pressure, d is the diameter, and t is the thickness.

Summary & Key Takeaways

• The problem involves a cylindrical shell filled with an incompressible fluid and an additional volume of the fluid being pumped in.

• The first question is to calculate the internal pressure exerted by the fluid on the cylinder.

• The second question is to determine the hoop stress induced in the cylinder.