Savchenko Problem 4.1.7
Physics · mechanics · fluid-mechanics
Problem
A spherical balloon of radius R with walls of thickness ∆ is ruptured by internal pressure P. Determine the tensile strength of the wall material. 130Intuitive explanation
The key is recognizing that the internal pressure creates a stress in the balloon's thin spherical shell. Imagine the balloon cut in half—the pressure pushes outward on the curved surface, and the material must pull itself together across any imaginary plane to hold it. By balancing the outward force from pressure against the inward tension distributed through the thin wall thickness, you can find the stress (force per unit area) the material must withstand before rupturing.
Intuitive explanation
The key is recognizing that the internal pressure creates a stress in the balloon's thin spherical shell. Imagine the balloon cut in half—the pressure pushes outward on the curved surface, and the material must pull itself together across any imaginary plane to hold it. By balancing the outward force from pressure against the inward tension distributed through the thin wall thickness, you can find the stress (force per unit area) the material must withstand before rupturing.