Question

A spherical balloon with an outer diameter of 500 mm and thickness 0.3 mm is filled with a gas. Cal- culate maximum permissible pressure in the balloon if the allowable normal strain at the outer surface of the balloon is 0.1. Assume E 5 4 MPa and n 5 0.45.

Answer 1

The maximum permissible pressure is 0.0024 MPa.

Step-by-step explanation:

To calculate the maximum permissible pressure in the balloon, we need to consider the normal strain at the outer surface of the balloon. The normal strain is given by the change in diameter divided by the original diameter. In this case, the change in diameter is the thickness of the balloon, which is 0.3 mm, and the original diameter is 500 mm. So, the normal strain is 0.3 mm / 500 mm = 0.0006.

The maximum permissible normal strain is given as 0.1. Using Hooke's law, which relates stress to strain, we can calculate the maximum permissible stress. The stress is equal to the product of Young's modulus (E) and the strain.

The maximum permissible stress = E * normal strain = 4 MPa * 0.0006 = 0.0024 MPa. This is the maximum permissible pressure in the balloon.