The hoop stress in a thin-walled cylinder is given by pr/t, which is actually a _________.

The hoop stress in a thin-walled cylinder is given by pr/t, which is actually a measure of the stress experienced by the material in the circumferential or "hoop" direction. This formula is derived from the principles of mechanical engineering and materials science.

Here's a step-by-step breakdown:

1. The formula pr/t is used to calculate hoop stress. In this formula, 'p' represents the internal pressure within the cylinder, 'r' is the radius of the cylinder, and 't' is the thickness of the cylinder wall.

2. The hoop stress is a type of mechanical stress that occurs in a thin-walled cylinder. It's called "hoop stress" because it acts along the circumference of the cylinder, similar to the way a hoop or ring might be stressed if it were being stretched.

3. This stress is significant in engineering and materials science because it can affect the structural integrity of cylindrical objects under pressure, such as pipes, barrels, or the fuselage of an airplane.

4. Therefore, the formula pr/t is a measure of this hoop stress. By using this formula, engineers can ensure that their designs are safe and able to withstand the pressures they will be subjected to in use.