Question

Which of the following correctly describes the relationship between the circumferential stress ($\sigma$), package diameter ($d$), wall's thickness ($L$) and the internal pressure ($P$) of a glass packaging material/bottle?

• A. $\sigma = \frac{2L}{P \times d}$
• B. $P = \frac{2\sigma}{L \times d}$
• C. $\sigma = \frac{P \times d}{2L}$
• D. $P = \frac{L \times d}{2\sigma}$

Hint:

Hoop stress: $\sigma = \frac{P \times d}{2L}$.
Used for thin-walled pressure vessels.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The relationship between stress, pressure, diameter, and wall thickness is given by a standard formula.
This is based on thin-walled pressure vessel theory.

Step 2: Key Formula or Approach:
Circumferential stress (hoop stress) = $\frac{P \times d}{2L}$.

Step 3: Detailed Explanation:
For a thin-walled cylinder, the hoop stress is:
$\sigma = \frac{P \times d}{2L}$
Where:
- $\sigma$ = circumferential stress
- P = internal pressure
- d = diameter
- L = wall thickness
Other options have incorrect arrangements.
Thus, the correct formula is $\sigma = \frac{P \times d}{2L}$.

Step 4: Final Answer:
The correct relationship is $\sigma = \frac{P \times d}{2L}$.
Hence, the correct option is (C).