To calculate the circumferential stress (also known as hoop stress) in a thin cylindrical pressure vessel, you can use the following formula:

$\sigma_c = \frac{p \cdot d}{2 \cdot t}$

Where:

• $\sigma_c$ is the circumferential (hoop) stress.
• $p$ is the internal pressure.
• $d$ is the internal diameter of the cylinder.
• $t$ is the wall thickness of the cylinder.

Given:

• Internal pressure, $p = 2 \, \text{N/mm}^2$
• Internal diameter, $d = 1000 \, \text{mm}$
• Wall thickness, $t = 12 \, \text{mm}$

Now, substitute the given values into the formula:

$\sigma_c = \frac{2 \, \text{N/mm}^2 \times 1000 \, \text{mm}}{2 \times 12 \, \text{mm}}$

$\sigma_c = \frac{2000}{24} \, \text{N/mm}^2$

$\sigma_c = 83.33 \, \text{N/mm}^2$

So, the circumferential stress developed in the cylinder is 83.33 N/mm².

Would you like more details or have any other questions?

Here are five related questions you might find useful:

1. How do you calculate the longitudinal stress in a thin-walled pressure vessel?
2. What is the difference between circumferential and longitudinal stress?
3. How would the circumferential stress change if the thickness were doubled?
4. What are the safety factors typically applied in the design of pressure vessels?
5. How does internal pressure affect the overall structural integrity of a pressure vessel?

Tip: Always ensure that units are consistent when performing calculations to avoid errors.