Question

A cylindrical vessel is said to be thin if the ratio of its internal diameter to the wall thickness is

• A. Less than 20
• B. Equal to 20
• C. More than 20
• D. Equal to 25

Hint:

Remember:
- Thin Cylinder $\to$ $\frac{d}{t} > 20$ (Stress assumed uniform)
- Thick Cylinder $\to$ $\frac{d}{t} \leq 20$ (Stress varies parabolically across wall)

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
This question asks for the geometric criterion used to classify cylindrical pressure vessels as "thin-walled" or "thick-walled" in strength of materials.

Step 2: Key Formula or Approach:
The standard classification depends on the ratio of the wall thickness ($t$) to the internal diameter ($d$).
A vessel is classified as thin-walled if:
\[ \frac{t}{d} \leq \frac{1}{20} \quad \text{or} \quad \frac{d}{t} \geq 20 \]

Step 3: Detailed Explanation:

• In pressure vessel analysis, we assume stress distributions are uniform across the wall thickness if the wall is thin.

• For thin-walled cylinders, the radial stress is neglected, and only hoop stress ($\sigma_h = \frac{Pd}{2t}$) and longitudinal stress ($\sigma_l = \frac{Pd}{4t}$) are analyzed.

• If the thickness $t$ is small compared to the diameter $d$, typically $t < \frac{d}{20}$ (which is equivalent to $\frac{d}{t} > 20$), the variation of stresses across the thickness is negligible.

• If $\frac{d}{t} < 20$, the vessel is considered thick-walled, and Lame's equations must be used because the radial stress variation becomes highly significant.

Step 4: Final Answer:
A cylindrical vessel is thin if the ratio of its internal diameter to wall thickness is more than 20.