Question

A closed thin cylindrical tank with a mean diameter \( d = 300 \, {mm} \) and thickness \( t = 2 \, {mm} \), is subjected to a uniform internal gas pressure \( p \). The allowable shear stress on the curved wall of the tank is 70 MPa. Based on the Tresca criteria, which one of the following options for the maximum safe value of \( p \) (in MPa) is CORRECT?

• A. 3.73
• B. 7.46
• C. 1.87
• D. 5.60

Hint:

For thin-walled pressure vessels, the Tresca criterion relates the shear stress to the internal pressure and the geometry of the vessel. Always remember to convert units appropriately for consistency.

Answer 1

The Correct Option is C

We are given the following values:
- Mean diameter of the cylindrical tank, \( d = 300 \, {mm} = 0.3 \, {m} \)
- Thickness of the tank wall, \( t = 2 \, {mm} = 0.002 \, {m} \)
- Allowable shear stress, \( \tau = 70 \, {MPa} = 70 \times 10^6 \, {Pa} \)
To determine the maximum safe value of the internal gas pressure \( p \), we use the Tresca criterion for a thin-walled cylindrical pressure vessel, which is given by the equation: \[ \tau = \frac{p \cdot d}{4 t}. \] Rearranging the formula to solve for \( p \): \[ p = \frac{4 \tau t}{d}. \] Substituting the known values into the equation: \[ p = \frac{4 \times (70 \times 10^6) \times 0.002}{0.3} = \frac{560 \times 10^6}{0.3} = 1.87 \times 10^6 \, {Pa} = 1.87 \, {MPa}. \] Thus, the correct answer is \( p = 1.87 \, {MPa} \), so the correct option is (C).