A cast iron main tube 800 mm in diameter carries water at pressure head of 100 m. If the maximum permissible tensile stress is 20 MN/m² and the weight of water is 10 kN/m³, the required thickness of the metal will be
- A5 mm
- B10 mm
- C15 mm
- D20 mmCorrect
Solution
Concept
Hoop stress in a thin cylinder
Formula
t = p D / (2 σ)
Step-by-step solution
1. p = γ h = 10 × 100 = 1000 kN/m² = 1 MN/m². 2. t = p D / 2σ = 1 × 0.8 / (2 × 20) = 0.02 m = 20 mm.
Explanation
The hoop stress governs the wall thickness of a pipe under internal pressure.
Why the other options are wrong
5, 10 and 15 mm give hoop stresses of 80, 40 and 26.7 MN/m², more than the permissible 20.
Shortcut
t = pD/2σ.
Common mistake
Using the radius or forgetting the factor 2.
Correct answer: D) 20 mm