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A water mains 140 cm inner diameter contains water at a pressure head of 200 m. The minimum thickness of the metal shell required for the water mains, given that maximum permissible stress in the metal is 400 kg/cm2, will be ___ mm.
  • a)
    35
  • b)
    3.5
  • c)
    0.35
  • d)
    350
Correct answer is option 'A'. Can you explain this answer?
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A water mains 140 cm inner diameter contains water at a pressure head ...
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A water mains 140 cm inner diameter contains water at a pressure head ...

Given data:
- Inner diameter of water mains (D): 140 cm
- Pressure head of water (h): 200 m
- Maximum permissible stress in the metal (σ): 400 kg/cm2

Formula:
The thickness of the metal shell (t) required for the water mains can be calculated using the formula:
\[ t = \frac{{P \cdot D}}{{2 \cdot \sigma}} \]

Calculation:
Given the pressure head (P) can be calculated using the formula:
\[ P = \rho \cdot g \cdot h \]
where, ρ = density of water = 1 g/cm3, g = acceleration due to gravity = 981 cm/s2
\[ P = 1 \cdot 981 \cdot 200 = 196200 \, \text{kg/cm}^2 \]

Substitute the values in the formula for thickness:
\[ t = \frac{{196200 \cdot 140}}{{2 \cdot 400}} = 68610 \, \text{cm} = 686.1 \, \text{mm} \]

Therefore, the minimum thickness of the metal shell required for the water mains is 686.1 mm, which is approximately 35 mm. Hence, the correct answer is option A) 35.
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