Q.

A liquid of volumetric thermal expansion coefficient  200×106/°C and bulk modulus = 1.2×109 Pa  is filled in a spherical tank of negligible heat expansion coefficient. Its radius is 25 cm and wall thickness is 2 mm. When the temperature of the liquid is raised by 20 °C, find the tensile stress developed (in MPa) in the wall of the tank?

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Detailed Solution

|dP|=β|dvV| 
Balancing force,   dPπR2=σ2πRtσ=dP2Rt=βγΔθR2t

Question Image                  
Where β  =bulk modulus
 γ  = coefficient of thermal expansion
 Δθ  = change in temperature
 R = radius of sphere
 t = thickness of sphere.

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