A liquid of volumetric thermal expansion coefficient = γ and bulk modulus B is filled in a spherical tank of negligible heat expansion coefficient. Its radius is R and wall thickness is ‘t’ (t <R). When the temperature of the liquid is raised by θ, the tensile stress developed in the walls of the tank is :

Engineering

Physics

Thermal Expansion

Stress Strain and Hookes Law New

Question

A liquid of volumetric thermal expansion coefficient = γ and bulk modulus B is filled in a spherical tank of negligible heat expansion coefficient. Its radius is R and wall thickness is ‘t’ (t <R). When the temperature of the liquid is raised by θ, the tensile stress developed in the walls of the tank is :

2BγθR/t

BγθR/4t

BγθR/2t

BγθR/t

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ΔV = VθY , $\frac{ΔV}{V}$ = Yθ
Stress = $(\frac{ΔV}{V}) B$
ΔP = YθB
$\frac{F}{{πR}^{2}}$ = YqB
F = YθB (πR²)

tensile stress = $\frac{F}{2 πRt}$ = $\frac{YθB}{2 π Rt}$
Tensile stress = $(\frac{YθBR}{2 t})$