A spherical vessel with thin walls has a diameter D = 4 m, and is used...

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A spherical vessel with thin walls has a diameter D₁ = 4 m, and is used to store liquefied natural gas (LNG), so its temperature under normal operating conditions is, Ti = 112 K. A larger thin-walled spherical container of diameter D. = 4.2 m surrounds the LNG vessel, and both are concentric about a common centre, so that the intervening cavity is uniform in thickness, and filled with atmospheric helium (k = 0.1151 W/m K). The air surrounding the outer sphere is normally at T = 300 K. What is the mass rate in kg/s at which gaseous methane vents from the system? Use 5.1 x 10³ J/kg as methane's latent heat of vaporization, and for air you may use p = 1.7458 kg/m³, cp = 1007 J/kg⋅K, μµ = 132.5 x 10-7 kg/s¹m, k = 0.0181 W/mK, a = 1.03 x 10-7 m²/s, and Pr = 0.737. You can estimate the natural-convection heat-transfer coefficient for the sphere from Nup = 2 + 1/4 0.589 Rap Pr≥ 0.7 [1+ (0.469/Pr) 9/164/9Rap ≤ 1011 Rayleigh number for the relevant characteristic length x is Rax= 8B(T-T)x³ να For a sphere, thermal resistance Re, cand = R 47k (15 marks) A spherical vessel with thin walls has a diameter D₁ = 4 m, and is used to store liquefied natural gas (LNG), so its temperature under normal operating conditions is, Ti = 112 K. A larger thin-walled spherical container of diameter D. = 4.2 m surrounds the LNG vessel, and both are concentric about a common centre, so that the intervening cavity is uniform in thickness, and filled with atmospheric helium (k = 0.1151 W/m K). The air surrounding the outer sphere is normally at T = 300 K. What is the mass rate in kg/s at which gaseous methane vents from the system? Use 5.1 x 10³ J/kg as methane's latent heat of vaporization, and for air you may use p = 1.7458 kg/m³, cp = 1007 J/kg⋅K, μµ = 132.5 x 10-7 kg/s¹m, k = 0.0181 W/mK, a = 1.03 x 10-7 m²/s, and Pr = 0.737. You can estimate the natural-convection heat-transfer coefficient for the sphere from Nup = 2 + 1/4 0.589 Rap Pr≥ 0.7 [1+ (0.469/Pr) 9/164/9Rap ≤ 1011 Rayleigh number for the relevant characteristic length x is Rax= 8B(T-T)x³ να For a sphere, thermal resistance Re, cand = R 47k (15 marks)

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Diameter of inner LNG sphere D1 4 m Diameter of outer helium sphere D2 42 m Temperature of LNG Ti 11... View the full answer