A natural gas (methane, CH4) storage facility uses 3-cm-diameter by 6-m-long vent tubes on its storage tanks to keep the pressure in these tanks at atmospheric value. If the diffusion coefficient for methane in air is 0.2 × 10?4 m2/s and the temperature of the tank and environment is 300 K, the rate at which natural gas is lost from a tank through one vent tube is
(a) 13?×?10?5 kg/day
(b) 3.2?×?10?5 kg/day
(c) 8.7?×?10?5 kg/day
(d) 5.3?×?10?5 kg/day
(e) 0.12?×?10?5 kg/day
(a) 13?×?10?5 kg/day
d=0.03 [m]
L=6 [m]
D_AB=0.2E-4 [m^2/s]
P=101 [kPa]
T=300 [K]
M=16 [kg/kmol]
A=pi*d^2/4
Ndot=(D_AB*A/(R#*T))*(P/L)
Mdot=Ndot*M*Convert(day, s)
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