In order to test an automotive$-$exhaust$-$emission$-$control device, we want to make a gaseous mixture of $5\mathrm{.}0ppm($vol$)($i$.$e$.,$ parts per million on a volumetric or molar basis$)$ of a hydrocarbon in air. The mixture is made by allowing the hydrocarbon to diffuse out of a small tube into a stream of air. The hydrocarbon liquid level is heldconstant in the tube by a suitable reservoir. For an air flow rate of $1\mathrm{.}67{10}^{-5}\frac{m^3}{s},$ what diameter of tube is needed if the liquid level is $0\mathrm{.}1m$ below the end of the tube exposed to the flowing air?

Diffusion coefficient for hydrocarbon $=1\mathrm{.}0{10}^{-5}\frac{m^2}{s}$

Vapor pressure of hydrocarbon $=10132\mathrm{.}5Pa$

Total pressure $=101325Pa$

Temperature $=25C=298K$