$10-23.$

a$.$ Calculate the mass flux $(k\frac{g}{m^2}(s))$ of gaseous material through a leak assuming

that the material is stored at its vapor pressure within the vessel

abs$).$ Assume that the material is stored at $25C,$ that it is discharged to $1$atm

pressure, and that its molecular weight is $44.$

b$.$ Calculate the mass flux $(k\frac{g}{m^2}(s))$ of two$-$phase material through the same leak

under the same conditions of part a$.$ Assume that the discharge length is greater

than $10cm.$ Additional physical property data are

Heat $of$ vaporization: $3\mathrm{.}33{10}^5\frac{J}{k}g$

$v_{fg}$:$,0\mathrm{.}048\frac{m^3}{k}g$

Heat capacity $of$ liquid: $2\mathrm{.}23{10}^3\frac{J}{k}gK$

Heat capacity $of$ vapor: $1\mathrm{.}70{10}^3\frac{J}{k}gK$

c$.$ Comment on the difference in flux rates between parts a and b$.$ In general, relief

systems designed for two$-$phase flow must be larger than those for all$-$vapor flow.

Is this consistent with the results of parts a and $b?$ Why?

d$.$ Calculate the energy discharge rate for the discharge of part a$.$ Assume that the

energy content of the vapor is due to the heat of vaporization of the liquid to gas.

e$.$ Calculate the energy discharge rate for the discharge of part b$.$ Assume that the

energy is due to the sensible heat increase of the two$-$phase discharge stream and

that the temperature of the discharge is $10K$ higher.

f$.$ Compare the results of parts $d$ and $e.$ How many times larger must the area of the

two$-$phase discharge be in order to remove energy at the same rate as the single$-$

phase relief? Comment on the implications for relief systems on reactor vessels.