Page 590 - Bird R.B. Transport phenomena

570 Chapter 18 Concentration Distributions in Solids and in Laminar Flow

stream of pure В will be directed vertically upward, and the gas composition will be mea-
sured at several points along the z-axis.
(a) Calculate the gas-injection rate W in g-moles/s required to produce a mole fraction x A ~
A
0.01 at a point 1 cm downstream of the source, in an ideal gaseous system at 1 atm and 800°C,
2
if v 0 = 50 cm/s and ЯЬ ~ 5 cm /s.
АВ
(b) What is the maximum permissible error in the radial position of the gas-sampling probe,
if the measured composition x is to be within 1 % of the centerline value?
A
18A.6. Determination of diffusivity for ether-air system. The following data on the evaporation of
ethyl ether (C2H5OC2H5) have been tabulated by Jost. 2 The data are for a tube of 6.16 mm di-
ameter, a total pressure of 747 mm Hg, and a temperature of 22°C
Decrease of the ether level Time, in seconds, required
(measured from the open for the indicated
end of the tube), in mm Hg decrease of level
from 9 to 11 590
from 14 to 16 895
from 19 to 21 1185
from 24 to 26 1480
from 34 to 36 2055
from 44 to 46 2655
The molecular weight of ethyl ether is 74.12, and its vapor pressure at 22°C is 480 mm Hg. It
may be assumed that the ether concentration at the open end of the tube is zero. Jost has
2
given a value of %b for the ether-air system of 0.0786 cm /s at 0°C and 760 mm Hg.
AB
(a) Use the evaporation data to find ЯЬ at 747 mm Hg and 22°C, assuming that the arith-
АВ
metic average gas-column lengths may be used for z 2 - z } in Fig. 18.2-1. Assume further that
the ether-air mixture is ideal and that the diffusion can be regarded as binary.
(b) Convert the result to ЯЬ at 760 mm Hg and 0°C using the results of §17.3.
АВ
18A.7. Mass flux from a circulating bubble.
(a) Use Eq. 18.5-20 to estimate the rate of absorption of CO (component A) from a carbon
2
dioxide bubble 0.5 cm in diameter rising through pure water (component B) at 18°C and at a
э
2
3
pressure of 1 atm. The following data may be used: ЯЬ = 1.46 X 10 cm /s, c = 0.041 g-
АВ A0
mole/liter, v = 22 cm/s.
t
(b) Recalculate the rate of absorption, using the experimental results of Hammerton and Gar-
4
ner, who obtained a surface-averaged k of 100 cm/hr (see Eq. 18.1-2).
c
6
6
Answers: (a) 1.171 X 10~ g-mol/cm 2 s; (b) 1.140 X 10~ g-mol/cm 2 s. (This is regarded as un-
usually good agreement.)
18B.1. Diffusion through a stagnant film—alternate derivation» In §18.2 an expression for the
evaporation rate was obtained in Eq. 18.2-14 by differentiating the concentration profile
found a few lines before. Show that the same results may be derived without finding the con-
centration profile. Note that at steady state, N Az is a constant according to Eq. 18.2-3. Then Eq.
18.2-1 can be integrated directly to get Eq. 18.2-14.

2
W. Jost, Diffusion, Academic Press, New York (1952), pp. 411-413.
3
G. Tammann and V. Jessen, Z. anorg. allgem. Chem., 179,125-144 (1929); F. H. Garner and
D. Hammerton, Chem. Eng. Sci., 3,1-11 (1954).
4
D. Hammerton and F. H. Garner, Trans. Inst. Chem. Engrs. (London), 32, 518 (1954).