CHEMICAL ENGINEERING

230 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

The general solution of equation (i) is:

CADAcoshayCBsinhay ii

whereAandBare constants.
The boundary conditions are:
AtyDL, CAD 0 iii
AtyD 0 ,CADCAi iv
Substituting equation (iii) in equation (ii):
0 DAcoshaLCBsinhaL

and substituting equation (iv) in equation (ii):

CAiDAC0andADCAiand

BDCAicoshaL/sinhaL

∴ CADCAicoshayCAi

coshaL

sinhaL

sinhay

D

CAi

sinhaL

coshaysinhaLcoshaLsinhay

D

CAisinhaLy



sinhaL

DCAi

sinhaLy



sinhaL

DCAi

sinh

p

k/DLy



sinh

p

k/DL

Rate of absorption: NADD

(

dCA

dy

)

yD 0

AssumingCAto be small so that bulk flow can be neglected, then:

NADD

d

dy

(

sinhaLy



sinhaL

)

D

DCAiacoshaL

sinhaL

DDCAia/tanhaLDDCAiaL/LtanhaL

kLDD/L

ˇD

√

Dk/kLD

√

k/D LDaL

∴ NAD

kLCAiˇ

tanhˇ

PROBLEM 10.14

The diffusivity of the vapour of a volatile liquid in air can be conveniently determined
by Winkelmann’s method, in which liquid is contained in a narrow diameter vertical tube