CHEMICAL ENGINEERING

314 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

Evaluating:yC:

yC RHS

10 11.26

15 12.27

20 13.00

25 13.5

8 10.7

7 10.4

12 11.71

11 11.5

11.5 11.6

11.6 11.62

and:yCD 11. 6

The equation forbuffer zonemay be written as:

uCDAlnyCCB

WhenyCD 5 ,uCD 5

WhenyCD 30 ,uCD 2 .5ln30C 5. 5

Thus: 5 DAln 5CB

5. 5 C 2 .5ln30DAln 30CB

Substracting: 0. 5 C 2 .5ln30DAln 6

Thus:AD 0. 5 C 2 .5ln30/ln 6D 5 .02 and:BD 5 Aln 5D 3. 08

The difference in the two values ofuCis a maximum whenyCD 11 .6.

From the two-layer theory:uCD 11. 6

From the buffer-layer theory:

uCD 5 .02 lnC 11. 6  3. 08 D 9. 2

The maximum difference in the two values ofuCis then: 2. 4

PROBLEM 12.22

In the universal velocity profile a “dimensionless” velocityuCis plotted against lnyC,
whereyCis a “dimensionless” distance from the surface. For the region where eddy
transport dominates (eddy kinematic viscosity×kinematic viscosity), the ratio of the
mixing lengthEto the distanceyfrom the surface may be taken as approximately
constant and equal to 0.4. Obtain an expression for duC/dyCin terms ofyC.
In the buffer zone the ratio of duC/dyCtoyCistwicethe value calculated above. Obtain
an expression for the eddy kinematic viscosityEin terms of the kinematic viscosity/
andyC. On the assumption that the eddy thermal diffusivityEHand the eddy kinematic