Page 208 - Bird R.B. Transport phenomena

192 Chapter 6 Interphase Transport in Isothermal Systems

X ВUI•ke and Plummer
0 E r un
g
100 \ - л ivicircuin
о ° % ^ n Oman and Watson
6
5
4
f
3
4
2

10 X A
о
4 . *4v
N
V ^ ч
5 •* * Д А
\
4 \ 4 4J Ergun equation
д
о
3 \ хдд.
\ *x
2 X > M
• i •*• 3К 1 D n
Вurke-Plu mmer equ ati( )П д x
1
3 4 5 6 2 3 4 5 6 3 4
10 10 3

Fig. 6.4-2. The Ergun equation for flow in packed beds, and the two related asymptotes, the Blake-Kozeny equa-
tion and the Burke-Plummer equation [S. Ergun, Chem. Eng. Prog., 48, 89-94 (1952)].

The above discussion of packed beds illustrates how one can often combine solu-
tions of elementary problems to create useful models for complex systems. The constants
appearing in the models are then determined from experimental data. As better data be-
come available the modeling can be improved.

QUESTIONS FOR DISCUSSION
1. How are graphs of friction factors versus Reynolds numbers generated from experimental
data, and why are they useful?
2. Compare and contrast the friction factor curves for flow in tubes and flow around spheres.
Why do they have different shapes?
3. In Fig. 6.2-2, why does the / versus Re curve for turbulent flow lie above the curve for laminar
flow rather than below?
4. Discuss the caveat after Eq. 6.2-18. Will the use of the mean hydraulic radius for laminar flow
predict a pressure drop that is too high or too low for a given flow rate?
5. Can friction factor correlations be used for unsteady flows?
6. What is the connection, if any, between the Blake-Kozeny equation (Eq. 6.4-9) and Darcy's
law (Eq. 4C.3-2)?