Page 96 - Modelling in Transport Phenomena A Conceptual Approach

76 CHAPTER 4. EVALUATION OF TRANSFER COEFFICIENTS

a) Calculate the Archimedes number from Eq. (4.3-6),
b) Substitute the Archimedes number into Eq. (4.3-12) and determine the Reynolds
number,
c) Once the Reynolds number is determined, the terminal velocity can be calculated
from the equation

(4.3-13)

Example 4.4 Calculate the velocities at which a drop of water, 5 mm in diameter,
would fall in air at 20°C and the same size air bubble would rise throagh water at
20 "C.
Solution
Physical properties

p = 999 kg/ m3
For water at 20 "C (293 K) :
= lool 10-6 kg/ m.
For air at 2ooc (293 K, ' p = 1.2047 kg/ m3
= 18.17 x 10-6 kg/ m.

Analysis
Water droplet falling in air
To determine the terminal velocity of water, it is necessary to calculate the Archimedes
nzlmber wing Eq. (4.3-6):

D%P (PP - PI
Ar=
P2
- (5 x 10-3)3(9.8)(1.2047)(999 - 1.2047) = 4,46
-
(18.17 x 10-6)2 106
The Reynolds number is calculated from Eq. (4.3-12):

Rep = (1 + 0.0579
18
- - 4.46 x 106 [1+ 0.0579 (4.46 x 106)0*412]-1'214 3581
=
18
Hence, the terminal velocity is
ut = -
P Rep
PDP
- (18.17 x 10-6)(3581) = 10.8m/ s
-
(1.2047)(5 x