Page 216 - Modelling in Transport Phenomena A Conceptual Approach

196 CHAPTER 7. UNSTEADY-STATE MACROSCOPIC BALANCES

Eq. (7.47) gives

0.31 Re; -1
x I"' (Ar - 18%~ - 3.~4Re;~'~ ) dRep (7.4-8)
-
1 + 16,300 Rei1*''
Equation (7.4-8) should be evaluated numerically.

Example 7.5 Calculate the time required for a spherical lead particle, 1.5mm in
diameter, to reach 60% of its terminal velocity in air at 50 "C.

Solution
Physical properties

For lead at 50 "C : p = 11,307 kg/ m3

Analysis

When the particle reaches its terminal velocity, the value of the Reynolds number
can be calculated from Eq. (4.3-12). The Archimedes number is

- (1.5 x 10-3)3(9~8)(1~0928)(11~307) 1.067
-
~
(19.57 x 10-6)2 106
Substitution of this value into Eq. (4.3-1.2) gives the Reynolds number under steady
conditions as
Ar -1.214
RepI,=,, = - (1 + 0.0579Ar0.412)
18
- 1.067 x lo6 [1+ 0.0579 (1.067 x 106)0'412]
- -1.214 = 1701
18
In this problem it is required to calculate the time for the particle to reach a Reynolds
number of
Rep = (0.6)(1701) = 1021
Therefore, the required time can be calculated from Eq. (7.4-8) as

(11,307)(1.5 x 10-3)2 I
t=
19.57 x