Page 214 - Modelling in Transport Phenomena A Conceptual Approach

194 CHAPTER 7. UNSTEADY-STATE MACROSCOPIC BALANCES

Substitution of the values into Eq. (5) gives the required time as
3
t=- (1145)(0.02)2 = 2.59 x lo5 s N 3 days
32 (128)(5.17 x 10-4)(8.25 x

b) When air Bows with a certain velocity, the Ranz-Marshall correlation can be
expressed as
&)DP
- =2+0.6
DAB
or.
(7)
where the coeficients a and p are defined by

= 2DAB = 2 (8.25 x = 1.65 x (8)

1 /2
) (2.66)lI3 = 3.27 x (9)
= (0.6)(8.25 x (21.95 x

Substitution of Eqs. (7)-(9) into Eq. (2) gives

DP
t=
1.65 x + 3.27 x 10-3.\/Da
Analytical evaluation of the above integral is possible and the result is
t = 3097 s e 52 min

Verification of the pseudo-steady-state approximation

DAB t (8.25 x 10-6)(3097) =64>1
-- -
D; (2 x 10-2)2

7.4 CONSERVATION OF MOMENTUM

According to Newton’s second law of motion, the conservation statement for linear
momentum is expressed as
Time rate of change of Forces acting )
( linear momentum of a body ) = ( onabody (7.4-1)
In Section 4.3, we considered the balance of forces acting on a single spherical
particle of diameter Dp, falling in a stagnant fluid with a constant terminal velocity