Page 125 - Modelling in Transport Phenomena A Conceptual Approach

4.5. FLOW IN CIRCULAR PIPES 105

In problems dealing with the flow of compressible fluids, it is customary to define
mass velocity, G, as
m
A
G=-=p( v) (2)
The advantage of wing G is the fact that it remains constant for steady flow of
compressible fluids through ducts of uniform cross-section. In this case
G = (1.2047)(50) = 60.24 kg/ m2. s

The inventory rate equation for energy is written as
Rate of energy in = Rate of energy out (3)
Equations (3)-(5) of Example 4.15 are also applicable to this problem. Therefore,
we get -- f E ( Tw - Tbi, )
L
In
D-4 Nu Tw - Gout (4)
The Nzlsselt number in Eq. (4) can be determined only if the Reynolds number is
known. The Reynolds number is calculated as
DG
Re = -
P
- + Turbulent flow
- (0*015)(60*24) = 45,636
19.80 x
The value of L depends on the comlations as follows:

Dittus-Boelter correlation
Substitution of Eq. (4.5-26) into Eq. (4) gives

L
-=
D
-
- (45, 636)0.2(0.707)0.6 (150 - 20) = 58.3
0.092 150 - 90
Therefore, the required length is
L = (58.3)(1.5) = 87cm

Sieder-Tate correlation
Substitution of Eq. (4.5-27) into Eq. (4) gives

(23.86 x )
(45,636)0.2(0.707)2/3 19.80 x loq6 -0'14 150 - 20 = 49.9
-
- 0.108 ln(150-90)