Page 70 - Design and Operation of Heat Exchangers and their Networks

Basic thermal design theory for heat exchangers 57

the Darcy friction factor. Eq. (2.133) is not explicit; therefore, an iteration
with an initial value of f D ¼0.03 can be performed.
Churchill (1977) suggested a single correlation of the Darcy friction
factor for laminar, transitional, and turbulent flow:

" # 1=12
12
64 1
f D ¼ + (2.134)
Re ð A + BÞ 3=2
where
( " #) 16
0:9 16
7 R 13,269
A ¼ 2lg + , B ¼
Re 3:7d i Re
Churchill equation is very practical for the calculation of the Darcy
6
friction factor for Re<10 . For Re>15,800, we can use Eq. (2.134) to
get an initial value for the calculation using the Colebrook-White equation
(2.133) without further iteration, and the deviation is less than 0.2%.

2.2.1.2 Frictional pressure drop in laminar flow in rectangular ducts
For fully developed laminar flow in a rectangular duct, the analytical solution
of the Fanning friction factor can be expressed for the aspect ratio γ in the
range of 0<γ 1 as (See Shah and London, 1978, Eqs. (333) and (340))
24
f Re ¼ " # (2.135)
∞
192λ X 1 ð 2n +1Þπ
2
ð 1+ γÞ 1 tanh
π 5 5 2γ
n¼0 ð 2n +1Þ
Table 2.1 Darcy friction factor for fully developed flow in a smooth circular tube (Kast,
2010, 2013).
Correlation Valid range

Hagen-Poiseuille f D ¼64/Re Re<2320
equation
Blasius equation f D ¼0.3164Re 0.25 3000<Re<10 5
4
Konakov equation f D ¼[1.8lg(Re) 1.5] 2 10 <Re<10 6
4
Hermann equation f D ¼0.0054+0.3964Re 0.3 2 10 <Re<2 10 6
p
Prandtl-von Karman p 1 ffiffiffi ¼ 2lg Re f D =2:51ð ffiffiffiffi Þ Re>10 6
equation f D
5
Filonenko equation p 1 ffiffiffi ¼ 1:819lg Reð Þ 1:64 10 <Re<5 10 7
f D