Page 63 - Process Equipment and Plant Design Principles and Practices by Subhabrata Ray Gargi Das

3.2 Design 59

p 2 2
Where the cross-sectional area is D D . Eq. 3.13b has been used for evaluation of both
o
io
4
Nusselt Number as well as Reynolds number.
However, the Reynolds number estimation for calculation of pressure drop is always based on
Eq. 3.13a. In this book, D e both for thermal as well as pressure drop calculations have been evaluated
by Eq. 3.13a.
For plain multi-tube hairpin exchangers containing n tubes each of OD (D o ) housed within an outer
2 2
pipe of diameter (D io ), the expressions for flow area [A ¼ðp =4Þ D nD ] and wetted perimeter
io o
½ðpÞðD io þ nD o ފ gives the expression for equivalent diameter as
2 2
D nD o
io
(3.13c)
D e 0¼
ðD io þ nD o Þ
The above expression reduces to Eq. 3.13a for n ¼ 1.
In a finned annulus, with the fin length being L f , the equivalent diameter D ef obtained as four times
2 2
the flow area A ¼ðp=4Þ D nD nN f L f t f divided by the wetted perimeter for heat transfer
io o
½ðpÞðD io þ nD o Þþ 2nN f L f Š is
2 2
p D nD o 4nN f L f t f
io
D ef ¼ (3.13d)
pðD io þ nD o Þþ 2nN f L f

3.2.7 Hydraulic design
The pressure drop for flow through the straight length of annulus is expressed in liquid (fluid) head as.
2
4f o G L o
o
2gr De
DH fo ¼ 2 (3.14a)
o
Pressure drop in straight length

and for the inner pipe, it is

2
4fG L i
i
2
DH fi ¼ (3.14b)
2gr D i
i
G is the mass velocity of the fluid, g is the acceleration due to gravity, r is fluid density, L is the length
of the corresponding section, and f is the Fanning friction factor. When several double-pipe exchangers
are connected in series, annulus to annulus and pipe to pipe, the length (L)in Eq. (3.14), is the total for
the entire path. The friction factor ( f )in Eq. 3.14 is expressed as a function of Reynolds number,
defined as
G i D i
(3.15a)
m i;average
Re i ¼