Page 100 - Process Equipment and Plant Design Principles and Practices by Subhabrata Ray Gargi Das

4.5 Pressure drop estimation 97

Considering negligible dependence of loss coefficients on Reynolds number, K c and K e can be
expressed in terms of area ratio as

2
e (4.20a)
K e z ð1 b Þ
and
2
i (4.20b)
K c z 0:42 ð1 b Þ
Total pressure drop: The total pressure drop Dp t and Dp s across the tube side and the shell side of
the heat exchanger is obtained by adding the individual contributions explained above.

Dp t ¼ Dp in;t þ Dp c;t þ Dp a;t þ Dp e;t (4.21a)
and
Dp s ¼ Dp in;s þ Dp c;s þ Dp a;s þ Dp e;s (4.21b)
In all expressions, subscripts t and s signify the tube side and the shell side, respectively.
Fluid pumping power is related to the total pressure drop and flow rate as
!

1 m t 1 m s
Dp s (4.22)
W p;t ¼ Dp t ; and W s;t ¼
p s
h ; t e t h ;t e s
where h is pump efficiency.
p
Kern (Kern, Donald Quentin. Process heat transfer. Tata McGraw-Hill Education, 1997) suggested
another way to estimate pressure drop
a) For the tube-side fluid, one velocity head loss per return bend is considered and the expression is

1 2 4f t L p N p
t t
2 D i
Dp t ¼ r u þ 4N p (4.23)
where u t is tube-side velocity, L p is the tube length per pass, N p is the number of tube passes, D i is tube
inside diameter, r is the average density of the tube-side fluid, f t is the Fanning’s friction factor for the
t
flow condition in the tubes decided by the Reynolds’ number for flow through tubes.
b) For the shell-side fluid considering cross flow across the tube banks, the pressure drop expression is
2
f s G ðN b þ 1ÞD s
s
2r De
Dp s ¼ (4.24)
s
where N b is the number of baffles and ðN b þ1Þ is the number of crosses, i.e., the number of times the
shell-side fluid crosses the tube bundle. There is an odd number of crosses when both shell nozzles are
on opposite sides of the shell and an even number if both shell nozzles are on the same side. For close
baffle spacing ð 152.4 mm; i.e. 6 Þ, one baffle may be omitted if the number of crosses is not an
00
integer.
6
f s , the Fanning’s friction factor, can be expressed in the range: 400 < Re s 10 as
(4.25)
f ¼ expf0:576 0:19 lnðRe s Þg
As mentioned earlier, Re s ¼ G s De=m in the shell considering cross flow across the tube bank
s
m s P t
,where ðC ¼ P T d o Þ is the gap between the outer
D s C B
and shell-side mass flux, G s ¼