Page 226 - Design and Operation of Heat Exchangers and their Networks

Optimal design of heat exchangers 215

The Blasius equation can be used to calculate the friction factor for fully
developed flow in a smooth circular tube:

f D,t ¼ 0:3164Re 0:25
t (5.94)
¼ 0:3164 32401 0:25 ¼ 0:02358
From Eq. (5.90), we obtain the tube-side total pressure drop for two
tube passes:
_ m t 18:1 2
G t ¼ 2 ¼ 2 ¼ 1608 kg=m s
N t,p πd =4 52 π 0:0166 =4
i
G 2 t 2 L 2
Δp t ¼ N p 1 σ + K c + f D,t 1 σ K e
2ρ t d i
1608 2 2 4:3
¼ 2 1 0:2538 +0:3778 +0:02358 0:3977
2 1021 0:0166
¼ 17,803Pa

(7) Calculation of shell-side pressure drop
To calculate the pressure drop in an ideal tube bundle, we use Eq. (5.74) to
determine the number of tube rows in the flow direction along which the
maximum velocity occurs. Since s l <s l,min , we have
∗
N ¼ N rc 1 ¼ 9 1 ¼ 8
rc
The pressure drop in an ideal tube bundle is then given by
μ 2 0:02981 2
Δp b,id ¼ N ∗ s Hg ¼ 8 48,114 ¼ 1092 Pa
rc 2 2
ρ d 867:1 0:019
s o
The pressure drop in an ideal window section can be determined by
Eq. (5.75), in which the mass velocity in the window section is defined
by Eq. (5.77) as
_ m s 36:3 2
G w ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffip ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffip ¼ 1786 kg=m s
0:03209 0:01287
A sc A sw
Because Re sd >100, we have
2
G w 1786 2
ð
ð
Δp w,id ¼ 1+ 0:3N rw Þ ¼ 1+ 0:3 3Þ ¼ 6990 Pa
ρ s 867:1
The correction factors for the shell-side pressure drop are calculated
with Eqs. (5.60), (5.66), (5.69) respectively:
ð
ð
ð
ð
ζ ¼ e 1:33 1 + r s Þr 0:8 0:15 1 + rs Þ ¼ e 1:33 1 + 0:4265Þ0:1132 0:8 0:15 1+ 0:4265Þ ¼ 0:5890
lm
l
Since Re sd >100 and r ss <0.5, Eq. (5.66) can be expressed as follows with
C bp ¼3.7:
1=3 1=3
½
½
ð
ζ ¼ e C bp r b 1 2r ss Þ Š ¼ e 3:7 0:263 1 2 0:1111Þ Š ¼ 0:6814
ð
b