Page 346 - Fluid mechanics, heat transfer, and mass transfer

MISCELLANEOUS DESIGN EQUATIONS 327

& When more accurate results are desirable, Bell & For square pitch,
Delaware method is a better choice. This method 0:5
T c ffi 1:19 ðnumber of tubesÞ : ð10:89Þ
requires awareness of the configuration of the ex-
changer, as it is based on correction factors of the & For triangular pitch,
configuration of the exchanger, leakage and bypass 0:5
T c ffi 1:1 ðnumber of tubesÞ : ð10:90Þ
flow corrections. It requires baffle configuration,
leakage through the gaps between tubes and baffle . Give Taborek equation for the estimation of number of
and baffles and shell, bypassing of the flow between tubes and state its applicability.
shell and tube bundle and baffle configuration. 2 2
N t ¼ 0:7854D =C 1 L ; ð10:91Þ
tp
ctl
where N t is the number of tubes, D ctl is the centerline
tube limit diameter, L tp is the tube pitch, and C 1 is
10.3 MISCELLANEOUS DESIGN EQUATIONS
the constant (1.0 for square and rotated square tube
. What are the recommended design guidelines for de- layouts and 0.866 for triangular tube layouts).
termining shell diameter and tube counts for a heat . Give an equation for the estimation of number of tubes
exchanger?
based on maximum allowable pressure drop for a
& Shell Diameter: The design process is to fit the
liquid–liquid exchanger.
number of tubes into a suitable shell to achieve the
desired shell side velocity of 1.219 m/s (4 ft/s), sub- p 3 2
N ¼ðm=1:111Þ½ f t LN =rD DP t Š; ð10:92Þ
i
t
ject to pressure drop constraints.
& Most efficient conditions for heat transfer are to have where DP t is in Pa, N is the number of tubes, m is the
the maximum number of tubes possible in the shell to mass flow rate on the shell side, f t is the tube side friction
maximize turbulence. factor, L is the length of tube bundle, N t is the number of
& Preferred tube length to shell diameter ratio is in the tube side passes, D i is the inside tube diameter, and DP t
is the maximum allowable DP.
range 5–10.
. Give an equation for DP across a tube bank.
& Criteria for tube count data are as follows:
& For turbulent flow on shell side,
➢ Tubes are eliminated to provide entrance area for
2
a nozzle equal to 0.2 times shell diameter. DP ¼ K s ½2N R f G =g c rFŠ:
0
s ð10:93Þ
➢ Tube layouts are symmetrical about both the hor-
0
izontal and vertical axes. f ¼ bðD o G s =mÞ 0:15 : ð10:94Þ
➢ Distance from tube O.D. to centerline of pass 1:08
partition 7.9 mm (5/16 in.) for shell I.D. <559 mm b ¼ 0:23 þ 0:11=ðx T 1Þ ð10:95Þ
(22 in.) and 9.5 mm (3/8 in.) for larger shells. for staggered arrangement.
. Givean equation for the estimation of number of baffles.
ð0:43 þ 1:13=x L Þ
b ¼ 0:044 þ 0:08x L =ðx T 1Þ ð10:96Þ
Number of baffles ¼ 10 T l =ðB P ; % of D i ÞðD i Þ; for inline arrangement.
ð10:86Þ
K s ¼ correction factor ð1 þ number of bafflesÞ:
where T l is the tube length, B P is the baffle pitch, D i is the
ð10:97Þ
shell I.D.
N R ¼ number of tube rows across which shell side
. Give equations for (i) space available for flow on shell
fluid flows.
side and (ii) free area for flow between baffles. f ¼ modified friction factor.
0
(i) W ¼ D i ðd o T c Þ; ð10:87Þ x T , x L ¼ ratio of pitch transverse, parallel to flow-to-
tube outside diameter.
2
where W is the space for flow (in. ), D i is the shell I.
0:14
D. (in.), d o is the tube O.D. (in.), and T c is the F ¼ 1:02ðm =m Þ : ð10:98Þ
w
b
number of tubes across centerline.
. Give an equation for shell side DP.
(ii) A f ¼ WðB P 0:187Þ; ð10:88Þ
2 0:14
DP s ¼ fG ½fðL=BÞ 1gþ 1ŠD s =2rD e ðm =m Þ :
s b w
where A f is free area between baffles and B P baffle
ð10:99Þ
pitch, in.
. Giveequations for calculation of number of tubes across
f ¼ exp½0:576 0:19lnðN Re s ފ: ð10:100Þ
the centerline of tube bundle.