40 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS
Solution
A force balance on an element offluid of radiusrgives:
Pr^2 D 2 rl
du
dr
or:
du
dr
D
Pr
2 l
or uD
Pr^2
4 l
Cconstant
WhenrDd/ 2 Da,uD0 and the constantD
(
Pa^2
4 l
)
∴ uD
P
4 l
a^2 r^2
Theflow, dQ, through an annulus, radiusrand thickness dris given by:
dQD 2 rdrur
D 2 rdr
[
P
4 l
a^2 r^2
]
and: QDa^4
(
P
8 l
)
The average velocity is: uavDQ/a^2
D
Pa^2
8 l
The radius at whichuDuavis:
Pa^2
8 l
D
P
4 l
a^2 r^2
from which:
r^2 Da^2 / 2 Dd^2 /8andrD 0. 35 d
PROBLEM 3.28
Cooling water supplied to a heat exchangerflows through 25 mm diameter tubes each
5 m long arranged in parallel. If the pressure drop over the heat exchanger is not to
exceed 8000 N/m^2 , how many tubes must be included for a totalflowrate of water of
110 tonne/h? Density of waterD1000 kg/m^3. Viscosity of waterD1mNs/m^2. Assume
pipes to be smooth-walled.
If ten per cent of the tubes became blocked, what would the new pressure drop be?
Solution
R
u^2
ðRe^2 D
Pd^3
4 l^2
(equation 3.23)
D 8000 ð 0. 025 ^3 ð 1000 / 4 ð 5 ð 1 ð 10 ^3 ^2 D 6. 25 ð 106