CHEMICAL ENGINEERING

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