CHEMICAL ENGINEERING

64 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

From Fig. 3.7 this corresponds to a value ofe/dof approximately 0.002, which is
reasonable for a steel pipe.
For compressible flow:

G/A^2 lnP 1 /P 2 CP^22 
P^21 / 2 P 1 v 1 C 4 R/u^2 l/dG/A^2 D 0 (equation 4.55)

Substituting:

G/A^2 ln 8. 0 / 7. 5 C 7. 52 
 8. 02  1012 / 2 ð 8. 0 ð 106 ð 0. 15 

C 4  0. 003  30 / 0. 05 G/A^2 D 0

from which:G/AD667 kg/m^2 sandGD 667 ð/ 4  0. 05 ^2 D 1 .31 kg/s
Little error is made by the simplifying assumption in this particular case.
The power requirement is given by equation 8.71:

D 1 /GP 1 v 1 lnP 1 /P 2 

If the compressor efficiencyD60%,

power requirementD 1 / 0. 6 ð 1. 31 ð 8. 0 ð 106 ð 0 .15 ln 8 / 7. 5 

D 1. 69 ð 105 W or 169 kW

PROBLEM 4.5

A vacuum distillation plant operating at 7 kN/m^2 pressure at the top has a boil-up rate of
0.125 kg/s of xylene. Calculate the pressure drop along a 150 mm bore vapour pipe used
to connect the column to the condenser. The pipe length may be taken as equivalent to
6m,e/dD 0 .002 andD 0 .01 mN s/m^2.

Solution

From vapour pressure data, the vapour temperatureD338 K and the molecular weight of
xyleneD106 kg/kmol.
In equation 4.55:

G/A^2 lnP 1 /P 2 CP 22 
P^21 / 2 P 1 v 1 C 4 R/u^2 l/dG/A^2 D 0

Cross-sectional area of pipe,AD/ 4  0. 15 ^2 D 1. 76 ð 10 
^2 m^2

G/AD 0. 125 / 1. 76 ð 10 
^2 D 7 .07 kg/m^2 s

The Reynolds number, isud/DdG/A/

D 0. 15 ð 7. 07 / 0. 01 ð 10 
^3 D 1. 06 ð 105

From Fig. 3.7, withe/dD 0 .002 andReD 1. 06 ð 105 ,R/u^2 D 0 .003.

Specific volume,v 1 D 22. 4 / 106  338 / 273  101. 3 / 7. 0 D 3 .79 m^3 /kg.