CHEMICAL ENGINEERING

72 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

and: P 1 v 1

∫

dP

P

C

∫

gdzD 0

and: P 1 v 1 lnP 2 /P 1 Cgz 2
z 1 D 0

v 1 D 22. 4 / 29  288. 7 / 273  101. 3 / 98. 4 D 0 .841 m^3 /kg.

∴ 98 , 400 ð 0 .841 lnP 2 / 98. 4 C 9. 81  3000
0 D 0

and: P 2 D 68 .95 kN/m^2

The relationship between vapour pressure and temperature may be expressed as:

logPDaCbT

When, TD 288. 7 ,PD 1 .77 kN/m^2

and when, TD 373 ,PD 101 .3kN/m^2

∴ logPD
5. 773 C 0. 0209 T

WhenP 2 D 68 .95,TD364 K.

PROBLEM 4.13

A 150 mm gas main is used for transferring gas (molecular weight 13 kg/kmol and kine-
matic viscosity 0.25 cm^2 /s) at 295 K from a plant to a storage station 100 m away, at a
rate of 1 m^3 /s. Calculate the pressure drop if the pipe can be considered to be smooth.
If the maximum permissible pressure drop is 10 kN/m^2 , is it possible to increase the
flowrate by 25%?

Solution

If the flow of 1 m^3 /s is at STP, the specific volume of the gas is:

 22. 4 / 13 D 1 .723 m^3 /kg.

The mass flowrate,GD 1. 0 / 1. 723 D 0 .58 kg/s.
Cross-sectional area,AD/ 4  0. 15 ^2 D 0 .0176 m^2

∴ G/AD 32 .82 kg/m^2 s

/D 0 .25 cm^2 /sD 0. 25 ð 10 
^4 m^2 /s

and D 0. 25 ð 10
^4  1 / 1. 723 D 1. 45 ð 10
^5 Ns/m^2

∴ ReD 0. 15 ð 32. 82 / 1. 45 ð 10
^5 D 3. 4 ð 105

For smooth pipes,R/u^2 D 0 .0017, from Fig. 3.7.
The pressure drop due to friction is:

4 R/u^2 l/dG/A^2 D 4  0. 0017  100 / 0. 15  32. 82 ^2 D4883 kg^2 /m^4 s^2

and:
PD 4883 / 1. 723 D2834 N/m^2 or 2.83 kN/m^2.