CHEMICAL ENGINEERING

FLOW OF COMPRESSIBLE FLUIDS 63

Substituting:

 2. 02 
 2. 62  1012 / 2 ð 2. 6 ð 106 ð 0. 468 C 4  0. 0023  500 / 0. 05 G/A^2 D 0

from whichG/AD111 kg/m^2 s.

∴ ReDdG/A/D 0. 05 ð 111 / 0. 009 ð 10
^3 D 6. 2 ð 105

Thus the chosen value ofRewas too high. IfReis taken as 6. 0 ð 105 and the problem
reworked,G/AD108 kg/m^2 sandReD 6. 03 ð 105 which is in good agreement.

AD/ 4  0. 05 ^2 D 0 .00197 m^2

and: GD 108 ð 0. 00197 D 0 .213 kg/s

The power requirement is given by equation 8.71 as 1 /GP 1 v 1 lnP 1 /P 2 

If a 60% efficiency is assumed, then the power requirement is:

D 1 / 0. 6 ð 0. 213 ð 2. 6 ð 106 ð 0 .468 ln 2. 6 / 2 

D 1. 13 ð 105 W or 113 kW

PROBLEM 4.4

In a synthetic ammonia plant the hydrogen is fed through a 50 mm steel pipe to the
converters. The pressure drop over the 30 m length of pipe is 500 kN/m^2 , the pressure
at the downstream end being 7.5MN/m^2. What power is required in order to overcome
friction losses in the pipe? Assume isothermal expansion of the gas at 298 K. What error
is introduced by assuming the gas to be an incompressible fluid of density equal to that
at the mean pressure in the pipe?D 0 .02 mNs/m^2.

Solution

If the downstream pressureD 7 .5MN/m^2 and the pressure drop due to frictionD
500 kN/m^2 , the upstream pressureD 8 .0MN/m^2 and the mean pressureD 7 .75 MN/m^2.
The mean specific volume is:vmD 22. 4 / 2  298 / 273  0. 1013 / 7. 75 D 0 .16 m^3 /kg

and: v 1 D 22. 4 / 2  298 / 273  0. 1013 / 8. 0 D 0 .15 m^3 /kg

It is necessary to assume a value ofR/u^2 , calculateG/Aand the Reynolds number and
check that the value ofe/dis reasonable. If the gas is assumed to be an incompressible
fluid of density equal to the mean pressure in the pipe andR/u^2 D 0 .003, the pressure
drop due to frictionD500 kN/m^2 is:

∴  500 ð 103 / 0. 16 D 4  0. 003  30 / 0. 05 G/A^2

and G/AD658 kg/m^2 s.

ReDdG/A/D 0. 05 ð 658 / 0. 02 ð 10 
^3 D 1. 65 ð 106