CHEMICAL ENGINEERING

FLOW OF COMPRESSIBLE FLUIDS 65

Substituting in equation 4.55:

 7. 0 ^2 ln 7 /P 2 CP^22 
 72 ð 106 / 2 ð 7 ð 103 ð 3. 79 C 4 ð 0. 003  6 / 0. 15  7. 07 ^2 D 0

whereP 2 is the pressure at the condenserkN/m^2 .
Solving by trial and error:

P 2 D 6 .91 kN/m^2

∴ P 1
P 2 D 7. 0
6. 91 D 0 .09 kN/m^2 or 90 N/m^2

PROBLEM 4.6

Nitrogen at 12 MN/m^2 pressure is fed through a 25 mm diameter mild steel pipe to a
synthetic ammonia plant at the rate of 0.4 kg/s. What will be the drop in pressure over
a 30 m length of pipe assuming isothermal expansion of the gas at 300 K? What is the
average quantity of heat per unit area of pipe surface that must pass through the walls in
order to maintain isothermal conditions? What would be the pressure drop in the pipe if
it were perfectly lagged?D 0 .02 mNs/m^2.

Solution

At high pressure, the kinetic energy term in equation 4.55 may be neglected to give:

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

Specific volume at entry of pipe,v 1 D 22. 4 / 28  300 / 273  0. 1013 / 12 
D 0 .00742 m^3 /kg
Cross-sectional area of pipe,AD/ 4  0. 025 ^2 D 0 .00049 m^2

∴G/AD 0. 4 / 0. 00049 D816 kg/m^2 s.

Reynolds number,dG/A/D 0. 025 ð 816 / 0. 02 ð 10 
^3 D 1. 02 ð 106

Ife/dD 0 .002 andReD 1. 02 ð 106 ,R/u^2 D 0 .0028 from Fig. 3.7.

Substituting: 122 
P^22  1012 / 2 ð 12 ð 106 ð 0. 00742 D 4  0. 0028  30 / 0. 025  816 ^2

and:P 2 D 11 .93 MN/m^2

and: pressure dropD 12. 0 
 11. 93 D 0 .07 MN/m^2 70 kN/m^2

The heat required to maintain isothermal flow is given in Section 4.5.2 asGu^2 /2.

The velocity at the high pressure end of the pipeDvolumetric flow/area

DG/Av 1 D 816 ð 0. 0072 D 6 .06 m/s

and the velocity in the plant is taken as zero.

Thus: Gu^2 / 2 D 0. 4 ð 6. 06 ^2 / 2 D 7 .34 W