CHEMICAL ENGINEERING

FLOW OF COMPRESSIBLE FLUIDS 61

The kinetic energy termDG/A^2 lnP 1 /P 2 D 4. 413 ^2 ln 111. 1 / 101. 3 

D 1 .81 kg^2 /m^4 s^2

This is negligible in comparison with the other terms which equal 5539 kg^2 /m^4 s^2 so
that the initial approximation is justified. If the pipe is not horizontal, the termgdzin
equation 4.49 must be included in the calculation. If equation 4.49 is divided byv^2 ,this
term on integration becomesgz/v^2 m.

∴ vmD 0. 923 ð 111. 1 C 95. 25 / 111. 1 D 1 .781 m^3 /kg

vairD 24. 0 / 29 D 0 .827 m^3 /kg

As the gas is less dense than air,vmis replaced byvair
vmD
0 .954 m^3 /kg.

∴ gz/v^2 mD 9. 81 ð 150 / 0. 9542 D1616 N/m^2 or 0.16 kN/m^2

(i) If the delivery point is 150 m above the entry level, then since gas is less dense,

P 1 D 111. 1 
 0. 16 D 110 .94 kN/m^2

(ii) If the delivery point is 150 m below the entry level then,

P 1 D 111. 1 C 0. 16 D 111 .26 kN/m^2

PROBLEM 4.2

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 1.25 kg/s. What will be the pressure drop over
a 30 m length of pipe for isothermal flow of the gas at 298 K? Absolute roughness
of the pipe surfaceD 0 .005 mm. Kilogram molecular volumeD 22 .4m^3. Viscosity of
nitrogenD 0 .02 mN s/m^2.

Solution

Molecular weight of nitrogenD28 kg/kmol.
Assuming a mean pressure in the pipe of 10 MN/m^2 , the specific volume, vm at
10 MN/m^2 and 298 K is:

vmD 22. 4 / 28  101. 3 / 10 ð 103  298 / 273 D 0 .00885 m^3 /kmol

Reynolds number,ud/DdG/A/.

AD/ 4  0. 025 ^2 D 4. 91 ð 10 
^3 m^2.

∴G/AD 1. 25 / 4. 91 ð 10 
^3 D2540 kg/m^2 s

and: ReD 0. 025 ð 2540 / 0. 02 ð 10
^3 D 3. 18 ð 106