CHEMICAL ENGINEERING

SECTION 4

Flow of Compressible Fluids

PROBLEM 4.1

A gas, having a molecular weight of 13 kg/kmol and a kinematic viscosity of 0.25 cm^2 /s,
flows through a pipe 0.25 m internal diameter and 5 km long at the rate of 0.4m^3 /s
and is delivered at atmospheric pressure. Calculate the pressure required to maintain this
rate of flow under isothermal conditions. The volume occupied by 1 kmol at 273 K and
101 .3kN/m^2 is 22.4m^3. What would be the effect on the required pressure if the gas
were to be delivered at a height of 150 m (i) above, and (ii) below its point of entry into
the pipe?

Solution

From equation 4.57 and, as a first approximation, omitting the kinetic energy term:

P 2 
P 1 /vmC 4 R/u^2 l/dG/A^2 D 0

At atmospheric pressure and 289 K, the densityD 13 / 22. 4  273 / 289 D 0 .542 kg/m^3

Mass flowrate of gas,GD 0. 4 ð 0. 542 D 0 .217 kg/s.

Cross-sectional area,AD/ 4  0. 25 ^2 D 0 .0491 m^2.

Gas velocity,uD 0. 4 / 0. 0491 D 8 .146 m/s

∴ G/AD 0. 217 / 0. 0491 D 4 .413 kg/m^2 s

Reynolds number, ReDdu/

D 0. 25 ð 8. 146 / 0. 25 ð 10 
^4 D 8. 146 ð 104

From Fig. 3.7, fore/dD 0. 002 ,R/u^2 D 0. 0031

v 2 D 1 / 0. 542 D 1 .845 m^3 /kg

v 1 D 22. 4 / 13  298 / 273  101. 3 /P 1 D 190. 5 /P 1 m^3 /kg

and: vmD 0. 923 P 1 C 95. 25 /P 1 m^3 /kg

Substituting in equation 4.57:

P 1 P 1 
 101. 3  103 / 0. 923 P 1 C 95. 25 D 4  0. 0031  5000 / 0. 25  4. 726 ^2

and: P 1 D 111 .1kN/m^2

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