CHEMICAL ENGINEERING

FLOW OF COMPRESSIBLE FLUIDS 69

Whene/dD 0 .002 andReD 105 ,R/u^2 D 0 .003 from Fig. 3.7.

G/A^2 lnP 1 /P 2 CP^22 
P^21 / 2 P 1 v 1 C 4 R/u^2 l/dG/A^2 D 0 (equation 4.55)

Substituting:

G/A^2 ln 1. 0 / 0. 1 C 0. 12 
 12 ð 106 / 2 ð 1 ð 103 ð 83. 98 

C 4  0. 003  30 / 0. 15 G/A^2 D 0

and:G/AD 1 .37 kg/m^2 s.
The viscosity of air is 0.018 mN s/m^2.

∴ReD 0. 15 ð 1. 37 / 0. 018 ð 10 
^3 D 1. 14 ð 104

Thus the chosen value of Reis too high. WhenReD 1 ð 104 ,R/u^2 D 0 .0041 and
G/AD 1 .26 kg/m^2 s.
Renow equals 1. 04 ð 104 which agrees well with the assumed value.

Thus: GD 1. 26 ð/ 4 ð 0. 15 ^2 D 0 .022 kg/s

PROBLEM 4.9

A vacuum system is required to handle 10 g/s of vapour (molecular weight 56 kg/kmol)
so as to maintain a pressure of 1.5kN/m^2 in a vessel situated 30 m from the vacuum
pump. If the pump is able to maintain a pressure of 0.15 kN/m^2 at its suction point, what
diameter of pipe is required? The temperature is 290 K, and isothermal conditions may
be assumed in the pipe, whose surface can be taken as smooth. The ideal gas law is
followed. Gas viscosityD 0 .01 mN s/m^2.

Solution

Use is made of equation 4.55 to solve this problem. It is necessary to assume a value of
the pipe diameterdin order to calculate values ofG/A, the Reynolds number andR/u^2.
IfdD 0 .10 m,AD/ 4  0. 10 ^2 D 0 .00785 m^2

∴ G/AD 10 ð 10
^3 / 0. 00785 D 1 .274 kg/m^2 s

and ReDdG/A/D 0. 10 ð 1. 274 / 0. 01 ð 10
^3 D 1. 274 ð 104

For a smooth pipe,R/u^2 D 0 .0035, from Fig. 3.7.

Specific volume at inlet,v 1 D 22. 4 / 56  290 / 273  101. 3 / 1. 5 D 28 .7m^3 /kg

G/A^2 lnP 1 /P 2 CP^22 
P^21 / 2 P 1 v 1 C 4 R/u^2 l/dG/A^2 D0 (equation 4.55)

Substituting gives:

 1. 274 ^2 ln 1. 5 / 0. 15 C 0. 152 
 1. 52 ð 106 / 2 ð 1. 5 ð 103 ð 28. 7 

C 0. 0035  30 / 0. 10  1. 274 ^2 D
 16. 3

and the chosen value ofdis too large.