CHEMICAL ENGINEERING

FLOW OF COMPRESSIBLE FLUIDS 67

v 2 may be calculated from equation 4.77 using specified values ofG/Aand substituted in
equation 4.72 to obtain the value ofP 2. In this way the required data may be calculated.

8 R/u^2 l/dD

[


1

2 

C

P 1

v 1

(

A

G

) 2 ][

1

(

v 1

v 2

) 2 ]

C 1



ln

(

v 2

v 1

)

(equation 4.77)

0. 5 G/A^2 v^21 C[/
 1 ]P 1 v 1 D 0. 5 G/A^2 v^22 C[/
 1 ]P 2 v 2

(equation 4.72)

or:

0. 5 G/A^2 v^21 
v^22 C[/
 1 ]P 1 v 1

[/
 1 ]v 2

DP 2

WhenP 2 DP 1 D10 MN/m^2 ,G/AD0.
IfG/Ais 2000 kg/m^2 s, then:

ReD 0. 01 ð 2000 / 0. 018 ð 10 
^3 D 1. 11 ð 106

Whene/dD 0 .0002,R/u^2 D 0 .0028 from Fig. 3.7 and:

v 1 D 22. 4 / 29  290 / 273  0. 1013 / 10 D 0 .0083 m^3 /kg

Substituting in equation 4.77:

8  0. 0028  30 / 0. 01 D

[

0. 36

2 ð 1. 36

C

10 ð 106

0. 0083

(

1

2000

) 2 ]

ð

[

1

(

0. 0083

v 2

) 2 ]

2. 36

1. 36

ln

( v

2

0. 0083

)

and:v 2 D 0 .00942 m^3 /kg.
Substituting forv 2 in equation 4.72 gives:

P 2 D[0. 5  2000 ^2  0. 00832 
 0. 009422 C 1. 36 / 0. 36  10 ð 106 ð^0.^0083 ]/ 1. 36 / 0. 36 

ð 0. 00942

and:P 2 D 8 .75 MN/m^2.

In a similar way the following table may be produced.

G/Akg/m^2 s v 2 m^3 /kgP 2 MN/m^2 

0 0.0083 10.0

2000 0.00942 8.75

3000 0.012 6.76

3500 0.0165 5.01

4000 0.025 3.37

4238 0.039 2.04