CHEMICAL ENGINEERING

68 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

5000

4000

3000

G

/A

(kg / m

2 s)

2000

1000

0

987 65

Pressure P 2 (MN /m^2 )

10 432 10

Figure 4a.

These data are plotted in Fig. 4a. It is shown in Section 4.5.4, Volume 1, that the
maximum velocity which can occur in a pipe under adiabatic flow conditions is the sonic
velocity which is equal to

p

P 2 v 2.

From the above table

p

P 2 v 2 at maximum flow is:

√

1. 36 ð 2. 04 ð 106 ð 0. 039 D329 m/s

The temperature at this condition is given byP 2 v 2 DRT/M, and:

T 2 D 29 ð 0. 039 ð 2. 04 ð 106 / 8314 D227 K

The velocity of sound in air at 227 KD334 m/s, which serves as a check on the
calculated data.

PROBLEM 4.8

Over a 30 m length of 150 mm vacuum line carrying air at 293 K, the pressure falls
from 1 kN/m^2 to 0.1kN/m^2. If the relative roughnesse/dis 0.002, what is approximate
flowrate?

Solution

The specific volume of air at 293 K and 1 kN/m^2 is:

v 1 D 22. 4 / 29  293 / 273  101. 3 / 1. 0 D 83 .98 m^3 /kg
It is necessary to assume a Reynolds number to determineR/u^2 and then calculate a
value ofG/Awhich should correspond to the original assumed value. Assume a Reynolds
number of 1ð 105.