CHEMICAL ENGINEERING

84 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

At 6 MN/m^2 and 1 MN/m^2 , the masses of air in the cylinder are 2308 and 383.4 kg
respectively.

∴ The time for the pressure to fall to 1 MN/m^2 D9240 ln 2308 / 3834. 4 

D 16 ,600 s 4 .61 h

As 0.15 MN/m^2 is still within the linear region, the time for the pressure to fall to this
value is 34,100 s. 9 .47 h

PROBLEM 6.7

Air, at 1500 kN/m^2 and 370 K, flows through an orifice of 30 mm^2 to atmospheric pres-
sure. If the coefficient of discharge is 0.65, the critical pressure ratio 0.527, and the ratio
of the specific heats is 1.4, calculate the mass flowrate.

Solution

If the critical pressure ratiowc is 0.527 (from Problem 6.6), sonic velocity will occur
until the pressure falls to 101. 3 / 0. 527 D 192 .2kN/m^2. For pressures above this value,
the mass flowrate is given by:

GDCDA 0

√

kP 1 /v 1 [2/kC 1 ]kC^1 /k^1  (equation 6.29)

IfkD 1. 4 ,GDCDA 0

√

 1. 4 P 1 /v 1  2 / 2. 4 ^2.^4 /^0.^4 DCDA 0

p

 0. 468 P 1 /v 1 

P 1 D 1 , 500 ,000 N/m^2

and: v 1 D 22. 4 / 29  370 / 273  101. 3 / 1500 D 0 .0707 m^3 /kg

Substituting gives:GD 0. 65 ð 30 ð 10 ^6 

p

 0. 486 ð 1 , 500 , 000 / 0. 0707 D 0 .061 kg/s

PROBLEM 6.8

Water flows through an orifice of 25 mm diameter situated in a 75 mm pipe at the rate of
300 cm^3 /s. What will be the difference in level on a water manometer connected across
the meter? Viscosity of water is 1 mN s/m^2.

Solution

See Volume 1, Example 6.1.

PROBLEM 6.9

Water flowing at 1.5 l/s in a 50 mm diameter pipe is metered by means of a simple
orifice of diameter 25 mm. If the coefficient of discharge of the meter is 0.62, what will