FLOW OF COMPRESSIBLE FLUIDS 71
PROBLEM 4.11
Air is flowing at the rate of 30 kg/m^2 s through a smooth pipe of 50 mm diameter and
300 m long. If the upstream pressure is 800 kN/m^2 , what will the downstream pressure
be if the flow is isothermal at 273 K? Take the viscosity of air as 0.015 mN s/m^2 and
assume that volume occupies 22.4m^3. What is the significance of the change in kinetic
energy of the fluid?
Solution
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)The specific volume at the upstream condition is:
v 1 D 22. 4 / 29 273 / 273 101. 3 / 800 D 0 .098 m^3 /kg
G/AD30 kg/m^2 s∴ ReD 0. 05 ð 30 / 0. 015 ð 10 ^3 D 1. 0 ð 105
For a smooth pipe,R/u^2 D 0 .0032 from Fig. 3.7.
Substituting gives:
30 ^2 ln 800 /P 2 CP^22 8002 ð 106 / 2 ð 800 ð 103 ð 0. 098 C 4 0. 0032 300 / 0. 05 30 ^2 D 0and the downstream pressure,P 2 D793 kN/m^2
The kinetic energy termDG/A^2 ln 800 / 793 D 7 .91 kg^2 /m^4 s^2
This is insignificant in comparison with 69,120 kg^2 /m^4 s^2 which is the value of the
other terms in equation 4.55.
PROBLEM 4.12
If temperature does not change with height, estimate the boiling point of water at a height
of 3000 m above sea-level. The barometer reading at sea-level is 98.4kN/m^2 and the
temperature is 288.7 K. The vapour pressure of water at 288.7 K is 1.77 kN/m^2 .The
effective molecular weight of air is 29 kg/kmol.
Solution
The air pressure at 3000 m isP 2 and the pressure at sea level,P 1 D 98 .4kN/m^2.
∫
vdPC
∫
gdzD 0vDv 1 P/P 1