SECTION 5Flow of Multiphase Mixtures
PROBLEM 5.1
It is required to transport sand of particle size 1.25 mm and density 2600 kg/m^3 at the
rate of 1 kg/s through a horizontal pipe 200 m long. Estimate the air flowrate required,
the pipe diameter, and the pressure drop in the pipe-line.
Solution
For conventional pneumatic transport in pipelines, a solids-gas mass ratio of about 5 is
employed. Mass flow of airD 1 / 5 D 0 .20 kg/s
and, taking the density of air as 1.0 kg/m^3 , volumetric flowrate of airD 1. 0 ð 0. 20
D 0 .20 m^3 /sIn order to avoid excessive pressure drops, an air velocity of 30 m/s seems reasonable.
Ignoring the volume occupied by the sand (which is about 0.2% of that occupied by the
air), the cross-sectional area of pipe requiredD 0. 20 / 30 D 0 .0067 m^2 ,
equivalent to a pipe diameter of
p
4 ð 0. 0067 /D 0 .092 m or 92 mm.
Thus a pipe diameter of 101.6mm(100 mm) would be specified.
From Table 5.3 for sand of particle size 1.25 mm and density 2600 kg/m^3 , the free-
falling velocity is:
u 0 D 4 .7m/s
In equation 5.37,uGusD 4. 7 /[0. 468 C 7. 25p
4. 7 / 2600 ]D 6 .05 m/s
The cross-sectional area of a 101.6 mm i.d. pipeDð 0. 10162 / 4 D 0 .0081 m^2.∴ air velocity,uGD 0. 20 / 0. 0081 D 24 .7m/s
and: usD 24. 7 6. 05 D 18 .65 m/s
Taking the viscosity and density of air as 1. 7 ð 10 ^5 Ns/m^2 and 1.0 kg/m^3 respectively,
the Reynolds number for the air flow alone is:
ReD 0. 102 ð 24. 7 ð 1. 0 / 1. 7 ð 10 ^5 D 148 , 000and from Fig. 3.7, the friction factor D 0 .002.