FLOW OF MULTIPHASE MIXTURES 75
PairD 4 l/du^2 (equation 3.18)
D 4 ð 0. 002 200 / 0. 102 ð 1. 0 ð 24. 72 D9570 N/m^2 or 9.57 kN/m^2assuming isothermal conditions and incompressible flow.
Px/Pairu^2 s/FD 2805 /u 0 (equation 5.38)∴ PxD 2805 PairF/u 0 u^2 sD 2805 ð 9. 57 ð 1. 0 / 4. 7 ð 18. 652
D 16 .4kN/m^2PROBLEM 5.2
Sand of a mean diameter 0.2 mm is to be conveyed in water flowing at 0.5 kg/s in a
25 mm ID horizontal pipe 100 m long. What is the maximum amount of sand which may
be transported in this way if the head developed by the pump is limited to 300 kN/m^2?
Assume fully suspended heterogeneous flow.
Solution
See Volume 1, Example 5.2.
PROBLEM 5.3
Explain the various mechanisms by which particles may be maintained in suspension
during hydraulic transport in a horizontal pipeline and indicate when each is likely to be
important.
A highly concentrated suspension of flocculated kaolin in water behaves as a pseudo-
homogeneous fluid with shear-thinning characteristics which can be represented approx-
imately by the Ostwald – de Waele power-law, with an index of 0.15. It is found that, if
air is injected into the suspension when in laminar flow, the pressure gradient may be
reduced, even though the flowrate of suspension is kept constant. Explain how this is
possible in “slug” flow, and estimate the possible reduction in pressure gradient for equal
volumetric, flowrates of suspension and air.
Solution
Ifuis the superficial velocity of slurry, then:
For slurry alone:
The pressure drop in a pipe of lengthlis:Kunl.
If the air: slurry volumetric ratio isR, there is no slip between the slurry and the air
and the system consists of alternate slugs of air and slurry, then:
The linear velocity of slurry isRC 1 u