the effect of the particle size distribution on non-newtonian turbulent ...

Chapter 5 Discussion Page 5.10
Moody chart. This is ano<strong>the</strong>r downfall <strong>of</strong><strong>the</strong> Bowen method. However, if using <strong>the</strong> Slatter
method you would simply select <strong>the</strong> appropriate roughness <strong>effect</strong> for <strong>the</strong> Roughness Reynolds
Number (ie. <strong>the</strong> representative <strong>particle</strong> <strong>size</strong> or <strong>the</strong> pipe hydraulic roughness, whichever is <strong>the</strong>
greater). It is suggested however, that test work is first conducted in smooth pipes to ensure
that <strong>particle</strong> roughness turbulence is indeed occurring. If testing takes place in a pipe with
pipe hydraulic roughness higher than <strong>the</strong> representative <strong>particle</strong> <strong>size</strong> <strong>the</strong> <strong>particle</strong> roughness
<strong>effect</strong> will not be detected.
This investigation does highlight <strong>the</strong> fact that <strong>the</strong> <strong>particle</strong> roughness <strong>effect</strong> is valid for <strong>the</strong>
slurries tested and must be used in turbulent flow modelling. The <strong>particle</strong> roughness <strong>effect</strong>
should be incorporated in <strong>the</strong> turbulent analysis <strong>of</strong> non-Newtonian slurries, as has been used
in <strong>the</strong> <strong>the</strong>ory for Slatter's analysis, to account for rough wall turbulent flow and to predict
<strong>the</strong> change from smooth wall to rough wall turbulent flow.
5.8 REYNOLDS NUMBER VS FRICTION FACTOR PLOTS
Figure 5.3 to Figure 5.5 shows <strong>the</strong> plot <strong>of</strong> Reynolds number vs friction factor, also called
Moody plots, for <strong>the</strong> Newtonian approximation Reynolds Number, Metzner & Reed Reynolds
Number, and a Reynolds number published by Slatter & Lazarus (1993) <strong>of</strong> <strong>the</strong> form
Re = 8 P V 2
Ty"'K D
[ 8V) n
(5.1)
which can be derived by considering <strong>the</strong> Newtonian approximation and substituting <strong>the</strong> bulk
shear rate in place <strong>of</strong> true shear rate (Slatter, 1994). Included in <strong>the</strong> plots are <strong>the</strong> laminar
flow line (ie. f=16/Re) and <strong>the</strong> Prandtlline (Newtonian smooth wall).
The Moody chart shows that for <strong>the</strong> turbulent flow <strong>of</strong> Newtonian fluids, pipe roughness can
have an appreciable <strong>effect</strong>. As can be seen from Figure 5.3 <strong>the</strong> turbulent flow data tends to
lie in straight horizontal lines for <strong>the</strong> various slurries and does not follow <strong>the</strong> oblique Prandtl
line as suggested by Kemblowski & Kolodziejski (1973). This indicates that f is constant
with increasing Reynolds numbers and hence it is independent <strong>of</strong> rheology. This trend is