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

Chapter 2 Literature Review Page 2.40
Two equations were postulated by Maude & Whitrnore (1958) for turbulent flow. The
criterion as to which equation to use being when <strong>the</strong> <strong>particle</strong> diameter is greater than half <strong>the</strong>
thickness <strong>of</strong><strong>the</strong> viscous sub-layer. The equation for determining <strong>the</strong> thickness <strong>of</strong><strong>the</strong> viscous
sub-layer was given by:
o = [11,7 p. - .!.k' Cd] (l - k'cr l .
P, V. 2
The turbulent flow equations for 0 ;:: lhd is given by:
1 _ -0,815 I [66,3 1 _ d k'c ]
If - 0,408p oglO Re If (1 - k'c) D (1 - k'c)
The turbulent flow equations for 0 < lhd is given by:
1
If
2.11.7
-0,815 I [66,3] _ 0,531 + 4 14
oglO ' .
0,408p Re If 0,408p
The Bowen Correlation
(2.81)
_ 0,531 + 4,14 .(2.82)
0,408p
(2.83)
Bowen (1961) noted that no universal correlation had been suggested for non-Newtonian
flUids and hence published a method which appeared to be applicable to all fluids. The basis
<strong>of</strong> his method was his finding that on a log-log pseudo-shear diagram <strong>the</strong> turbulent branches
<strong>of</strong>different diameters appeared to describe similar straight lines, with each branch appearing
to be almost parallel to <strong>the</strong> next. He suggested that if <strong>the</strong> shear stress or shear rate were
mUltiplied by a function <strong>of</strong> <strong>the</strong> diameter, a correlation <strong>of</strong> <strong>the</strong> turbulent data might be
obtained. Hence, he was able to correlate <strong>the</strong> diameter <strong>effect</strong> by adapting <strong>the</strong> Blasius
equation (equation 2.28) for Newtonian fluids and obtain <strong>the</strong> following correlation:
Where k and b are constants.
Bowen presented four worked examples to substantiate his method.
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