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

Chapter 2 Literature Review Page 2.21
I{ =
4 log(Re If) - 0,4 .
(2.30)
Even though this equation was proposed for a much wider range <strong>of</strong> Reynolds numbers, <strong>the</strong>
Reynolds numbers <strong>of</strong> <strong>the</strong> vast majority <strong>of</strong>non-Newtonian fluids rarely exceeds 100 000 due
to <strong>the</strong> viscous nature <strong>of</strong> <strong>the</strong>se fluids.
However, even though <strong>the</strong> simple Blasius type equations can be used, most <strong>of</strong> <strong>the</strong> work to
develop semi-<strong>the</strong>oretical models for turbulent flow <strong>of</strong> Newtonian fluids in pipes has centred
around <strong>the</strong> mixing length model <strong>of</strong> Prandtl (1926).
0.01
0.00 1-f---r--r-;..-rrTT.,,---.----.T"T"T"TTTT--r-r.....,...,....,.-T"TTi
1000 10000 100000 1000000
Reynolds Number (Re)
Figure 2.9: Graphical comparison <strong>of</strong> Blasius, Knudsen & Katz and von
Karmen friction factor equations for turbulent flow
2.9.5 Smooth Wall Turbulence
In turbulent flow, <strong>the</strong> interchange <strong>of</strong>momentum between layers, due to eddy formation, sets
up shear stresses, also koown as Reynolds stresses (Schlichting, 1968). The shear stress in
<strong>the</strong> turbulent core must be related to <strong>the</strong> shear rate in order to obtain <strong>the</strong> velocity <strong>distribution</strong>
and flow rate (Janna, 1983).