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

Chapter 2 Literature Review
• ..Page
2.20
Figure 2.8: Magnified view <strong>of</strong> a rough pipe wall showing <strong>the</strong> viscous sub-layer
and <strong>the</strong> slurry <strong>particle</strong>s
The Blasius equation is applicable to <strong>the</strong> range 3000 < Re < 100 000 where,
f = 0,079 Reo. 25 • (2.28)
Knudsen & Katz (1958) proposed a similar equation for fully developed turbulent Newtonian
flow supposedly applicable to <strong>the</strong> range 5000. < Re < 200 000 where,
f = 0,046 Reo. 2 •
(2.29)
Equation 2.29 is about 10% below equation 2.28 at low Reynolds numbers but meets it at
higher Reynolds numbers (Bowen, 1961). A logarithmic plot <strong>of</strong>f vs Re (Figure 2.8) for <strong>the</strong>
above equations yields a straight line and over <strong>the</strong> years evidence has supported this single
line correlation. For example, Cadwell & Babbitt (1941), who studied <strong>the</strong> flow <strong>of</strong> muds,
Sludges and suspensions in circular pipes concluded that head loss in <strong>the</strong> turbulent flow
regime can be calculated from <strong>the</strong> Blasius equation if<strong>the</strong> density <strong>of</strong> <strong>the</strong> slurry and a proper
viscosity (defined under larninar flow conditions) are used.
The von Karmen equation (1930) based on <strong>the</strong> Prandtl (1926) mixing length model was
proposed to represent moreexactly <strong>the</strong> experimental data for Reynolds numbers for <strong>the</strong> range
3000 < Re < 300 000 where,