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

Chapter 2 Literature Review Page 2.12
The partial integration <strong>of</strong> equation 2.9 using equation 2.10 and equation 2.12 leads to:
3
rD '. du
Q = - - • J r- - - dT ,
8 [ TO ] 0 dr
where <strong>the</strong> shear stress at <strong>the</strong> wall is given by:
T = Ddp
o 4 L
(2.12)
(2.13)
(2.14)
The flow rate for <strong>the</strong> yield pseudoplastic model, <strong>the</strong> Bingham plastic model or <strong>the</strong> power law
model can hence be obtained by substitution <strong>of</strong> <strong>the</strong> relevant rheological equation ie. equation
2.6, equation 2.7 or equation 2.8 respectively. As mentioned, <strong>the</strong> yield pseudoplastic model
- - -is
to used for this study <strong>the</strong>refore substituting equation 2.6 into equation 2.13 yields:
4n
1
• n 3
TO
K
2.7.3 Generalized Approach for Laminar Flow
(2.15)
Metzner & Reed (1955) proposed a generalized correlation for any time independent fluid.
This is based upon a relationship developed by Rabinowitsch (1929) and Mooney (1931) for
<strong>the</strong> calculation <strong>of</strong> shear rates at <strong>the</strong> wall <strong>of</strong> a pipe, where:
[ _dU] = l. [ 8Y]
dr 0 4 D
I 8Y
+ - - To'
4 D
(2.16)