## 1000

Figure 5-22. Logarithmic plot of consistency curves for Newtonian fluids.

unsheared material. The flattening occurs because the local shear rate decreases towards the center of the pipe, and the local viscosity increases accordingly. The degree of flattening increases with decrease in n, according to the following equation:18

Figure 5-23. Dependence of velocity profiles upon flow behavior index. Average velocity of 5 ft/sec in all cases. (From MetznerS7 Courtesy of Academic

Press.)

Figure 5-23. Dependence of velocity profiles upon flow behavior index. Average velocity of 5 ft/sec in all cases. (From MetznerS7 Courtesy of Academic

Press.)

5 9 shows that the arithmetic plots of multispeed viscometer data are not linear at low rotor speeds, contrary to the Reiner-Riwlin equation, and Figure 5 24 shows that (except for one polymer-brine fluid) the logarithmic plots are also not linear, contrary to the ideal power law. Similarly, Speers19a found that a linear regression technique for calculating n and K from the Fann 600 and 300 rpm readings did not give valid results with a bentonite suspension because of the non-linearity of the log-log plot. Low-solid and polymer fluids, clay muds heavily treated with thinners, and oil-base muds all tend towards pseudoplastic behavior; high-solid muds, and untreated and flocculated clay muds act more like Bingham plastics.

The generalized power law extends the power law (Equation 5 31) to covcr the flow behavior of these diverse fluids. The non-linearity of their logarithmic consistency curves shows that n and K are not constant with rate of shear, as required by the power law, and therefore Equation 5-39 cannot be used to determine the flow behavior of such fluids in pipes. Metzner and Reed20 developed the generalized power law to avoid this difficulty. Their work was based on concepts originally developed by Rabinowitsch.-1 and also by Mooney,22 who showed that for laminar flow of any fluid whose

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