Metzner-Reed Reynolds number ReMR

In general, non-Newtonian flow behavior (or rheology) is of dominant importance in laminar flow because it influences viscous shear. The transition from laminar to turbulent flow is much less sharply defined for non-Newtonian fluids than it is for Newtonian, and it is difficult to predict with any degree of accuracy. However, a value of the Metzner-Reed Reynolds number (ReMR) of 2000 is still a reasonable estimate for the transition from laminar to turbulent flow. 

A typical graph of drag ratio as a function of superficial air velocity is shown in Figure 5.5 in which each curve refers to a constant superficial liquid velocity. The liquids in question exhibited power law rheology and the corresponding values of the Metzner and Reed Reynolds numbers ReMR based on the superficial liquid velocity uL (see Chapter 3) are given. The following characteristics of the curves may be noted ... 

Yooi24) has proposed a simple modification to the Blasius equation for turbulent flow in a pipe, which gives values of the friction factor accurate to within about 10 per cent. The friction factor is expressed in terms of the Metzner and Reed(I8) generalised Reynolds number ReMR and the power-law index n. 

ReMR Metzner and Reed Reynolds number for power-law fluid (see Chapter 3) ... 

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