Generalised Reynolds number for the flow of time-independent fluids

5 Generalised Reynolds number for the flow of time-independent fluids 

It is useful to define an appropriate Reynolds number whieh will result in a unicpie frietion factor-Reynolds number curve for all time-independent fluids in laminar flow in circular pipes. Metzner and Reed [1955] outlined a generalised approach obviating this difficulty. The starting point is equation 3.21  

Applying the Leibnitz rule to the integral on the right-hand side gives  

Introducing a factor of 4 on both sides and further rearrangement of the terms on the left-hand side gives  

(8V/D) is the wall shear rate for a Newtonian fluid and is referred to as the nominal shear rate for a non-Newtonian fluid which is identical to ecjuation (2.5) in Chapter 2. Alternatively, writing it in terms of the slope of logT - log(8V/D) plot s. 

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