Laminar Flow of Nonnewtonian Fluids in Circular Tubes

3 LAMINAR FLOW OF NONNEWTONIAN FLUIDS IN CIRCULAR TUBES 

Most fluids with pronounced nonnewtonian behavior have such high viscosities that their flow is laminar in most industrially interesting situations. We saw in Sec. 6.3 that for any fluid the shear stress at any point in a horizontal circular pipe is given by 

For laminar flow of newtonian fluids we substituted Newton s law of viscosity for the shear stress and integrated twice to find Pois ille s equation. 

For nonnewtonian fluids we can experimentally determine a plot like Fig. 1,5 of the shear stress as a function of dVIdy (which [equals dV/dr for circular pipe flow). From this plot we can find the equivalent of Poiseuille s equation by two graphical integrations.. This is tedious and has prompted much of the work of trying to find equations that will represent the data in curves such as Fig. 1.5. If the data can be fit by the power law (Eq. 15.2), then the two 

The laminar flow of various kinds of fluids in circular pipes can be easily compared by plotting (DI4) —dPldx) versus 32QI irD ) = SV JD, as shown in Fig, 15.3. This plot (or its equivalent on logarithmic paper) is very widely used in nonnewtonian flow calculations and publications. Its merit can be seen by rewriting Poiseuille s equation (Eq. 6.8) in the form 

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