Laminar flow of inelastic fluids in non-circular ducts

7 Laminar flow of inelastic fluids in non-circular ducts 

Note that since for a circular tube, a = 1/4 and b = 3/4, equation (3.91) is consistent with that for circular pipes, equation (3.37). The limited data available on turbulent flow in triangular [Irvine, Jr., 1988] and rectangular ducts [Kostic and Hartnett, 1984] conforms to equation (3.91). In the absence 

Scant analytical and experimental results suggest that visco-elasticity in a fluid may induce secondary motion in non-circular conduits, even rmder laminar conditions. However, measmements reported to date indicate that the friction factor - Reynolds ntrmber behavioin is little influenced by such secondary flows [Hartnett and Kostic, 1989]. 

A power-law fluid (m = 0.3 Pa-s and n = 0.72) of density 1000 kg/m is flowing in a series of ducts of the same flow area but different cross-sections as listed below  

Estimate the pressure gradient required to maintain an average velocity of 1.25 m/s in each of these channels. Use the geometric parameter method. Also, calculate the value of the generalised Reynolds number as a guide to the nature 

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