Laminar non-Newtonian flow in open channels of different cross-sectional shapes: An alternative approach

摘要

An alternative approach based on a general expression derived for laminar non-Newtonian flow in open channels of different cross-sectional shapes using key primary variables is presented. This enabled the channel flow data, which is traditionally presented as a plot of f vs Re_H on logarithmic coordinates from which C is obtained from the -1 slope for laminar flow, to be presented in the form of a plot of Q~n+(τ_yA~(2n))/(K2~nP~n) vs (2~(4-n)gp)/K[(A~(1+2n)sinθ)/P~(1+n)] (i.e. Y vs X) on linear coordinates where the slope of 1/C will be obtained. Example comparisons of the C values obtained from the / vs Re// plots and their corresponding Y vs X plots were presented for fluids exhibiting Newtonian, power law, Bingham plastic and Herschel-Bulkley behaviour. For each of these fluids, good agreement was obtained between these two C values. Of the two plots, the Y vs X plot was found to be the better plot for detecting the change of slope between laminar and transitional flow for each channel angle. This was found to occur when Re_H ＞ 700 for the Newtonian fluid and Re_H = 500 for three different non-Newtonian fluids.