Comparison of methods for predicting head loss in turbulent pipe flow of non-Newtonian fluids

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Abstract
The flow behaviour of a large variety of industrially important, non-Newtonian fluids can be described well using the Herschel-Bulkley model relating shear stress τ to shear rate γ by τ = τy + Kγn . The three parameters τy, K and n are determined experimentally using viscometers. Depending on the experimental spread of the τ, γ data, estimates of the parameters will have associated confidence intervals at any chosen level (eg 90%), and both estimates and confidence intervals will also depend on the regression method adopted; two methods are compared in this paper. Th e prediction of head losses for laminar flow of the fluid in a pipeline requires a single equation derived from the Herschel-Bulkley model and presents no difficulty. For turbulent head loss prediction the situation is far more complicated. There are many different methods available, and there exist no guidelines regarding which method should be adopted. This paper demonstrates that predictions from these methods differ very widely, and that the uncertainty is compounded by that arising from estimating the τy , K and n parameters due to scatter in viscometric data. It is concluded that head-loss predictions should be made using as many prediction methods as possible, so that an engineering judgement may be made about which prediction is most appropriate for a given set of conditions. Head-loss estimates for turbulent non-Newtonian flow can vary by ±50%. This contrasts starkly with the situation for turbulent Newtonian flow where head-loss estimates vary by no more than ± 4%. A lthough there are a dozen or more methods for Newtonian flow, the Moody equation is used most frequently and is quite adequate.