Non-Newtonian fluid in turbulent flow

A large body of literature is available on estimating friction loss for laminar and turbulent flow of Newtonian and non-Newtonian fluids in smooth pipes. For laminar flow past solid boundaries, surface roughness has no effect (at least for certain degrees of roughness) on the friction pressure drop of either Newtonian or non-Newtonian fluids. In turbulent flow, however, die nature... 

Non-Newtonian fluids in turbulent flow generally show lower friction factors and, consequently, lower pressure drops than do Newtonian fluids at corresponding Reynolds number. A detailed analysis of non-Newtonian flow at turbulent regime began with two papers published by Dodge and Metzner (1959) and Shaver and Merrill (1959). Dodge and Metzner used solutions of carboxymethylcellulose and carbopal (a B. F. Goodrich soluble thickener), as well as clay suspensions. They presented a viscous correlation in terms of parameters from shear-stress-shear-rate data and concluded that... 

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