Bingham plastics, fluid flow circular pipes

For a Bingham plastic fluid flow in a circular pipe and annular space, the effective viscosities are given as [61]. 

A Bingham plastic material is flowing under streamline conditions in a pipe of circular cross-section. What are the conditions for one half of the total flow to be within the central core across which the velocity profile is fiat The shear stress acting within die fluid Ry varies with velocity gradient du,/dy according to the relation ... 

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