Abstract: When Bingham fluid is in motion, plugged flow often occurs at places far from the boundary walls. As there is not a decisive formula of constitutive relation for plugged flow, in some problems the solutions obtained may be indefinite. In this paper, annular flow and pipe flow are discussed, and unique solution is obtained in each case by utilizing the analytic property of shear stress. The solutions are identical in form with the commonly used formula for the pressure drop of mud flow in petroleum engineering.

Key words: finite elastic-plastic deformations, generalized Prandtl-Reuss constitutive equations, the corotational rates of stress tensor, simple shear stress oscillation