A systematic procedure to determine the minimum pressure gradient required for the flow of viscoplastic fluids in pipes of symmetric cross-section

Using two Lemmas proved by Mosolov and Miasnikov in 1965 for Bingham fluids, a systematic procedure is developed to determine the minimum pressure drop per unit length to initiate the flow of viscoplastic fluids in pipes of symmetric cross-section. It is shown that the Mosolov–Miasnikov approach applies to all viscoplastic fluids with a constant yield stress, such as Casson and Herschel–Bulkley fluids. Explicit values for the pressure drop are found for pipes of the following symmetric cross-sections: circular, annular, square, rectangle, equilateral triangle and L-shaped, when the latter has a pair of equal arms. The case of a pipe of elliptical cross-section is also discussed.