Similarity relations for laminar pipe flows of Bingham fluids in friction coordinates

We introduce novel similarity relations, along with their corresponding symmetry groups, for examining the velocity profile and friction factor of laminar Bingham fluid flows using friction coordinates. Specifically, we provide a valuable new expression for calculating the friction factor of Bingham plastic fluids when pressure gradient data is accessible. Our findings reveal that there are no clear similarity relations for the mean velocity profile (MVP) and friction factor formulas in bulk coordinates. Consequently, friction coordinates serve as the most suitable framework for describing this problem.