We introduce 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 expression for calculating the friction factor of Bingham plastic fluids when pressure gradient data are accessible. Our findings reveal that there are no clear similarity relations for the mean velocity profile and friction factor formulas in bulk coordinates. Consequently, friction coordinates serve as the most suitable framework for describing this problem.

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• Laminar flows
• Non-Newtonian fluids
• Self-similarity