A note on the Buckingham equation

Friction losses of the laminar flow of a Bingham plastic fluid through a pipe is characterised by a friction factor, f, which depends on two dimensionless parameters, the Reynolds and the Bingham numbers. The relationship is a fourth degree equation for f, named after Buckingham (1921). In this short communication, we present a novel expression for its only physically meaningful solution, which is easier to handle than those presented previously by other authors.