  The 80 year-old empirical Colebrook function, widely used as an informal
standard for hydraulic resistance, relates implicitly the unknown flow friction
factor, with the known Reynolds number and the known relative roughness of a
pipe inner surface. It is based on logarithmic law in the form that captures
the unknown flow friction factor in a way that it cannot be extracted
analytically. As an alternative to the explicit approximations or to the
iterative procedures that require at least a few evaluations of computationally
expensive logarithmic function or non-integer powers, this paper offers an
accurate and computationally cheap iterative algorithm based on Pade
polynomials with only one log-call in total for the whole procedure (expensive
log-calls are substituted with Pade polynomials in each iteration with the
exception of the first). The proposed modification is computationally less
demanding compared with the standard approaches of engineering practice, but
does not influence the accuracy or the number of iterations required to reach
the final balanced solution.
