  Ever since Nikuradse's experiments on turbulent friction in 1933, there have
been theoretical attempts to describe his measurements by collapsing the data
into single-variable functions. However, this approach, which is common in
other areas of physics and in other fields, is limited by the lack of rigorous
quantitative methods to compare alternative data collapses. Here, we address
this limitation by using an unsupervised method to find analytic functions that
optimally describe each of the data collapses for the Nikuradse dataset. By
descaling these analytic functions, we show that a low dispersion of the scaled
data does not guarantee that a data collapse is a good description of the
original data. In fact, we find that, out of all the proposed data collapses,
the original one proposed by Prandtl and Nikuradse over 80 years ago provides
the best description of the data so far, and that it also agrees well with
recent experimental data, provided that some model parameters are allowed to
vary across experiments.
