  The friction f is the property of wall-bounded flows that sets the pumping
cost of a pipeline, the draining capacity of a river, and other variables of
practical relevance. For highly turbulent rough-walled pipe flows, f depends
solely on the roughness length scale r, and the f -- r relation may be
expressed by the Strickler empirical scaling f $\propto$ r$^{\frac{1}{3}}$.
Here, we show experimentally that for soap film flows that are the
two-dimensional (2D) equivalent of highly turbulent rough-walled pipe flows, f
$\propto$ r and the f -- r relation is not the same in 2D as in 3D. Our
findings are beyond the purview of the standard theory of friction but
consistent with a competing theory in which f is linked to the turbulent
spectrum via the spectral exponent $\alpha$: In 3D, $\alpha$ = 5/3 and the
theory yields f $\propto$ r$^{\frac{1}{3}}$; in 2D, $\alpha$ = 3 and the theory
yields f $\propto$ r.
