  Since the 1930s, theories of skin-friction drag from plates with rough
surfaces have been based by analogy to turbulent flow in pipes with rough
interiors. Failure of this analogy at slow velocities has frustrated attempts
to create a comprehensive theory.
  Utilizing the concept of a self-similar roughness which disrupts the boundary
layer at all scales, this investigation derives formulas for a rough or smooth
plate's skin-friction coefficient and forced convection heat transfer given its
characteristic length, root-mean-squared (RMS) height-of-roughness, isotropic
spatial period, Reynolds number, and the fluid's Prandtl number.
  This novel theory was tested with 456 heat transfer and friction measurements
in 32 data-sets from one book, six peer-reviewed studies, and the present
apparatus. Compared with the present theory, the RMS relative error (RMSRE)
values of the 32 data-sets span 0.75% through 8.2%, with only four data-sets
exceeding 6%. Prior work formulas have smaller RMSRE on only four of the
data-sets.
