  We present convincing evidence of a direct connection between the pressure
drop, viscous dissipation, and the turbulent energy spectrum. We use this
finding to explain Nikuradse's experimental results of pressure drop for
turbulent flows in rough pipes, in terms of a modified Kolmogorov length scale
that varies with the surface roughness. Furthermore, we use Laufer's
measurements of turbulent energy spectra in pipe flow to calculate -- to a good
approximation -- the turbulent component of the pressure drop directly from an
averaged turbulent energy spectrum. We also show that the incompressibility
assumption, leads to the conclusion that viscous dissipation in fully-developed
(laminar and turbulent) pipe flow, cannot increase the temperature of the fluid
through viscous heating.
