On the missing link between pressure drop, viscous dissipation and the turbulent energy spectrum

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.