Title: On the missing link between pressure drop, viscous dissipation, and the turbulent energy spectrum,
Abstract: After decades of experimental, theoretical, and numerical research in fluid
dynamics, many aspects of turbulence remain poorly understood. The main reason
for this is often attributed to the multiscale nature of turbulent flows, which
poses a formidable challenge. There are, however, properties of these flows
whose roles and inter-connections have never been clarified fully. In this
article, we present a new connection between the pressure drop, viscous
dissipation, and the turbulent energy spectrum, which, to the best of our
knowledge, has never been established prior to our work. We use this finding to
show analytically that viscous dissipation in laminar pipe flows cannot
increase the temperature of the fluid, and to also reproduce qualitatively
Nikuradse's experimental results involving pressure drops in turbulent flows in
rough pipes.