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

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.