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After decades of experimental, theoretical, and numerical research in fluiddynamics, many aspects of turbulence remain poorly understood. The main reasonfor this is often attributed to the multiscale nature of turbulent flows, whichposes a formidable challenge. There are, however, properties of these flowswhose roles and inter-connections have never been clarified fully. In thisarticle, we present a new connection between the pressure drop, viscousdissipation, and the turbulent energy spectrum, which, to the best of ourknowledge, has never been established prior to our work. We use this finding toshow analytically that viscous dissipation in laminar pipe flows cannotincrease the temperature of the fluid, and to also reproduce qualitativelyNikuradse's experimental results involving pressure drops in turbulent flows inrough pipes.

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