Revisiting a Reynolds experiment: head loss in non-fully developed, unsteady flow - H.S. Tang; Priata Saha (Physics Open)
Head loss plays a central role in fluid flows. The head loss in fully developed, steady flows is relatively clear, and its calculation has matured and been applied widely in practical problems with success. However, there is a lack of understanding and effective methods to estimate head loss in non-fully developed, unsteady flows. This paper revisits a Reynolds experiment, which, unlike the original experiment by Reynolds in 1883, adopts unsteady flows (with non-constant water heads) exhibiting negative inertia heads. It discusses their head loss in a tube section where the flows have not fully developed. It shows that the head loss is higher in unsteady flows than in steady flows, with the difference being about two orders of magnitude greater than the inertia head. Also, it illustrates that the Darcy-Weisbach equation cannot replicate the measurement data for the head loss in both steady and unsteady, non-fully developed flows. Moreover, the paper presents an expression for head loss in such unsteady flows in terms of steady-flow head loss and inertia head.