Energy dissipation during laminar planar jump of a generalised time-independent non-Newtonian liquid – An analytical approach

This study presents an in-depth analysis of the energy dissipation and momentum balance during a laminar planar hydraulic jump in a viscous free surface flow, with shallow flow theory used to estimate the relevant jump parameters. The inclusion of momentum and kinetic energy correction factors incorporates the influence of the fluid nature. The fluid is described by the generalised Herschel–Bulkley model with Papanastasiou regularisation, which reduces to the Bingham plastic, power-law and Newtonian models under relevant limiting conditions. The analysis, extensively validated against experimental and simulated data, is explored to understand the physics of free surface flow during jump formation. Energy dissipation increases with an increase in the flow behaviour index n , flow consistency index k and yield stress τ o since each of them increases the apparent viscosity. Interestingly, it is higher in the supercritical (upstream) compared with the subcritical (downstream) zone. For constant discharge rate and film thickness, the specific energy depends on the velocity profile and is thus a function of n and τ o but not k, and the mechanism of influence of n and τ o are also different. For a generalised approach, energy dissipation and jump parameters are discussed as a function of relevant non-dimensional numbers obtained from SFT. Energy dissipation during a hydraulic jump in non-Newtonian liquids is a hitherto unexplored aspect. In fact, energy dissipation during a planar jump in a viscous Newtonian liquid is also rare, although hydraulic jumps are primarily used as energy dissipators in free surface flows.