Viscous Newtonian laminar flow in a rectangular channel: Application to Etna lava flows

We introduce a 3D model for near-vent channelized lava flows. We assume the lava to be an isothermal Newtonian liquid flowing in a rectangular channel down a constant slope. The flow velocity is calculated with an analytical steady-state solution of the Navier-Stokes equation. The surface velocity and the flow rate are calculated as functions of the flow thickness for different flow widths, and the results are compared with those of a 2D model. For typical Etna lava flow parameters, the influence of levees on the flow dynamics is significant when the flow width is less than 25 m. The model predicts the volume flow rate corresponding to the surface velocity, taking into account that both depend on flow thickness. The effusion rate is a critical parameter to evaluate lava flow hazard. We propose a model to calculate the effusion rate given the lava flow width, the topographic slope, the lava density, the surface flow velocity, and either the lava viscosity or the flow thickness.