Evaluation of flow rate for a one-dimensional lava flow with power-law rheology

During the emplacement lava behaves as a non- Newtonian, pseudoplastic fluid. Laboratory experiments on lava samples suggest that a power-law constitutive equation may be appropriate. We consider a horizontally unbounded, isothermal layer of lava, flowing down a slope driven by the gravity force. We consider a constitutive equation where shear stress is proportional to strain rate raised to a power n, ranging from 0 to 1, and we take into account the temperature dependence of the rheological parameters. Formulae are obtained relating the lava rheology to the geometric and dynamic parameters of a lava flow. Under the model assumptions, if we know the temperature dependence of the rheological parameters, these formulae allow to evaluate the flow rate from the field measurements of the temperature, and the thickness or the surface velocity of a lava flow.