Flow sensors, systems, and methods for continuous in situ monitoring of a rheologically complex fluid flow within a vessel, such as particulate and multiphase media for ascertaining certain fluid flow parameters, such as flow rate, dynamic viscosity, fluid density, fluid temperature, particle density and particle mass, from flow sensor measurements. The system involves a fluid flow sensor having a body member with internalized strain gauges configured to measure the deformation of certain segments of the body member. Based, at least in part, on these deformation measurements, the system is used to compute the fluid flow parameters.