A flow measurement apparatus can include a main flow passage, a bypass flow passage having an inlet and an outlet connected with the main flow passage, a mass flowmeter connected in the bypass flow passage between the inlet and the outlet, and a flow restrictor connected in the bypass flow passage between the inlet and the outlet. A method can include connecting the flow measurement apparatus, so that a fluid flow in the well also flows through the flow measurement apparatus, and determining at least one rheological parameter of a non-Newtonian fluid, based on an output of the flow measurement apparatus.