A flow measurement assembly that includes a production string and a flow meter fluidically coupled to the production string. The flow meter includes a variable Venturi tube attached to and configured to flow production fluid received from the production string. The variable Venturi tube includes an end fixed to the production string and at least one Venturi throat. The flow meter also includes an actuator configured to move the variable Venturi tube with respect to the fixed end. The flow meter includes a processor communicatively coupled sensors coupled to the variable Venturi tube. The processor determines, based on a first fluid parameter and the second fluid parameter received from the sensors, at least one of a mass flow rate of the production fluid, a density of the production fluid, a viscosity of the production fluid, or a coefficient of discharge of the production fluid.