Multiphase flowmeters and related methods are disclosed herein. An example apparatus includes a flowmeter and a fluid conduit to provide a flow path for a fluid relative to the flowmeter. The example apparatus includes a sensor coupled to the fluid conduit to generate data indicative of at least one of a presence, an absence, or a mass flow rate of solids in the fluid during flow of the fluid through the fluid conduit. The example apparatus includes a processor. The sensor is to be communicatively coupled to the processor. The processor is to selectively determine flow rates for one or more phases of the fluid based on data generated by the flowmeter and a first algorithmic mode or a second algorithmic mode selected based on the sensor data.