Abstract: Described herein are thermal mass flow sensors that combine calorimetric and anemometric (e.g., hot-wire) elements to provide a hybrid approach to determining flow rate of a liquid. The flow probes or flow sensors are configured to use a heater to apply heat to a thermally-conducting material in contact with the flowing liquid, to measure a temperature of the thermally-conducting material upstream of the heater and downstream or at the heater, to adjust power to the heater to achieve a targeted temperature difference, and to determine a flow rate based at least in part on the power supplied to the heater and the measured temperatures. This approach provides flow rate due at least in part to the fluid cooling the thermally-conductive material proportionate to flow rate with non-linear effects. This hybrid approach can provide accurate readings of flow rates of liquids delivered through an IV line to a patient.