A dryer appliance and a method of operating the same to detect blockages are provided. The dryer appliance includes an exhaust conduit that defines a flow restriction and is in fluid communication with a drying chamber. A differential pressure sensor is operably coupled to the exhaust conduit at the flow restriction and a controller is configured for using a measured pressure differential to obtain an air flow rate and determine whether a blockage is present in the exhaust conduit, e.g., by comparing the measured flow rate to a baseline, zero-blockage flow rate.