An ultrasonic flowmeter of the upstream/downstream sonic propagation type includes two transducers mounted externally on the same side of a flow conduit. The transducers are coupled to respective sonic probes which transmit and receive acoustic pulses between the transducers through the fluid by "bouncing" the pulses off the opposite pipe wall. Additionally the meter maintains a smooth bore in the measurement region so that the acoustic pulses are refracted at the probe/fluid interface and hence propagate along a sonic path that varies depending on the sonic velocities within the fluid and the probe. An acoustic path of known length is included within at least one of the probes along which a portion of the generated acoustic pulses propagates, thereby providing for a third sonic measurement which represents the transmit time in the probe. The three sonic propagation time measurements are necessary and sufficient to specify the flow velocity independent of sound velocity changes in the fluid and the probe and hence of changes in the path of propagation.