Imagine two identical swimmers crossing a river on the same
diagonal line, one with the flow and the other against the flow. The
swimmer moving with the flow needs much less time to reach the
opposite bank.

Ultrasonic waves behave exactly the same way.

The sound wave that flows in the direction of the stream moves
faster than the one that flows against the stream.
The transit times TAB (Transit time of ultrasonic waves from sensor
A to sensor B) and TBA (from sensor B to A) are measured
continuously. The time difference (TBA - TAB) is directly
proportional to the mean flow velocity (Vm) of the liquid.

The flow rate is a result of the velocity multiplied by the
cross section area of the flow tube size.