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When ultrasound is transmitted from Transducer ‘X’ to Transducer ‘Y’ the speed at which the sound travels through the liquid is accelerated by the velocity of the liquid.
 
If sound is transmitted in the opposite direction it decelerates because it is travelling against the flow of the liquid.
X Y
The differences in time taken to travel the same distance but in opposite directions are directly proportional to the flow velocity of the liquid. Having measured the flow velocity and knowing the pipe cross-sectional area, the volumetric flow can be easily calculated.
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