How ultrasonic flow meters work and where the error comes from

Full article available in Uzbek and Russian.

Ultrasonic flow meters most commonly use the transit-time method: two transducers mounted diagonally across the flow send pulses upstream and downstream. Water movement makes the downstream pulse arrive faster and the upstream pulse slower; the time difference Δt is proportional to flow velocity via v ≈ (c²·Δt)/(2L·cosθ), where c is the speed of sound in water (~1480 m/s at 20°C) — since c enters squared, temperature compensation matters a lot. Doppler-type meters instead measure frequency shift off suspended particles/bubbles and suit turbid water better than clean water.

In a closed pipe, Q = A×v is straightforward since the cross-section is fixed. In an open channel — the relevant case for Uzbekistan's irrigation canals — cross-sectional area varies with water level, so meters combine a velocity sensor with a level sensor: Q(t) = A(h(t)) × v(t). Two independent measurement errors now multiply into the final discharge figure.

Installation requires a straight, undisturbed channel run upstream and downstream, typically 5-10 channel widths, avoiding gates, bends, and pump outlets that generate turbulence.

Field accuracy degrades from vendor-claimed ±1-2% (lab, clean water, straight pipe) due to: silt/sediment on the transducer face, aquatic vegetation, air bubbles, uncompensated temperature effects, poorly calibrated channel geometry curves, and level-sensor drift. Realistic field accuracy with good installation is ±3-5%; poorly installed or unmaintained systems can drift to 20-30% error.