# Acoustic Flowmeter

Written by Jerry Ratzlaff on . Posted in Fluid Dynamics

This type of flowmeter (ultrasonic) can give a continuous measurement of the flow rates of both open channel or pipe. It is nonintrusive, nonmechanical and can give a reading in either flow direction.

There are two types used:

• Ultrasonic Doppler Meter
• Ultrasonic Transit-time Meter

## Acoustic Flowmeter FORMULA

 $$\large{ v_a = \frac {l} {2 \; \cos \; \theta} \left( \frac {1} {t_d} - \frac {1} {t_u} \right) }$$

### Where:

$$\large{ v_a }$$ = average axial velocity of water flow

$$\large{ l }$$ = acoustic path length between transducer faces

$$\large{ t_d }$$ = acoustic signal downstream travel time

$$\large{ t_u }$$ = acoustic signal upstream travel time

$$\large{ \theta }$$ = angle between acoustic path and the pipe's longitudinal axis

### Solve for:

$$\large{ l = \frac {2\; v_a \cos \theta} { \left( \frac {1} {t_d} \;-\; \frac {1} {t_u} \right) } }$$

$$\large{ t_d = \frac {1} { \frac {2 \;v_a \; \cos \; \theta} {l} \;+\; \frac {1} {t_u} } }$$

$$\large{ t_u = \frac {1} { \frac {1} {t_d} \;-\; \frac {2\; v_a \; \cos \; \theta} {l} } }$$

$$\large{ \theta = \arccos \; \left( \frac {l} {2\; v_a} \left( \frac {1} {t_d} - \frac {1} {t_u} \right) \right) }$$