Acoustic Flowmeter

Written by Jerry Ratzlaff on . Posted in Fluid Mechanics

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

FORMULA

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

Where:

\(v_a\) = average axial velocity of water flow

\(l\) = acoustic path length between transducer faces

\(\theta\) = angle between acoustic path and the pipe's longitudinal axis

\(t_d\) = acoustic signal downstream travel time

\(t_u\) = acoustic signal upstream travel time

Solve for:

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

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

\(t_d  =   \frac {1}        {  \frac {2 v_a  \cos \theta} {l}   \;+\;  \frac {1} {t_u} } \)

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