Question

Figure given below shows an ultrasound flow meter with the transducers separated by a distance $100mm$ with the line joining the transducers making an angle ${60}^o$ with the direction of the flow. The transit time difference between upstream and downstream measurements is $20ns$ with the sound velocity in the medium being $1000m/s$. Assuming that the size of the transducers is very small as compared to the diameter of the pipe, the flow velocity is

• A. $0.2m/s$
• B. $2m/s$
• C. $0.8m/s$
• D. $40m/s$

Answer 1

The correct option is A $0.2m/s$

Given
$\Delta t=20\times {10}^{-9}sec$

$V_s=1000m/sec$

$d=100mm$

$\theta ={60}^o$

So,
$V_f=\frac{\Delta t\times V_s^2}{2dcos\theta }$

$=\frac{20\times {10}^{-9}\times (1000{)}^2}{2\times 100\times {10}^{-3}cos\left({60}^o\right)}$

$=0.2m/sec$