Question

A transit time ultrasonic flow meter is used for flow rate measurement of a clean liquid. The differential transit time measured using an electronic timer was found to be $1\mu sec.$ If the velocity of sound in the liquid is 1600 m/s and the transducer wedge angle is ${45}^0$ as shown then the approximate flow rate of the liquid $\left(\frac{m^3}{s}\right)$ is ?

• A. 1.0048

Answer 1

The correct option is A 1.0048
$\text{Give pipe diameter = 100 cm}$

Hence, the distance between the transmitter and the receiver pair is

$L=\frac{100}{sin{45}^0}=\sqrt{2}\times 100cm$

$\text{Now velocity is given as;}$

$\Delta T=\frac{2\upsilon Lcos\theta }{c^2}$

$\text{Where c = velocity of ultrasound = 1600 m/s}$

$\Delta T=\text{Differential transit time = 1}\mu \text{sec}$

$\theta =\text{Wedge angle}={45}^o$

$\upsilon =\text{velocity of flowing fluid}=?$

$\Rightarrow 1\mu sec=\frac{2\times \upsilon \times \sqrt{2}\times 100cos{45}^0\times {10}^{-2}}{(1600{)}^2}$

$\Rightarrow \upsilon =\frac{1\times {10}^{-6}\times (1600{)}^2}{2}$

$\upsilon =1.28m/s$

$\text{Flow rate}\left(Q\right)=\upsilon .A=\upsilon \times \frac{\pi }{4}{D}^2$

$=1.28\times \frac{\pi }{4}\times 1^2$

$Q=1.0048{\text{m}}^3/\text{s}$