A Doppler shift ultrasonic flow meter uses two piezoelectric crystals each having a natural frequency of 5 MHz. These crystals are used as transmitter and receiver. The transmitter directs an ultrasonic wave into the pipe which makes an angle of $45^{\circ}$ with the direction of flow calculate the received frequency (MHz) for a fluid velocity of 20 m/sec. Assume the velocity of sound in fluid to be 500 m/sec.

4.717

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Solution

The correct option is A 4.717
$Velocity (V) = \frac{C \times (f_{t} - f_{r})}{2 f_{t} cos θ}$

$\Rightarrow f_{r} = [1 - \frac{2}{C} V cos θ] f_{t}$

$Given, C = 500 m/s$

$V = 20 m / s$

$θ = 45^{\circ}$

$f_{t} = 5 M H z$

$On substituting$

$f_{r} = 4.717 M H z$

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The correct option is A 4.717Velocity(V)=C×(ft−fr)2ftcosθ ⇒fr=[1−2CVcosθ]ft Given, C = 500 m/s V=20m/s θ=45∘ ft=5 MHz On substituting fr=4.717 MHz

The correct option is A 4.717
$Velocity (V) = \frac{C \times (f_{t} - f_{r})}{2 f_{t} cos θ}$

$\Rightarrow f_{r} = [1 - \frac{2}{C} V cos θ] f_{t}$

$Given, C = 500 m/s$

$V = 20 m / s$

$θ = 45^{\circ}$

$f_{t} = 5 M H z$

$On substituting$

$f_{r} = 4.717 M H z$