Ever measured velocity of blood in an artery?

Classical Mechanics Level 4

Using a Venturi meter, the flow of blood in a large artery of anesthetized dog is diverted. The wider part of that meter has a cross-sectional area equal to that of the artery and has magnitude 8 mm 2 8\text{ mm}^2 . The narrower part has an area of 4 mm 2 4 \text{ mm}^2 . The pressure drop in the artery is 24 pascals. What is the speed of the blood in the artery in ms − 1 \text{ms}^{-1} ? Give your answer to correct three decimal places.

Take density of blood as 1.06 × 1 0 3 kg m − 3 1.06 \times 10^3 \text{ kg m}^{-3} .

Source: CBSE.


The answer is 0.125.

Nihar Mahajan by Nihar Mahajan , 20, India

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1 solution

Ayon Ghosh
Dec 6, 2017

Equation of continuity followed by Bernoulli Principle gives us

v a r t e r y = ( 2 P ρ ( A a ) 2 − 1 ) 0.5 ≈ 0.125 m / s v_{artery} = (\frac{2P}{\rho(\frac{A}{a})^2-1})^{0.5} \approx 0.125 m/s .

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