1. Tardigrade
  2. Question
  3. Physics
  4. The flow of blood in a large artery of an anesthetised dog is diverted through a venturimeter. The wider part of the meter has a cross-sectional area equal to that of the artery, i.e. 10 mm2 . The narrower part has an area 5 mm2 . The pressure drop in the artery is 22 Pa . (Take the density of the blood = 1.06 × 103 kg m-3 . The speed of the blood in the artery is

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Q. The flow of blood in a large artery of an anesthetised dog is diverted through a venturimeter. The wider part of the meter has a cross-sectional area equal to that of the artery, i.e. $ 10\, mm^{2} $ . The narrower part has an area $ 5 \,mm^{2} $ . The pressure drop in the artery is $ 22 \,Pa $ . (Take the density of the blood $ = 1.06 \times 10^{3} kg \,m^{-3} $ . The speed of the blood in the artery is

Mechanical Properties of Fluids

Solution:

Here, $ A = 10\, mm^{2} $ , $ a - 5 mm^{2} $ ,
$ \rho=1.06 \times 10^{3} kg \, m^{-3}=1060\, kg\,m^{-3}, P_{1}-P_{2}=22\,Pa $
Speed of the fluid through the wide neck is
$ v=\sqrt{\frac{2\left(P_{1}-P_{2}\right)}{\rho}} \left\{\left(\frac{A}{a}\right)^{2} -1\right\}^{-1/ 2} $
or $ \frac{A}{a}=\frac{10}{5}=2 $
$ \therefore v=\sqrt{\frac{2\times22}{1060\left(2^{2}-1\right)}} $
$ =0.12 \, m\, s^{-1} $