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Question: The flow of blood in a large artery of an anesthetised dog is diverted through a venturimeter. The w...

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.,1.06×103 kg m−31.06 \times 10 ^ { 3 } \mathrm {~kg} \mathrm {~m} ^ { - 3 }The speed of the blood in the artery is

A

0.12 m s−10.12 \mathrm {~m} \mathrm {~s} ^ { - 1 }

B

0.62 m s−10.62 \mathrm {~m} \mathrm {~s} ^ { - 1 }

C

0.24 m s−10.24 \mathrm {~m} \mathrm {~s} ^ { - 1 }

D

0.42 m s−10.42 \mathrm {~m} \mathrm {~s} ^ { - 1 }

Answer

0.12 m s−10.12 \mathrm {~m} \mathrm {~s} ^ { - 1 }

Explanation

Solution

Here,

A=10 mm2,a=5 mm2,ρ=1.06×103kgm−3\mathrm { A } = 10 \mathrm {~mm} ^ { 2 } , \mathrm { a } = 5 \mathrm {~mm} ^ { 2 } , \rho = 1.06 \times 10 ^ { 3 } \mathrm { kgm } ^ { - 3 }

Speed of the fluid through the wide neck is

Or