Consider a blood artery of cross section A=1.7mm^2. It branches into two identic

Question

Consider a blood artery of cross section A=1.7mm^2. It branches into two identical narrower arteries each of cross sectional area A'=0.85mm^2. An equal volume of blood flows in each branch. Blood flows in the larger artery at a speed of 1.5cm/s.

1) At what speed does blood flow in the narrower branches? Answer 1.5cm/s

2) Now one of the branches gets clogged by cholesterol deposits allowing no flow through it. At what speed would blood flow in the other branch? Answer 3cm/s

3) The blood pressure in the open branch compares to the blood pressure in the larger artery as floows: Answer smaller.

I thought the F would be smaller but the pressure would be the same.

I think i'm quite not sure of the fluid concept please help! THank you :)

Explanation / Answer

a) By equation of continuity,

Volume of blood flowing through  large artery = Volume of blood flowing through  both branches

Av = 2A’v’

v’ = (Av)/(2A’) = (1.7*1.5)/(2*0.85) = 1.5cm/s

b) Volume of blood flowing through  large artery = Volume of blood flowing through  one branch  

Av = A’v’

v’ = (Av)/(A’) = (1.7*1.5)/(0.85) = 3.0 cm/s

c) By Burnollie’s principle

P1 + 1/2**v^2 + gh = P2 + 1/2**v’^2 + gh’

Artery and the branch are at same height hence h=h’

and v=1.5cm/s = 0.015m/s  , v’=3cm/s = 0.03m/s

We get P1< P2

Thus the blood pressure in the open branch compares to the blood pressure in the larger artery is small.

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