The coefficient of viscosity of blood is 2.12×10−3 Pa-s and its density is 1.06×103 kgm-3 . Find the blood flow rate (in π×10−6m3s−1 ) corresponding to the largest average velocity in an artery of radius 2×10−3 m for the flow to be laminar.

D=2r=2×2×10−3m=4×10−3mFor laminar flow with maximum velocity, Reynold’s number is NR=2000NR=ρVDη⇒V=NRηρD=(2000)2.12×10−31.06×1034×10−3=1ms−1Corresponding flow rate is Q=AV=πr2VQ=π2×10−32×1=4π×10−6m3s−1x=4

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The coefficient of viscosity of blood is $2.12 \times 10^{- 3}$ Pa-s and its density is $1.06 \times 10^{3} {kgm}^{- 3}$ . Find the blood flow rate $(in π \times 10^{- 6} m^{3} s^{- 1})$ corresponding to the largest average velocity in an artery of radius $2 \times 10^{- 3}$ m for the flow to be laminar.

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Detailed Solution

$D = 2 r = 2 \times 2 \times 10^{- 3} m = 4 \times 10^{- 3} m$

For laminar flow with maximum velocity, Reynold’s number is $N_{R} = 2000$

$N_{R} = \frac{ρ VD}{η}$

$\Rightarrow V = \frac{N_{R} η}{ρ D} = \frac{(2000) (2.12 \times 10^{- 3})}{(1.06 \times 10^{3}) (4 \times 10^{- 3})} = 1 {ms}^{- 1}$

Corresponding flow rate is $Q = AV = (π r^{2}) V$

$Q = π {(2 \times 10^{- 3})}^{2} \times 1 = 4 π \times 10^{- 6} m^{3} s^{- 1}$

$x = 4$

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