__Question 10.26__:
(a)
What is the largest average velocity of blood flow in an artery of
radius 2 ×
10

^{–3}m if the flow must remain laminar? (b) What is the corresponding flow rate? (Take viscosity of blood to be 2.084 × 10^{–3}Pa s).

__Solution__:**(a)**Radius of the artery,

*r*= 2 × 10

^{–3 }m

Diameter of the artery,

*d*= 2 × 2 × 10

^{–3 }m = 4 × 10

^{– 3 }m

Viscosity of blood, η = 2.084 X 10

^{-3}Pa s

Density of blood,

*ρ*= 1.06 × 10

^{3}kg/m

^{3}

Reynolds’ number for laminar flow,

*N*

_{R}= 2000

The largest average velocity of blood is given by the relation:

V

_{arg}= N

_{R}η /

*ρ*d

= 2000 X 2.084 X 10

^{-3 }/ (1.06 X 10

^{3}X 4 X 10

^{-3})

= 0.983 m/s

Therefore, the largest average velocity of blood is 0.983 m/s.

**(b)**Flow rate is given by the relation:

*R*= π

*r*

^{2}V

_{avg}

= 3.14 X (2 X 10

^{-3})

^{2}X 0.983

= 1.235 X 10

^{-5}m

^{3}s

^{-1}

Therefore, the corresponding flow rate is 1.235 X 10

^{-5}m

^{3}s

^{-1}

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