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Home » (a) What is the largest average velocity of blood flow in an artery of radius 2×10–3m if the flow must remain lanimar? (b) What is the corresponding flow rate ? (Take viscosity of blood to be 2.084 × 10–3 Pa s).
(a) What is the largest average velocity of blood flow in an artery of radius 2×10–3m if the flow must remain lanimar? (b) What is the corresponding flow rate ? (Take viscosity of blood to be 2.084 × 10–3 Pa s).
CBSE | Class 11 | Mechanical Properties of Fluids | NCERT | Physics
(a) What is the largest average velocity of blood flow in an artery of radius 2×10–3m if the flow must remain lanimar? (b) What is the corresponding flow rate ? (Take viscosity of blood to be 2.084 × 10–3 Pa s).

Answer :

According to the question, the radius of the vein is

r = 2 × 10-3 m
And the diameter of the vein is

d = 2 × 1 × 10-3 m = 2 × 10-3 m
The viscosity of blood is given by

η = 2.08 x 10-3 m
The density of blood is

ρ = 1.06 × 103 kg/m3

(a) It is known that NR = 2000, i.e., Reynolds’ number for laminar flow
Therefore, expression for the greatest  average velocity of blood is

{{V}_{avg}}=\frac{{{N}_{R}}\eta }{\rho d}=\frac{2000\times 2.084\times {{10}^{-3}}}{1.06\times {{10}^{3}}\times 4\times {{10}^{-3}}}

{{V}_{avg}}=0.983m/s

(b) The flow rate is given by

R = Vavg π r2

R = 0.983 x 3.14 x ( 10-3)2

R = 1.235 x 10-6 m3/s

i

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