Mechanical Properties of Fluids NCERT Solutions Class 11 Physics - Solved Exercise Question 10.26

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 × 103 kg/m3
Reynolds’ number for laminar flow, NR = 2000
The largest average velocity of blood is given by the relation:
Varg = NRη / ρd
= 2000 X 2.084 X 10-3 / (1.06 X 103 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 r2Vavg
= 3.14 X (2 X 10-3)2 X 0.983
= 1.235 X 10-5 m3s-1
Therefore, the corresponding flow rate is 1.235 X 10-5 m3s-1

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