Ncert Exercises & Solutions

10.26 (a) What is the largest average velocity of blood flow in an artery of radius 2×10^–3m 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).

The radius of the artery, r = 2 × 10^–3 m

The diameter of the artery, d = 2 × 2 × 10^–3 m = 4 × 10^–3 m

The viscosity of blood, $η = 2.084 \times 10^{- 3} Pa s$

Density of blood, ρ = 1.06 × 10³ kg/m³

Reynolds’ number for laminar flow, N_R = 2000

The largest average velocity of blood is:

$v_{\arg} = \frac{N_{R} η}{ρd} = \frac{2000 \times 2.084 \times 10^{- 3}}{1.06 \times 10^{3} \times 4 \times 10^{- 3}} = 0.983 m / s$

Flow rate is given by:

$R = {πr}^{2} v_{\arg} = 3.14 \times {(2 \times 10^{- 3})}^{2} \times 0.983 = 1.235 \times 10^{- 5} m^{3} s^{- 1}$

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