(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).

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Solution

(a)Radius of the artery, r = 2 × 10^–3m

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

Viscosity of blood,

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

Reynolds’ number for laminar flow, N_R = 2000

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

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

(b) Flow rate is given by the relation:

R = π r²

Therefore, the corresponding flow rate is.

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