Question

What is the largest average velocity of the blood flow in an artery of diameter 2 × 10⁻³ m if the floor must remain laminar? Do the dissipative forces become more important as the fluid velocity increases? Discuss qualitatively.

Answer 1

Reynolds’s number, $Re=\frac{\rho vD}{\mu}$
Where,
ρ = density of the fluid
v = largest average velocity of the fluid
D = diameter of the duct
μ = viscosity of the fluid

We have,
Density of the blood, ρ = 1.06 × 10³ kg/m³
Reynolds’s number for laminar flow in duct, Re= 2000
Viscosity of the blood, μ = 2.084 × 10^-3 Nm/s
Thus,
Largest average velocity, $v=\frac{Re\mu}{\rho D}$

= (2000 × 2.084 × 10^-3)/(1.06 × 10³ × 2 × 10^-3)

= (2 × 2.084)/(1.06 × 2)

= 2.084/1.06 

= 1.966 m/s

Dissipative forces are more important when flow velocity is increasing because increase in flow leads to turbulence.