In deriving Bernoulli’s equation, we equated the work done on the fluid in the tube to its change in the potential and kinetic energy. (a) What is the largest average velocity of blood flow in an artery of diameter 2 × 10–3 m if the flow must remain laminar? (b) Do the dissipative forces become more important as the fluid velocity increases? Discuss qualitatively.
(a) Reynolds’s number,
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,
= 1.962 m/s
(b) Dissipative forces are more important when flow velocity is increasing because increase in flow leads to turbulence.