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=2.084×10-3 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:

varg=NRηρd=2000×2.084×10-31.06×103×4×10-3=0.983 m/s

Flow rate is given by:

R=πr2varg=3.14×2×10-32×0.983=1.235×10-5 m3s-1