(a) What is the largest average velocity of blood flow in an artery of radius 2×10–3m if the flow must remain lanimar? (b) What is the corresponding flow rate ? (Take viscosity of blood to be 2.084 × 10–3 Pa s).
(a) Radius of the artery r=2×10−3m Diameter, D=2×2×10−3m=4×10−3m Viscosity of the blood η=2.084×103Pa Density of the blood ρ=1.06×103kgm−3 Maximum valu of Reynold number of flow to be laminar, NR=20N Average velocity Vc=ρDNRη =1.06×103×4×1032000×2.084×103 =4.244.168=0.98m/s (b) Flow rate is given by the relation: R=πr2V(avg) =3.14×(2×10−3)2×0.983 =1.235×10−5 m3/s Therefore, the corresponding flow rate is 1.235×10−5m3/s.
