Question

(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).

Answer 1

Given that

r=2× 10 −3  m

d=2r=4× 10 −3  m

η=

Viscosity of the blood =2.084× 10 −3  Pa-s

ρ=

Density of the blood =1.06× 10 3   kgm -3

For laminar flow, N R =2000

(a)

The expression for the velocity is,

υ c = N R η ρd υ c = 2000×2.084× 10 −3 1.06× 10 3 ×4× 10 −3 υ c =0.98 m/s

Thus, the largest average velocity of blood flow in an artery is 0.98 m/s .

(b)

Volume of flow per second is given by,

V c =π r 2 υ c

Substitute the values.

V c = 22 7 × ( 2× 10 −3 ) 2 ×0.98 V c =1 .24×10 -5   m 3 s -1

Thus, the corresponding flow rate is 1 .24×10 -5   m 3 s -1 .