Question

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.

Answer 1

(a)

Given:

d=

Diameter of the artery =2× 10 −3  m

η=

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

ρ=

Density of the blood =1.06× 10 3   kg/ m 3

N R =Reynolds number for laminar flow =2000

Then the largest average velocity of the blood flow is given as,

υ c = N R η ρd

Substitute the values.

υ c = 2000×2.084× 10 −3 1.06× 10 3 ×2× 10 −3  m υ c =1.966 m/s

Then, the largest velocity of the flow of the blood is 1.966 m/s

(b)

Dissipative forces are the forces in which energy is lost from the system even in motion. If dissipative forces are present in the veins blood flow, then some of the force is spent against dissipative forces due to pressure difference, which causes pressure difference to become larger.

Dissipative forces are more important with increase in fluid velocity due to turbulence, which overcomes the damping effect of fluid viscocity.