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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 -

Answer: (a) 1.966m/s (b) Yes

(a) Diameter of theartery, d = 2 × 10–3 m

Viscosity of blood, 

Density of blood, ρ = 1.06 × 103 kg/m3

Reynolds’ number for laminar flow, NR =2000

The largest average velocity of blood is given as:

Therefore, the largest average velocity of blood is 1.966 m/s.

(b) As the fluid velocityincreases, the dissipative forces become more important. This is because of therise of turbulence. Turbulent flow causes dissipative loss in a fluid.

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