10.25 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.

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Vishal Baghel | Contributor-Level 10

5 months ago

Diameter of the artery, d = 2 $\times 10^{- 3}$ m

Viscosity of the blood, $η$ = 2.084 $\times 10^{- 3}$ Pa-s

Density of the blood, $ρ$ = 1.06 $\times 10^{3}$ kg/ $m^{3}$

Reynolds’s number for laminar flow, $R_{e}$ = 2000

$V_{a v g}$ = $\frac{R_{e} η}{ρ d}$ = $\frac{2000 \times 2.084 \times 10^{- 3}}{1.06 \times 10^{3} \times 2 \times 10^{- 3}}$ = 1.966 m/s

As the fluid velocity increases, the dissipative forces become more important. This is because of the rise of turbulence. Turbulent flow causes dissipative loss in a fluid.

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