10.26 (a) What is the largest average velocity of blood flow in an artery of radius 2×10–3m if the flow must remain laminar? (b) What is the corresponding flow rate? (Take viscosity of blood to be 2.084 × 10–3 Pa s).

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10.26 (a) What is the largest average velocity of blood flow in an artery of radius 2×10^–3m if the flow must remain laminar? (b) What is the corresponding flow rate? (Take viscosity of blood to be 2.084 × 10^–3 Pa s).

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Vishal Baghel | Contributor-Level 10

5 months ago

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

Diameter of the artery, d = 4 $\times 10^{- 3}$ m

Viscosity of 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

The largest velocity is given by the relation: $V_{a v g}$ = $\frac{R_{e} η}{ρ d}$

= $\frac{2000 \times 2.084 \times 10^{- 3}}{1.06 \times 10^{3} \times 4 \times 10^{- 3}}$ = 0.983 m/s

Flow rate is given by the relation:

R = $π r^{2} V_{a v g}$ = 3.1416 $\times ({2 \times 10^{- 3})}^{2} \times 0.983$ = 1.235 $\times 10^{- 5}$ $m^{3}$ /s

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10.26 (a) What is the largest average velocity of blood flow in an artery of radius 2×10^–3m if the flow must remain laminar? (b) What is the corresponding flow rate? (Take viscosity of blood to be 2.084 × 10^–3 Pa s).

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