The radius of the aorta is about 1 cm and the blood flowing through it has a speed of about 30 cm s⁻¹. Calculate the average speed of the blood in the capillaries, using the fact that although each capillary has a diameter of about 8 ｘ10⁻⁴ cm, there are literally millions of them so that the total cross section is about 2000 cm². (Ans: 5 ｘ10⁻⁴ m s⁻¹)



Data Given:


Radius of aorta = r₁ = 1 cm = 0.01 m

Speed of blood at aorta = v₁ = 30 cm s⁻¹ = 0.30 m s⁻¹

Diameter of capillaries = d₂ = 8 ｘ10⁻⁴ cm = 8 ｘ10⁻⁶ cm

Area of cross section of capillaries = 2000 cm² = 0.2 m² 


To Find:

Speed of blood at capillaries = v₂ = ?


Solution:


Using the equation of continuity i.e.

A₁v₁  = A₂v₂

or

v₂  = `\frac {A₁v₁}{A₂}`

Where A₁ = 𝜋 r₁² = 3.1416 ｘ(0.01 m)² = 0.00031416 m²  and A₂ = 0.2 m² (given) so,

putting values 


v₂ = `\frac {0.00031416 m² ｘ 0.30 m s⁻¹}{0.2 m²}`

v₂ = 0.00047124 m s⁻¹

v₂ = 4.7124 ｘ10⁻⁴ m s⁻¹

or

v₂ = 5 ｘ10⁻⁴ m s⁻¹ ----------Ans.



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