The radius of the aorta is «10 mm and the blood flowing through it has a speed of about 300 mm/s. a capillary has a radius of about 4ˆ10´3 mm but there are literally billions of them. the average speed of blood through the capillaries is about 5ˆ10´4 m/s. (i) calculate the effective cross sectional area of the capillaries and (ii) the approximate number of capillaries.

(I). The effective cross sectional area of the capillaries is 0.188 m².

(II). The approximate number of capillaries is

Explanation:

Given that,

Radius of aorta = 10 mm

Speed = 300 mm/s

Radius of capillary

Speed of blood

(I). We need to calculate the effective cross sectional area of the capillaries

Using continuity equation

Where. v₁ = speed of blood in capillarity

A₂ = area of cross section of aorta

v₂ =speed of blood in aorta

Put the value into the formula

(II). We need to calculate the approximate number of capillaries

Using formula of area of cross section

Put the value into the formula

Hence, (I). The effective cross sectional area of the capillaries is 0.188 m².

(II). The approximate number of capillaries is