Respuesta :
Answer:
(I). The effective cross sectional area of the capillaries is 0.188 m².
(II). The approximate number of capillaries is [tex]3.74\times10^{9}[/tex]
Explanation:
Given that,
Radius of aorta = 10 mm
Speed = 300 mm/s
Radius of capillary [tex]r=4\times10^{-3}\ mm[/tex]
Speed of blood [tex]v=5\times10^{-4}\ m/s[/tex]
(I). We need to calculate the effective cross sectional area of the capillaries
Using continuity equation
[tex]A_{1}v_{1}=A_{2}v_{2}[/tex]
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
[tex]A_{1}=A_{2}\times\dfrac{v_{2}}{v_{1}}[/tex]
[tex]A_{1}=\pi\times(10\times10^{-3})^2\times\dfrac{300\times10^{-3}}{5\times10^{-4}}[/tex]
[tex]A_{1}=0.188\ m^2[/tex]
(II). We need to calculate the approximate number of capillaries
Using formula of area of cross section
[tex]A_{1}=N\pi r_{c}^2[/tex]
[tex]N=\dfrac{A_{1}}{\pi\times r_{c}^2}[/tex]
Put the value into the formula
[tex]N=\dfrac{0.188}{\pi\times(4\times10^{-6})^2}[/tex]
[tex]N=3.74\times10^{9}[/tex]
Hence, (I). The effective cross sectional area of the capillaries is 0.188 m².
(II). The approximate number of capillaries is [tex]3.74\times10^{9}[/tex]
