Respuesta :
Answer:
The no. of capillaries are [tex]1.92\times 10^{10}[/tex]
Solution:
As per the question:
Speed of the blood carried by the aorta, [tex]v_{a} = 40\ cm/s[/tex]
Radius of the aorta, [tex]R_{a} = 1.1 cm[/tex]
Speed of the blood in the capillaries, [tex]v_{c} = 0.007\ cm/s[/tex]
Radius of the capillaries, [tex]R_{c} = 6.0\times 10^{- 4} cm[/tex]
Now,
To determine the no. of capillaries:
Cross sectional Area of the Aorta, [tex]A_{a} = \pi R_{a}^{2} = \pi \times (1.1)^{2} = 1.21\pi \ m^{2}[/tex]
Cross sectional Area of the Capillary, [tex]A_{c} = \pi R_{c}^{2} = \pi \times (6.0\times 10^{- 4})^{2} = (3.6\times 10^{- 7})\pi \ m^{2}[/tex]
Let the no. of capillaries be 'n'
Also, the volume rate of flow in the aorta equals the sum total flow in the 'n' capillaries:
[tex]A_{a}v_{a} = nA_{c}v_{c}[/tex]
[tex]1.21\pi\times 40 = n\times 3.6\times 10^{- 7}\pi\times 0.007[\tex]
[tex]n = 1.92\times 10^{10}[/tex]
