The aorta pumps blood away from the heart at about 40 cm/s and has a radius of about 1.0 cm. it then branches into many capillaries, each with a radius of about 5×10−4 cm carrying blood at a speed of 0.10 cm/s. how many capillaries are there?
a- 1.6×109
b- 16
c 8.0×105
d- 1.6×105

To solve this problem it is necessary to apply the continuity equations for which it is defined that

Where

Velocity at each state

Area at each state

If we consider the end of the section with a certain number of capillarities, the issue can be expressed as

This value only indicates that the proportionality relationship between the input section and the output section is equivalent to the number of capillarities.

Replacing with our values

Solving to N,

Therefore the correct answer is A.

b) phosphorus pentoxide