Question

3 polints Human blood flows from the aorta to the capilaries. A girl has an aorta radius of 10.9 mm. Assume she has 7 billion capillaries in the body, the caplllaries radius average fim (micrometer), and the blood speed average 0.5 mm/s in the capillaries. The blood speed is . mm/s in the aorta.

Answer 1

The blood speed in the aorta is approximately 0.296 meters per second (m/s).

The total cross-sectional area:

A_total = A_capillary * N_capillaries = π * (4 * 10^-6 m)² * 7 *
`10^9`

= 70.4π *
`10^-^3` m²

The Flow rate = A_total * v_capillary

`= 70.4 * 10^-^3 m^2 * 0.5 m/s\\ = 35.2 * 10^-^3 m^3/s.`

The flow rate through the aorta must be equal to the total flow rate through the capillaries, assuming no blood loss throughout the circulatory system.

The cross-sectional area of the aorta

A_aorta = π * (10.9 *
`10^-^3` m)²

= 118.15π *
`10^-^6` m²

Finally the blood speed: v_aorta = Flow rate / A_aorta

= (35.2π *
`10^-^3 m^3/s`) / (118.15π *
`10^-^6 m^2`)

= 0.296 m/s.