Question

The human circulatory system consists of a complex branching pipe network ranging in diameter from

Answer 1

Answer: the average velocity decreases

Explanation:

From the provided data we have:

Vessel    avg. diameter[mm] number

Aorta                 25.0                   1

Arteries             4.0                    159

Arteioles           0.06                 1.4*10^7

Capillaries         0.012               2.9*10^9

from the information, let $\hat{m}$ be the mass flow rate, $\rho$ is density, n number of vessels, and A is the cross-section area for each vessel

the flow rate is constant so it is equal for all vessels,

The average velocity is related to the flow rate by:

$\hat{m} = v* \rho * A * n$

we clear the side where v is in:

$v = \frac{\hat{m}}{\rho A n}$

area is π*R^2 where R is the average radius of the vessel (diameter/2)

we get:

$v = \frac{\hat{m}}{\rho \pi R^2 n}$

you can directly see in the last equation that if we go from the aorta to the capillaries, the number of vessels is going to increase ( n will increase and R is going to decrease ) . From the table, R is significantly smaller in magnitude orders than n, therefore, it wont impact the results as much as n. On the other hand, n will change from 1 to 2.9 giga vessels which will dramatically reduce the average blood velocity