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
be the mass flow rate,
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](https://tex.z-dn.net/?f=%5Chat%7Bm%7D%20%3D%20v%2A%20%5Crho%20%2A%20A%20%2A%20n)
we clear the side where v is in:
![v = \frac{\hat{m}}{\rho A n}](https://tex.z-dn.net/?f=v%20%3D%20%5Cfrac%7B%5Chat%7Bm%7D%7D%7B%5Crho%20A%20n%7D)
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}](https://tex.z-dn.net/?f=v%20%3D%20%5Cfrac%7B%5Chat%7Bm%7D%7D%7B%5Crho%20%5Cpi%20R%5E2%20n%7D)
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