To solve this exercise we must apply the concept of Flow as the measure given to determine the volume of a liquid flowing per unit of time, and that can be calculated through velocity and Area, mathematically this can be determined as
[tex]\bar{v}=\frac{Q}{A}[/tex]
Q = Discharge of Flow
A = Cross sectional Area
[tex]\bar{v} =[/tex] Velocity
The area of the cross section of the capillary tube is
[tex]A_c = \pi r^2[/tex]
[tex]A_c = \pi (\frac{d}{2})^2[/tex]
[tex]A_c = \pi (\frac{8*10^{-6}}{2})^2[/tex]
[tex]A_c = 5.02685*10^{-11}m^2[/tex]
The total Area by this formula:
[tex]A_1 = nA_c[/tex]
Where,
[tex]A_c =[/tex] Stands for area of capillary
n = Stands for number of blood vessels
[tex]A_1 = (1*10^9)(5.0265*10^{-11})[/tex]
[tex]A_1 = 5.0265*10^{-2}m^2[/tex]
Finally replacing at our first equation,
[tex]\bar{v} = (\frac{5L/min}{5.0265*10^{-2}m^2})(\frac{1000cm^3}{1L})(\frac{1min}{60s})[/tex]
[tex]\bar{v} = 1.66cm^3/s[/tex]
Therefore the average speed, in centimeters per second, of blood flow through each capillary vessel is 1.66cm^3/s
