Question

The human circulation system has approximately 1 × 109 capillary vessels. Each vessel has a diameter of about 8 μm .Assuming the cardiac output is 5 L/min, determine the average speed, in centimeters per second, of blood flow through each capillary vessel.

Answer 1

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

$\bar{v}=\frac{Q}{A}$

Q = Discharge of Flow

A = Cross sectional Area

$\bar{v} =$ Velocity

The area of the cross section of the capillary tube is

$A_c = \pi r^2$

$A_c = \pi (\frac{d}{2})^2$

$A_c = \pi (\frac{8*10^{-6}}{2})^2$

$A_c = 5.02685*10^{-11}m^2$

The total Area by this formula:

$A_1 = nA_c$

Where,

$A_c =$ Stands for area of capillary

n = Stands for number of blood vessels

$A_1 = (1*10^9)(5.0265*10^{-11})$

$A_1 = 5.0265*10^{-2}m^2$

Finally replacing at our first equation,

$\bar{v} = (\frac{5L/min}{5.0265*10^{-2}m^2})(\frac{1000cm^3}{1L})(\frac{1min}{60s})$

$\bar{v} = 1.66cm^3/s$

Therefore the average speed, in centimeters per second, of blood flow through each capillary vessel is 1.66cm^3/s