Final answer:
The average velocity of blood flow through each capillary vessel, given the cardiac output of 5 L/min and a capillary diameter of 8 μm, is approximately 0.00166 cm/s.
Step-by-step explanation:
To calculate the average velocity of blood flow through each capillary vessel, given a cardiac output and diameter of the capillaries, we use the equation of continuity that relates the flow rate (Q) to the cross-sectional area (A) and velocity (v) of fluid flow through a pipe or blood vessel.
This is given as Q = A∙v. Here, the cardiac output is the volume flow rate (Q) through the circulatory system.
First, we convert cardiac output to cm³/s from L/min:
1 L/min = 1000 cm³/min
5 L/min = 5000 cm³/min
= (5000 cm³/min) × (1 min/60 s)
= 83.33 cm³/s.
Next, we calculate the cross-sectional area of one capillary.
The formula for the area of a circle is A = π∙r², where r is the radius, but we have been given the diameter, which is twice the radius.
First, we convert 8 μm = 8 x 10⁻´ cm to radius by dividing by 2, thus getting 4 x 10⁻´ cm.
Plugging this into the area equation gives us A = π∙(4 x 10⁻´ cm)² ≈ 5.0265 x 10⁻₈ cm² for the area of one capillary.
Now, we can find the average velocity through one capillary by rearranging the equation to solve for v:
v = Q/A.
So, v = (83.33 cm³/s) /(5.0265 x 10⁻₈ cm²)× 10⁹ capillaries
= 0.00166 cm/s/capillary.
The average velocity of blood flow through each capillary vessel is therefore approximately 0.00166 cm/s.