# Calculating Capillary Amount Given Aorta Blood Flow

1. Oct 5, 2014

### casualdehyde

1. The problem statement, all variables and given/known data

When the rate of blood flow in the aorta is 5 litres per minute, the speed in the capillaries is about 0.33 mm per second. If the average diameter of a capillary is 8 microns (0.008 mm), calculate the number of capillaries in the circulatory system.

2. Relevant equations

Flow rate = volume/time - 1
Flow rate = Area x average velocity - 2
General form of equation of continuity: n1A1v1 = n2A2v2 - n1 and n2 = number of tube branches - 3 (rearrange to make n2 the subject)

3. The attempt at a solution

So I'm pretty sure I know how to solve this equation (find velocity of aorta by using equation 2 (replacing area with pi x r^2) and then subbing in all know variables to equation 3 to find n2 (number of capillaries). The problem is that my question hasn't provided me with the diameter of the aorta which I need to find the v1.

First Convert 5.0L/min into m^3 and seconds - 5.0L/min x 10^-3 m^3/L x 1min/60s = 1/12000m^3/s.
I would then divide this by the pi x r^2 to get velocity 1 (v1).

Now that I know all of the variables I can find n2.

n2 = n1A1v1/A2v2
= (1 x (pi x radius of aorta^2) x v1 found above)/(pi x (4x10^-6m)^2 x (0.33 x 10^-3 m/s) = Answer

(sorry for the mess I have no idea how to use latex, I just discovered this forum tonight!)
Is there another way to do this question or do I need to ask my teacher for a diameter?

2. Oct 10, 2014

### Greg Bernhardt

Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?