# Homework Help: 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