# Continuity: Constant mass flow rate

1. Jan 16, 2008

### chantalprince

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

The aorta carries blood away from the heart at a speed of about 40 cm/s and has a radius of approx. 1.1cm. The aorta branches eventually into a large number of tiny capillaries that distribute the blood to the various body organs. In a capillary, the blood speed is approx. 0.07 cm/s, and the radius is about 6 x 10 -4 cm. Treat the blood as an incompressible flulid and use these data to determine the approx number of capillaries in the human body.

2. Relevant equations

I think: A1 x V1 = A2 x V2 and A = pi (r)^2

A = cross sectional area of tube
V= velocity

3. The attempt at a solution

I have figured out the areas of the cross sections of the capillary and the aorta.

I have labeled them: Ac and Aa respectively.

Ac= 1.13097 x 10^-6 cm^2

Aa= 3.8013 cm^2

I cannot figure out where to go with this information. It seems like I need to know a volume or a length of some sort.

Can anybody help me out please?

Thanks!

Last edited: Jan 16, 2008
2. Jan 16, 2008

### stewartcs

Hint: The flow rate in must equal the flow rate out. The flow rate in is $$A_1 \cdot V_1$$ or about $$152.05 \frac{cm^3}{s}$$.

The flow rate out must equal this, no matter how many paths it takes. Therefore $$A_2 \cdot V_2 \cdot N$$ must equal 152.05, where N is the number of capillaries.

CS

3. Jan 16, 2008

### chantalprince

Thank you very much Stewartcs!