Poiseuille's Law

This law describes the relationship between pressure, flow, and resistance for liquid flowing through a cylindrical tube (blood flowing through a blood vessel). As you learned earlier, flow is only possible when there is a difference in pressure. If there is twice as much pressure difference there is also twice as much flow. Therefore flow (Q) is directly proportional to the pressure difference (P):

Q ~ P

In the early 19th century French physician Poiseuille did numerous experiments involving liquid and cylindrical tubes. What he came up with is the law which is now named after him. He observed that flow is proportional to the radius of the cylindrical tube raised to the 4th power. He also noticed that it is inversely proportional to the length of the tube and the liquid viscosity. So, the formula is:

Q = (k * P * r ^ 4)/(n * l)

Where Q is flow, P is the pressure difference, r is the radius, n is viscosity, l is length, and k is just a constant.

Obviously, from Poiseuille's law, the radius of the blood vessels plays by far the most prominent role in determining the amount of blood flow. For example, if the radius of the coronary artery decreases two-fold, the blood flow through it will decrease 16 times!
To understand this just imagine drinking water from a straw. Flow in this case is the amount of liquid that comes out of the cup into your mouth in a given period of time, and the pressure difference is provided by your lungs sucking in air. If the radius of the straw is twice as big you will get not twice as much, but 16 times as much liquid! On the other hand, if you are trying to suck syrup out of the straw, whose viscosity is much higher than water, the flow will be substantially diminished. In the same sense, the longer the straw you use, the less flow you will have.

 mmHg cm cm Poise mL/second Pressure Difference Radius Length Viscosity ----> Flow

Change the values for pressure difference, radius, length, and viscosity and hit the calculate button to see what the flow would be under those conditions. The viscosity for blood is .03 poise and for water is .01 poise.