Fluid with Viscosity

Internal friction in a fluid is a very important factor in the working of the human body. The friction, called viscosity, causes the flow to occur in layers which move relative to each other. For example in a pipe the friction with the walls causes the flow to be biggest in the center.

Every liquid has some viscosity, $\eta$, which describes the strength of the frictional force between layers of a laminar flow. The units of $\eta$ are Pa·s, also called the poiseuille (Pl). Typical values are 1.00·10^-3 for water and about 0.1 of that for oil. Poiseuille found that the rate of flow through a pipe is very dependent on the radius:

Poiseuille's Law:

where Q is the flow in m³/s, r is the radius in m, $\Delta$p is the pressure difference across the tube of length L.

Notice that reducing the diameter of an artery by a factor of 2 due to plaque build-up reduces the flow by a factor of 16. If you force the liquid to flow at too high a velocity, you go into turbulent flow and the equation is no longer valid. This turbulent flow causes noise, which can be observed by a physician looking for blockages.