4.3 Fluid Dynamics
101
Fig. 4.10 Electric circuit representation of blood circulatory system
Turbulent Flow in Capillaries
As we pointed out before, the flow of blood through our capillaries is nonNewtonian for a good reason. The capillaries have diameters which barely let red
corpuscles through (Fig. 4.4). The flow around the corpuscles becomes turbulent.
This has the advantage of mixing plasma nutrients and oxygen, so they reach the
capillary walls far faster than diffusion alone, and similarly for cell waste products
and carbon dioxide passing into the plasma, since the gradient of concentration of
these materials is greater across the capillary walls if they are strongly mixed in the
blood.
4.3.9 Circuit Analogy for Blood Flow
A dynamical model of the arterial system with a pumping heart can be constructed
using an electrical analog. This simple model for blood flow in the circulatory
system has all the elements of an electric circuit, including resistance, capacitance,
inductance, and, of course, a power source. (See Fig. 4.10.) The direct analog of
electric potential (measured by voltage) is the fluid pressure (measured by newtons
per square meter). Both represent a specific energy stored: In the electric case,
the potential gives the energy stored in charges per unit charge; in the fluid case,
pressure is the energy stored in the fluid volumes per unit volume. The analog of
electric current (measured in amperes) is fluid volume flow, measured by the volume
of fluid passing through a given area per unit time.
The passive elements in an electric circuit have the following analogs in fluid
flow:
Flow Resistance Fluid viscous drag in arteries and veins act as resistors in series
with the current flow. This drag is highest in arterioles and the capillary system.
From Poiseuille’s law,
101
Fig. 4.10 Electric circuit representation of blood circulatory system
Turbulent Flow in Capillaries
As we pointed out before, the flow of blood through our capillaries is nonNewtonian for a good reason. The capillaries have diameters which barely let red
corpuscles through (Fig. 4.4). The flow around the corpuscles becomes turbulent.
This has the advantage of mixing plasma nutrients and oxygen, so they reach the
capillary walls far faster than diffusion alone, and similarly for cell waste products
and carbon dioxide passing into the plasma, since the gradient of concentration of
these materials is greater across the capillary walls if they are strongly mixed in the
blood.
4.3.9 Circuit Analogy for Blood Flow
A dynamical model of the arterial system with a pumping heart can be constructed
using an electrical analog. This simple model for blood flow in the circulatory
system has all the elements of an electric circuit, including resistance, capacitance,
inductance, and, of course, a power source. (See Fig. 4.10.) The direct analog of
electric potential (measured by voltage) is the fluid pressure (measured by newtons
per square meter). Both represent a specific energy stored: In the electric case,
the potential gives the energy stored in charges per unit charge; in the fluid case,
pressure is the energy stored in the fluid volumes per unit volume. The analog of
electric current (measured in amperes) is fluid volume flow, measured by the volume
of fluid passing through a given area per unit time.
The passive elements in an electric circuit have the following analogs in fluid
flow:
Flow Resistance Fluid viscous drag in arteries and veins act as resistors in series
with the current flow. This drag is highest in arterioles and the capillary system.
From Poiseuille’s law,