Biomedical Engineering Reference
In-Depth Information
of as a measure of fluid friction. Thus, water is “thin,” having a lower viscosity, while
vegetable oil is “thick,” having a higher viscosity. All real fluids (except superfluids, such
as liquid nitrogen) have some resistance to stress and fluid flow, but a fluid that has no
resistance to shear stress is known as an ideal fluid or inviscid fluid. A real fluid with a non-
zero viscosity is called a viscous fluid. The study of viscosity of a real fluid is known as
rheology.
Isaac Newton postulated that for straight, parallel, and uniform flow, the shear stress,
t
,
between fluid layers is proportional to the velocity gradient,
@
u
/
@
y
, in the direction perpen-
dicular to the layers.
m
@
u
@
y
t
¼
Here, the constant
,
or the Newtonian viscosity. Many fluids, such as water and most gases, satisfy Newton's
criterion and are known as Newtonian fluids. Non-Newtonian fluids exhibit a more compli-
cated relationship between shear stress and velocity gradient than simple linearity. Many
such non-Newtonian fluids have a high concentration of suspended particles. Blood may
be one such fluid, since blood contains almost 50 percent of its volume as blood cells. In
the metric system, also known as the cgs (centimeter-gram-second) system, the unit of vis-
cosity is the
m
is known as the
coefficient of viscosity
, the
viscosity
, the
dynamic viscosity
, named after Jean Louis Marie Poiseuille, who formulated Poiseuille's law
of viscous flow. The value of viscosity is so small for many fluids (liquids and gases) that
their viscosity is often listed in cP, centipoise, or one-hundredth of a poise. A poise is equal
to one dyne/cm-sec.
As an example, the viscosity of water is approximately 1 cP with a density of 1 g/cc.
Blood has a viscosity of 3-4 cP, with a density of 1.05 g/cc. As can be seen, although the
densities of water and blood are fairly similar, their viscosities are not. This is due to the
large suspension of cells within blood, which adds to the resistance to blood flow. The more
solid/liquid boundaries in a fluid, where the shearing stresses tend to be higher, the higher
the viscosity. The cells within blood add numerous “solid”/liquid boundaries. Denser pure
fluids, such as honey and molasses, are thicker fluids with a much higher viscosity than
water or blood. When a pure liquid (without a suspension of particles) has a higher density,
its viscosity also tends to be proportionally higher.
Fluids with large suspensions, such as blood, have viscosities that are proportional to the
concentrations of particles. For blood, this is the hematocrit, which is the percentage of red
cells by volume in whole blood. Normally, the hematocrit is 45 percent. Figure 14.26 depicts
the relationship between blood hematocrit and viscosity.
The blood consists of a suspension of cells in a liquid called
poise
In an adult man, the
blood is about
1
/
12
the body weight, and this corresponds to 5-6 liters. Blood consists of
55 percent plasma and 45 percent cells, sometimes called
plasma.
. The blood per-
forms many important functions. By means of the hemoglobin contained in the erythrocytes
(red cells), it carries oxygen to the tissues and collects the carbon dioxide. It also conveys
nutritive substances (e.g., amino acids, sugars, mineral salts) and gathers the excreted mate-
rial that will be eliminated through the kidney. The blood also carries hormones, enzymes,
and vitamins. It performs the defense of the body by means of the phagocytic activity of the
leukocytes (white cells).
formed elements
