Biomedical Engineering Reference
In-Depth Information
3.2.1 Viscosity
Viscosity is one of those things that we all (roughly) understand, but for which we rarely get a
clear deinition. Viscosity is the property of a medium that allows transfer of shear forces from
one object to another within that medium. For example, we all understand that if we need to stir
some raw sugar into our latte, stirring the latte with a spoon will (eventually) move the cofee in
circles, but the cup is not going to move much. On the other hand, use the same spoon to stir a
cup of pure honey (assume you use the same force you used with the latte), and the cup will move
with the spoon, but you will not do much to the honey. Why? Because the viscosity of the honey
is a few thousand times higher than that of water, so the motion of the spoon is more eiciently
transmitted to the cup.
he conventional deinition for the
dynamic viscosity
μ (also called
absolute viscosity
) is the
tangential force per unit area required to slide one plane with respect to another a unit distance
apart at unit velocity. In the CGS system of units, the unit of dynamic or absolute viscosity is
the poise:
1 poise = dyne s/cm
2
= g/cm s = 1/10 Pa s
he usual units are centipoises, cP, in which units the viscosity of pure water is approximately
1 at room temperature.
he other commonly used measure of viscosity is
kinematic viscosity
, ν, which is the abso-
lute viscosity divided by the density, ρ.
ν
=
ρ
For water, because the density is approximately 1 g/cm
3
, the value for ν in centistokes (cSt) is,
again, approximately 1.
Note that to diferentiate the kinematic viscosity (the Greek letter nu, ν) from the veloc-
ity of a luid in equations, most texts use the Roman letter
u
for velocity, rather than the
Roman letter
v
, which, in some fonts designed with no scientiic insight, is indistinguishable
from ν.
3.2.2 Nondimensional Analysis: Reynolds Number and Peclet Number
Engineers are very fond of reducing extremely complex phenomena to simple “dimensionless”
expressions that allow one to predict behavior on the basis of one number. For low, there is a
quantitative dimensionless expression that allows one to predict the behavior of a system based
on the luid(s) involved, the dimensions of the container and how fast the luid is moving—the
Reynolds number
(
Re
). he deinition for the Re, which predicts whether the system will be
dominated by viscosity or momentum, is as follows:
Re
=
ρ
uL
(
3.1
)
where:
u
= average low speed (for example, the low speed in a river, in a pipe, or in a blood
artery)
L
= characteristic length (for example, the diameter of a cylindrical channel or the thick-
ness of the peanut butter layer)
μ = viscosity
