Biomedical Engineering Reference
In-Depth Information
large enough to extend and grow via fluid separation. At that stage, the disease grows
rapidly. However, since turbulence may exist downstream of the separation region, it is
possible to diagnose the disease by listening for turbulence with a stethoscope or other
diagnostic tool, such as ultrasound-based echocardiography.
14.2.6 Reynolds Number and Types of Fluid Flow
The differences between laminar and turbulent flow are considerable. Laminar flow,
sometimes known as streamline flow, occurs when a fluid flows in parallel layers, with no
disruption between the layers. It is the opposite of turbulent flow. In nonscientific terms, lam-
inar flow is “smooth,” while turbulent flow is “rough.” The dimensionless Reynolds number
is an important parameter in the equations that describe whether flow conditions lead to lam-
inar or turbulent flow. It indicates the relative significance of the viscous effect compared to
the inertia effect, with laminar flow being slower and more viscous in nature, while turbulent
flow can be faster and more inertial (accelerating) in nature. The Reynolds number is propor-
tional to the ratio of the inertial force (acceleration) to the viscous force (fluid deceleration).
The values of the Reynolds number for various types of flow are as follows:
laminar
if Re
2,000
transient
if 2,000
<
<
Re
<
3,000
turbulent
if 3,000
<
Re
These are approximate values. The Reynolds number can be affected by the anatomy/geometry
of the fluid flow field, the roughness of the vessel wall, and irregularities in pressure or external
forces acting on the fluid. When the Reynolds number is much less than 1, creeping motion or
Stokes flow occurs. This is an extreme case of laminar flow where viscous (friction) effects are
much greater than the virtually nonexistent inertial forces. Stokes flow was previously
described regarding the falling sphere viscometer and is also typical of blood flow in capillaries.
As already noted, the Reynolds number is dimensionless and gives a measure of the ratio
of inertial forces (Vr) to viscous forces (
/L), and, consequently, it quantifies the relative
importance of these two types of forces for given flow conditions. The equation for the
Reynolds number is
m
rVD
m
VD
n
QD
n
¼
¼
Re
¼
A
where
V
¼
the mean fluid velocity in (cm/s)
D
¼
the diameter (cm)
m
¼
the dynamic viscosity of the fluid (g/cm-sec)
/r) (cm
2
/s)
n ¼
the kinematic viscosity (
n ¼ m
the density of the fluid (g/cm
3
)
r
¼
the flow rate (cm
3
/s)
Q
¼
the pipe cross-sectional area (cm
2
)
A
¼
The first form of the equation is the most common form. In the circulatory system, the
Reynolds number is 3,000 (mean value) and 7,500 (peak value) for the aorta, 500 for a
