Biomedical Engineering Reference
In-Depth Information
Fig. 5.5 a
The motion of fluid in the laryngeal region taken at three locations.
b
Velocity profile
monitored at a fixed location at point
A
for a steady and unsteady flow.
c
The motion of a fluid
particle passing through points
A
,
B
,
C
Consider the steady flow of air passing Point A near the larynx of the respiratory
system (Fig.
5.5
). Under a steady flow, the velocity profile is a horizontal line which
means that the acceleration is zero. A breathing cycle may be represented idealis-
tically by a sinusoidal pattern which generates an unsteady airflow. The velocity
profile at Point A for an unsteady flow then simply follows the sinusoidal breathing
pattern. If we consider the vertical velocity component
v
as the flow direction, then
in the
y
-momentum equation the velocity profile at Point A is represented by the
local acceleration
term
∂v/∂t
for the velocity component
v
. This term describes the
motion of the fluid changing locally at a fixed point and varying with time.
The second term of the inertial force is the convection term, which describes the
fluid acceleration spatially. If we now follow a fluid particle that happens to pass
through points A, B, and C in the laryngeal region under a steady flow condition
so that the velocity in itself is not fluctuating with time, the velocity component
v
now has a local
acceleration
in space where the velocity is accelerating between the
locations of A and B, i.e. the velocity gradient in the term
v∂v
/
∂y
of Eq. (5.12) is
increasing. Similarly, after the larynx, from point B to C, the velocity is decreasing
and the local
acceleration
gradient in space is negative, i.e. a deceleration. We
describe the fluid motion sweeping past points in space by the convection term in
the momentum equations.
The pressure term describes the existence of a pressure gradient caused by a
pressure difference in the flow domain. If we consider the steady flow through the 2D
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