Biomedical Engineering Reference
In-Depth Information
Fig. 4.6  Streaklines for laminar, transitional and turbulent flows
dye streak for a laminar flow is characterised by a smooth relatively straight path as
the fluid particles pass over each other without little mixing. The effect of the fluid
viscosity dominates the flow 'holding' the fluid together in its layered formation.
The dye streak for a turbulent flow is characterised by the random fluctuations, ir-
regular and chaotic motion, and local regions of vortices. We may even observe a
breakdown of the dye streak because of such intense mixing.
The inertia of the fluid flow (i.e. its momentum) dominates, enabling transport
of fluid particles across many layers and regions. The dye streak is an irregular path
with no observable pattern. The presence of turbulence increases energy diffusion,
mixing, dissipation, and heat transfer. Many flows found in practice are turbulent in
nature such as smoke rising from a cigarette which starts of as a laminar flow and
transitions to turbulence as it progresses.
4.6
Introduction to Internal Pipe Flow
Blood flow through the circulatory system occurs primarily in vessels that essen-
tially form a network of pipes. It is for this reason that an introduction to internal
pipe flows is important.
4.6.1
Developing and Fully Developed Regions
If we consider fluid flowing with a constant velocity, then its profile is uniform
throughout. As the fluid enters a pipe its velocity profile exhibits a change starting
from the wall to the centre of the pipe (Fig. 4.7 ). Fluid particles at the wall inherit a
zero velocity due to the stationary wall, referred to as the “no-slip” condition. Be-
cause of the fluid viscosity, wall adjacent fluid particles are significantly influenced
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