Introduction to Sports Biomechanics: Analysing Human Movement ...

Laminar and turbulent flow
In laminar flow, the fluid particles move only in the direction of the flow. The
fluid can be considered to consist of discrete plates (or laminae) flowing past one
another. Laminar flow occurs at moderate speeds past objects of small diameter,
such as a table tennis ball, and energy is exchanged only between adjacent layers
of the flowing fluid. Turbulent flow is predominant in sport. The particles of fluid
have fluctuating velocity components in both the main flow direction and perpendicular
to it. Turbulent flow is best thought of as a random collection of rotating eddies
or vortices; energy is exchanged by these turbulent eddies on a greater scale than in
laminar flow.
The type of flow that exists under given conditions depends on the Reynolds number.
For low Reynolds numbers the fluid flow is laminar. At the ‘critical’ Reynolds
number, the flow passes through a transition region and then becomes turbulent at a
slightly higher Reynolds number. The Reynolds number at which flow changes from
laminar to turbulent depends very much on the object past which the fluid flows.
Consider a fairly flat boat hull moving through stationary water. Let us use the distance
along the hull from the bow as the ‘characteristic length’ for the ‘local’ Reynolds
number of the water flow past that point on the hull. Furthermore, we will define the
characteristic speed as that of the boat moving through the water. For this example,
the critical Reynolds number is in the range 100 000–3 000 000, depending on the
nature of the flow in the water away from the boat and the surface roughness of the hull.
The fluid flow close to the hull (in the ‘boundary layer’ discussed below) will change
from laminar to turbulent at the point along the hull where the ‘local’ Reynolds number
equals the critical value. If this does not happen, the flow will remain laminar along the
whole length of the hull. For flow past a ball, the ball diameter is used as the characteristic
length and the characteristic speed is the speed of the ball relative to the air. The
critical Reynolds number, depending on ball roughness and flow conditions outside
the boundary layer, is in the range 100 000–300 000.
The boundary layer
CAUSES OF MOVEMENT – FORCES AND TORQUES
When relative motion occurs between a fluid and an object, as for flow of air or water
past the sport performer, the fluid nearest the object is slowed down because of its
viscosity. The region of fluid affected in this way is known as the boundary layer.
Within this layer, the relative velocity of the fluid and object changes from zero at
the surface of the object to the free stream velocity, which is the difference between the
velocity of the object and the velocity of the fluid outside the boundary layer. The
slowing down of the fluid is accentuated if the flow of the fluid is from a wider to a
narrower cross-section of the object, as the fluid is then trying to flow from a lowpressure
region to a high-pressure region. Some of the fluid in the boundary layer may
lose all its kinetic energy. The boundary layer then separates from the body at the
separation points (S in Figure 5.7), leaving a low-pressure area, known as the wake,
behind the object.
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