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Chapter 15
Human Movement in a
Fluid Medium
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
McGraw-Hill/Irwin
© 2012 The McGraw-Hill Companies, Inc. All rights reserved.
The Nature of Fluids
What is a fluid?
• a substance that flows or continuously
deforms when subjected to a
shear stress
• both liquids and gases are fluids
• air and water are fluids that commonly
exert forces on the human body
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
15-2
The Nature of Fluids
What is relative velocity?
(velocity of a body with respect to the
velocity of something else, such
as the surrounding fluid)
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
15-3
The Nature of Fluids
Velocity of cyclist relative to wind (20 m/s)
Cyclist’s velocity (15 m/s)
Head wind
velocity
(5 m/s)
Velocity of cyclist relative to wind (10 m/s)
Cyclist’s velocity (15 m/s)
Tail wind
velocity
(5 m/s)
vc/w = vc- vw
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
15-4
The Nature of Fluids
What is laminar flow?
Laminar flow is characterized by smooth,
parallel layers of fluid.
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
15-5
The Nature of Fluids
What is turbulent flow?
Region of
turbulence
Motion of
sphere
Turbulent flow is characterized by mixing of
adjacent fluid layers.
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
15-6
The Nature of Fluids
What are relevant fluid properties?
• density - mass/volume
• specific weight - weight/volume
• viscosity - internal resistance of a
fluid to flow
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
15-7
Buoyancy
What is buoyancy?
a fluid force with:
• magnitude based on Archimedes’
principle,
• direction always vertically
upward,
• and point of application being a
body’s center of volume.
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
15-8
Buoyancy
What is Archimedes’ principle?
A physical law stating that the buoyant
force acting on a body is equal to
the weight of the fluid displaced by
the body: Fb = Vd
Where Fb = buoyant force,
Vd = displaced fluid volume,
 = fluid specific weight
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
15-9
Buoyancy
What determines whether a body floats
or sinks?
• Floating occurs when the buoyant
force is greater than or equal to
body weight.
• Sinking occurs when body weight is
greater than the buoyant force.
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
15-10
Buoyancy
What determines whether a body floats
or sinks?
The equation of static equilibrium for
vertical force can be used to
quantitatively answer this
question:
Fv = 0
0 = V - wt
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
15-11
Buoyancy
A floating body at
rest (position A) will
rotate until the
buoyant force and
weight force are
vertically aligned
(position B) so that
zero torque is
present.
Buoyant
force
A
B
Center of
volume
Weight
Center of
gravity Buoyant
force
Center of
volume
Center of
gravity
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
Weight
15-12
Drag
What is drag?
• a force caused by the dynamic action
of a fluid that acts in the direction
of the freestream fluid flow
• generally a resistance force that tends
to slow the motion of a body
moving through a fluid
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
15-13
Drag
What factors affect the total drag force?
FD = ½CDApv2
Where:
• FD = drag,
• CD = the coefficient of drag - a unitless number;
an index of a body’s ability to generate
fluid resistance
•  = fluid density
• Ap = body surface area perpendicular to
the fluid flow
• v = relative velocity of the body with respect
to the fluid
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
15-14
Drag
Drag force
Pattern of change in drag force with increasing relative velocity.
Laminar
Turbulent
v2
v1
Relative velocity
From 0 to v1 drag increases approximately with velocity squared (v2.) At
v1 there is sufficient relative velocity to generate a turbulent boundary
layer, which is why, from v1 to v2, form drag decreases. After v2, total drag
increases.
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
15-15
Drag
What is skin friction?
• drag derived from friction in adjacent
layers of fluid near a body moving
through the fluid
• AKA surface drag and viscous drag
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
15-16
Drag
Fluid flow
What is skin friction?
Turbulent boundary
layer
Laminar boundary
layer
Side view of fluid flow around a flat thin plate.
Skin friction is the form of drag that predominates
when the flow is primarily laminar.
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
15-17
Drag
What factors affect the magnitude of
skin friction?
Skin friction increases with:
• the relative velocity of fluid flow
• the surface area of the body over
which the flow occurs
• the roughness of the body surface
• the viscosity of the fluid
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
15-18
Drag
What is form drag?
Region of
turbulence
Motion of
sphere
Form drag is derived from a pressure differential
between the lead and rear sides of a body
moving through a fluid. It is also known as profile
drag and pressure drag.
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
15-19
Drag
What is form drag?
A
B
A streamlined shape (A) reduces form drag by
reducing the turbulence created at the trailing edge,
(thus reducing the pressure differential present in B.)
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
15-20
Drag
What factors affect the magnitude of
form drag?
Form drag increases with:
• the relative velocity of fluid flow
• the magnitude of the pressure gradient
between the front and rear ends of
the body
• the surface area of the body
perpendicular to the fluid flow
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
15-21
Drag
What is wave drag?
(drag derived from the generation of
waves at the interface between
two different fluids, such as air
and water)
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
15-22
Drag
What factors affect the magnitude of
wave drag?
Wave drag increases with:
• the vertical oscillation of the body with
respect to the fluid
• the relative velocity of the body in the
fluid
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
15-23
Lift
What is lift?
• a force acting on a body in a fluid in a
direction perpendicular to the fluid
flow
• generally a resistance force that tends
to slow the motion of a body moving
through a fluid
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
15-24
Lift
What factors affect lift force?
FL = ½CLApv2
Where:
• FL = lift,
• CL = the coefficient of lift - a unitless number; an
index of a body’s ability to generate lift
•  = fluid density
• AP = body surface area perpendicular to the fluid
flow
• v = relative velocity of the body with respect to the
fluid
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
15-25
Lift
What factors affect the magnitude of lift?
Lift increases with:
• the relative velocity of fluid flow
• the surface area of the flat side of the
foil
• the coefficient of lift
• the density of the fluid
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
15-26
Lift
What is a foil?
(a shape capable of generating lift in a fluid)
Lift generated by a High velocity
foil is directed from
the region of relative
high pressure on the
flat side of the foil
toward the region of
relative low pressure
on the curved side of
Low velocity
the foil.
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
low pressure
high pressure
15-27
Lift
What is the Bernouli principle?
• an expression of the inverse relationship
between relative velocity and relative
pressure in a fluid flow
• regions of low relative velocity are
associated with relative high pressure
• regions of high relative velocity are
associated with relative low pressure
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
15-28
Lift
What is the Bernouli principle?
P
v2
 + z + 2g = C
Where:
• p = pressure,
•  = specific weight of the fluid,
• z = elevation,
• v = relative velocity,
• g = acceleration of gravity, and
• C = a constant
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
15-29
Lift
What is the angle of attack?
(angle between the longitudinal axis of a
body and the direction of the fluid flow)
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
15-30
Lift
What is the Magnus effect?
• deviation in the trajectory of a
spinning object toward the
direction of spin
• results from the Magnus force
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
15-31
Lift
What is the Magnus force?
Backspin
Topspin
Relative low velocity flow
Relative high pressure
Relative high velocity flow
Relative low pressure
Magnus
force
Relative high velocity flow
Relative low pressure
Magnus
force
Relative low velocity flow
Relative high pressure
Magnus force results from a pressure differential
created by a spinning body.
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
15-32