1. Human Movement in a Fluid Medium
Chapter 15
Human Movement in a Fluid Medium
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.
© 2012 The McGraw-Hill Companies, Inc. All rights reserved.
McGraw-Hill/Irwin

2. Basic Biomechanics, 6th edition
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.

3. Basic Biomechanics, 6th edition
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.

4. The Nature of Fluids vc/w = vc- vw
Velocity of cyclist relative to wind (20 m/s)
Cyclist’s velocity (15 m/s)
Head wind
velocity
(5 m/s)
Tail wind
Velocity of cyclist relative to wind (10 m/s)
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.

5. Basic Biomechanics, 6th edition
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.

6. Basic Biomechanics, 6th edition
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.

7. Basic Biomechanics, 6th edition
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.

8. Basic Biomechanics, 6th edition
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.

9. Basic Biomechanics, 6th edition
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.

10. Basic Biomechanics, 6th edition
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.

11. Basic Biomechanics, 6th edition
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.

12. Basic Biomechanics, 6th edition
Buoyancy A B
Buoyant
force
Center of
volume
Weight
gravity
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.
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.

13. Basic Biomechanics, 6th edition
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.

14. Basic Biomechanics, 6th edition
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. Basic Biomechanics, 6th edition
Drag
Pattern of change in drag force with increasing relative velocity. v1 v2
Relative velocity
Drag force
Laminar
Turbulent
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.

16. Basic Biomechanics, 6th edition
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.

17. Drag What is skin friction?
Laminar boundary layer
Turbulent boundary layer
Fluid flow
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.

18. Basic Biomechanics, 6th edition
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.

19. Basic Biomechanics, 6th edition
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.

20. Basic Biomechanics, 6th edition
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.

21. Basic Biomechanics, 6th edition
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.

22. Basic Biomechanics, 6th edition
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.

23. Basic Biomechanics, 6th edition
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.

24. Basic Biomechanics, 6th edition
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.

25. Basic Biomechanics, 6th edition
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.

26. Basic Biomechanics, 6th edition
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.

27. Basic Biomechanics, 6th edition
Lift
What is a foil?
(a shape capable of generating lift in a fluid)
High velocity low pressure
Low velocity high pressure
Lift generated by a 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 the foil.
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.

28. Basic Biomechanics, 6th edition
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.

29. Basic Biomechanics, 6th edition
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.

30. Basic Biomechanics, 6th edition
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.

31. Basic Biomechanics, 6th edition
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.

32. What is the Magnus force?
Lift
What is the Magnus force?
Relative low velocity flow
Relative high pressure
Relative high velocity flow
Relative low pressure
Magnus
force
Topspin
Backspin
Magnus force results from a pressure differential created by a spinning body.
Basic Biomechanics, 6th edition
By Susan J. Hall, Ph.D.