chapter 15: human movement in a fluid...
TRANSCRIPT
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Chapter 15: Human Movement in a Fluid Medium
Basic Biomechanics, 4th edition Susan J. Hall
Presentation Created by TK Koesterer, Ph.D., ATC Humboldt State University
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Objectives • Explain the ways in which the composition and flow
characteristics of a fluid affect fluid forces
• Define buoyancy and explain the variables that determine whether a human body will float
• Define drag, identify the components of drag, and identify the factors that affect the magnitude of each component
• Define lift and explain the ways in which it can be generated
• Discuss the theories regarding propulsion of the human body in swimming
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The Nature of Fluids
Fluid:
• Air and water are fluids that exert forces on the human body.
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Relative Motion
Relative velocity:
• Of a body with respect to a fluid is the vector subtraction of the velocity of the fluid from the velocity of the body.
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Laminar versus Turbulent Flow
Laminar flow:
– Low velocity relative to fluid medium
Turbulent flow:
– High velocity relative to fluid medium
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Fluid Properties
• Density (ρ) = mass / volume
• Specific weight (γ) = ratio of weight to volume
• Viscosity = internal resistance to flow
Atmospheric pressure and temperature influence a fluid’s density, specific weight, and viscosity
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Buoyancy
Archimedes’ principle: the magnitude of the buoyant force acting on a given body is equal to the weight of the fluid displaced by the body.
• Fb = Vd γ
Center of Volume: point around which a body’s volume is equally distributed and at which the buoyant force acts.
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Flotation
• Depends on body’s buoyancy and its weight
• Weight = buoyant; body floats
• Weight > buoyant; body sinks
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Flotation of the Human Body
• Floatability is a function of body density
• For flotation, buoyant force must greater than or equal to body weight
• Orientation of the human body
• Torque on the floating human body
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Drag
• FD = ½CDρApv2
Coefficient of drag:
• Depends on shape & orientation of a body
Components of total drag force:
• Skin friction
• Form drag
• Wave drag
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Skin Friction
Skin friction, surface drag, or viscous drag:
• Fluid particles slowed due to shear stress
Boundary layer: layer of fluid immediately adjacent to the body
Factors that affect skin friction drag
• Velocity of fluid flow, surface area, roughness, and viscosity
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Wave Drag
Wave drag:
• Major effect on human swimmers
• Factors that affect wave drag
– Greater up-and-down motion
– Increased swimming speed
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Form Drag
Form drag, profile drag, pressure drag:
Pressure differential: between the lead and rear sides of a body moving through a fluid
• Factors that affect form drag:
– Relative velocity, pressure gradient, and surface area
• Streamlining helps to minimize form drag
• Cyclists drafting helps to minimize form drag
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Bernoulli’s principle
• Pressure in a fluid varies inversely with the velocity
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Lift Force
• Lift: force acting on a body in a fluid in a direction perpendicular to the fluid flow
• FL = ½CLρApv2
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Foil Shape
Foil: shape capable of generating lift in the presence of
a fluid flow
Bernoulli principle: inverse relationship between relative velocity and relative pressure in a fluid flow
Factors that Affect:
– Velocity, pressure, and lift force
Coefficient of lift: unitless number that is an index of a body’s ability to generate lift
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Foil Shape
• Semi-foil shape of projectiles such as the discus and javelin generate some lift force when oriented at appropriate angles with respect to the direction of the fluid flow.
• Angle of Attack: angle between the longitudinal axis of a body and the direction of the fluid flow
• Lift/drag ratio: the magnitude of the lift force divided by the magnitude of the total drag force acting on a body at a given time
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Magnus Effect
Magnus force: lift force created by spin
Magnus effect: deviation in the trajectory of a spinning object toward the direction of spin, resulting form the magnus force
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Propulsion in a Fluid Medium
• Resistive drag acts on a swimmer • Propulsive drag: force acting in the direction
of a body’s motion • Propulsive drag theory: attributes propulsion
in swimming to propulsive drag on the swimmer
• Propulsive lift theory: theory attributing propulsion in swimming at least partially to lift acting on the swimmer
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Propulsion in a Fluid Medium
Vortex Generation • may play a role in swimming propulsion
Stroke Technique • product of stroke length (SL) and stroke rate
(SR).
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Summary • The relative velocity of a body with respect to a fluid
and the density, specific weight, and viscosity of the fluid affect the magnitude of fluid forces.
• The fluid force that enables flotation is buoyancy.
• Drag is a fluid force that acts in the direction of the free stream fluid flow.
• Lift is a force that can be generated perpendicular to the freestream fluid flow by foil-shaped objects.
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The End