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Human Biomechanics

Chapter 8 Fluid Mechanics

Concepts •  Force •  Pressure •  Buoyancy •  Drag and lift forces •  Relative Movement •  Viscosity •  Magnus effect

Movement in a fluid •  What factors may affect your movement

(and speed) in a fluid? –  Velocity, Velocity of fluid, Density of fluid,

Surface area, Roughness of surface, Shape •  Two forces

–  Buoyant force –  Force due to relative motion in fluid

Buoyancy •  Related to water pressure •  Force of buoyancy

–  Push upward while immersed in a fluid •  Displacement of water by object or person •  Concept of equilibrium •  How does it work?

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Pressure equilibrium Pressure equilibrium (2)

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F =∑ Rl + (−Ru) + (−Ww ) = 0Analyzing at depth = 1 m:

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F =∑ 19,600N − 9,800N − 9,800N = 0Force of buoyancy = Difference between the forces acting on the “cube of water”

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F =∑ Rl + (−Ru) + (−Ww ) = 0F =∑ Fb + (−Ww ) = 0

Fb =Ww

Force of buoyancy •  Immersed body volume replaces water

volume •  Buoyant force is equal to the weight of

water displaced •  If weight of immersed body is less than

weight of water displaced, body will float…Why?

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F =∑ Fb + (−Wbody ) = m a

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Center of buoyancy •  Similar to center of gravity •  Point through which force of buoyancy acts •  Affects floating position…How?

Relative velocity •  Movement of the fluid relative to the

person •  Absolute velocity = velocity in comparison

to the ground •  When absolute velocities of fluid and

person opposite in direction, relative velocity increases

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Fluid •  Definition

–  Substance that flows when subjected to shear stress

•  Characteristics –  Pressure –  Flow (laminar vs turbulent)

Drag effects on flight •  Shape and surface

–  Laminar flow –  Turbulent flow

•  Boundary layer separation

Dynamic Fluid Force •  Movement within fluid •  Depends on:

–  Relative velocity –  Surface area –  Fluid density

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FD =12CD ρ A v

2

Drag Force Coefficient of Drag

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Drag forces •  Surface drag

–  Skin drag –  Related to surface in contact with fluid –  More prevalent at lower speeds –  Fluid viscosity

•  Form drag –  Profile drag –  Related to shape of object or person moving

through fluid –  More prevalent at high speeds

Surface drag

Form drag Drag Forces •  What can affect drag? •  Shape of object/person (CD) •  Density of fluid (mass/volume)

–  Air = 1 kg/m3 –  Water = 1000 kg/m3

•  Frontal area (A) •  Relative velocity of object/person •  Acts parallel to the direction of movement

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FD =12CD ρ A v

2

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Magnitude of drag forces •  Example 1

–  Sprint at 10 m/s vs run at 5 m/s –  A = 1 m2

–  CD = 0.8 –  FD = ??

•  Example 2 –  Differences between 2 tail winds: 2 vs 8 m/s –  Running at 5 m/s –  FD = ??

Mechanism of drag force •  Pressure difference

–  Drag force directed from high pressure to low pressure

Drag force

Terminal Velocity •  Example

–  Speed skier with v = 55 m/s, A = 1/2 m2, CD = 0.7

–  Force of drag?? –  What keeps the skier from going faster?

•  Terminal velocity –  Velocity reached when FD = Fg

Terminal Velocity (2)

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FD = Fg12CD ρ A v

2 = m g sinθ

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v =2 m g sinθCD ρ A

Angle of the slope of interest

What if vi is greater than terminal velocity?

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I am curious… •  Common observation:

–  Terminal velocity of a larger person seems to greater than that of a smaller person

–  Force of drag is larger for a larger person (see equation)

•  Contradiction? –  Explain how this observation can be true

without contradicting

Lift force •  Similar concept as drag force •  Related to pressure difference •  Acts perpendicular to direction of

movement

Bernoulli’s principle •  Daniel Bernoulli (1700-1782) •  When P high, fluid velocity low •  When P is low, fluid velocity high •  Force directed from high pressure to low

pressure

Lift force mechanism

Velocity Pressure

Velocity Pressure

Resulting Lift force

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Lift and drag forces Lift and drag forces (2)

Resultant Force

Magnus effect •  Heinrich Gustav Magnus (1802 - 1870) •  Lift forces due to spinning balls •  Collision at the level of boundary layer •  Creation of pressure difference

Magnus effect (2)

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Magnus effect (3)

Hydrostatic pressure •  Force exerted by a fluid •  Air pressure at sea level

–  14.7 lb/square inch (psi) = one atmosphere •  Hydrostatic pressure varies with altitude •  Water characteristics

–  Denser than air (more mass per unit of volume) •  When immersed,

–  Pressure increases by 14.7psi every 33ft –  Health issues