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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
