lecture 9 - fluid mechanics - ch 8 - spring 2011 - s

8/7/2019 Lecture 9 - Fluid Mechanics - Ch 8 - Spring 2011 - S

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FLUID MECHANICS

Mr. DicusSpring 2011

1ERS 202: Biomechanics



Objectives

Spring 2011ERS 202: Biomechanics

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Chapter 8 Gain a basic understanding of fluidforces

Buoyant Force

Dynamic Fluid Force Drag – Surface and Form How to alter drag

Lift Bernoulli’s Principle

Magnus Effect

Effects of dynamic force



Fluid Mechanics


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Force that fluids exert on objects

2 fluids we concern ourselves with:

Air & Water

Which plays a more important role?

2 Forces exerted via a fluid medium Buoyant Force

Vertical Due to immersion

Dynamic Force Drag and Lift

Due to relative motion



Buoyant Force


4

Floatation depends on volume and weight of object

This is compared to weight of same volume of water

Specific Gravity

Ratio of object weight to weight of equal volume of water

Specific Gravity of 1 or less ______

Density (ρ = m/V) Ratio of mass to volume

Water = 1000 kg/m3

Air = 1.2 kg/m3



Human Buoyancy


5

Bone and Muscle

Density > 1000 kg/m3

Fat

Density < 1000 kg/m3

Does someone with very little body fat float?

Do you have control over you own body density?



?WHY?


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Dynamic Force


7

Force due to relative motion

Object moving or fluid moving over object

Dynamic fluid force (F) is proportional to ( ):

Density of fluid (ρ)

Surface area of object immersed (A)

Square of relative velocity (v2)F ρAv2



Dynamic Force


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Relative velocity

Difference of the absolute velocity of object and

absolute velocity of fluid



Dynamic Force


9

Drag Acts in opposition to relative motion of object

Slow down or Speed up?

The backward force molecules of a fluid exert on an object(moving relative to the fluid)

Size of drag force is proportional to: The acceleration of fluid molecules

Mass of molecules that are slowed down

2 types of drag: Surface and Form



Drag Equation


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Surface Drag (skin friction, viscous drag)


11

As molecule slides past surface of an object, friction

slows the molecule down

Size of surface drag is affected by same factors as

drag force Coefficient of drag

Largely affected by surface drag

Where do we see this in athletics or elsewhere?

Viscosity of fluid

Internal friction between molecules of the fluid

Examples of viscous fluids?



Form Drag (shape drag, profile drag, pressure drag)


12

As an object moves through a fluid it is striking

molecules

Impact causes molecules to accelerate and change

direction (move out of the way)Molecules impart a force back onto the object (3rd law)

Larger change in direction = larger force exerted back

Amount of form drag will depend on the flow of

molecules as the object passes through

Laminar vs. Turbulent



Form Drag

Fluid molecules stay

close to object

Molecules separate

from surface Change in surface curve

too large

Velocity too great

Spring 2011

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ERS 202: Biomechanics

Laminar Flow Turbulent Flow



Form Drag


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Size of form drag

dependent on same factors

Coefficient of drag

Shape has greatest effect If molecules have to change

direction quickly then form drag

increases

Texture will affect form drag

Rough = turbulence



Will rough surface always increase form drag?


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How to reduce drag?


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Equation

What will have the greatest effect?

Fluid density: Can we control? What about Colorado, warm air, humid air?

Water temperature?

Altering coefficient of drag?

Relative velocity Drafting

Surface area? Frontal cross sectional area



Dilemma: Choosing the correct shape


17

Object Velocity

Faster velocity form drag accounts for more

Slower velocity surface drag accounts for more

Form Drag vs. Surface Drag

Small surface are will decrease surface drag

However…streamlining usually decreases form drag butincreases surface area

What should you do if you are going to move at faster

velocities?



Lift Force


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Component of Dynamic fluid force

Acts perpendicular to relative motion of object

Does not oppose relative motion

Lift will change direction of relative motion

Lift can be directed in any direction

Direction is dependent on direction of flow of fluid

Equation:



Lift Force


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Basically:

lift is caused by the lateral deflection of fluid molecules

as they pass an object

Newton’s 3rd Law: Examples of Lift force:

Air Chair

http://www.youtube.com/watch?v=ue1CQBvghDI

http://www.youtube.com/watch?v=ue1CQBvghDI



Lift Force


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Bernoulli’s Principle

Faster moving fluids produce less lateral force than

slower moving fluids



Lift Force


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Spin (the Magnus effect)

Gustav Magnus discovered that spinning balls have a

lift force

Ball moving L to R with top spin:

Backspin vs. Topspin

Sidespin



Effect of Dynamic Fluid Force


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Remember Newton’s 2nd law: ∑F=ma or a=∑F/m

Dynamic force equation:

Force is inversely proportional to mass?

Examples:



Questions?

Questions?

Spring 2011

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ERS 202: Biomechanics

lecture 9 - fluid mechanics - ch 8 - spring 2011 - s

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