8/7/2019 Lecture 9 - Fluid Mechanics - Ch 8 - Spring 2011 - S
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FLUID MECHANICS
Mr. DicusSpring 2011
1ERS 202: Biomechanics
8/7/2019 Lecture 9 - Fluid Mechanics - Ch 8 - Spring 2011 - S
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Objectives
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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
8/7/2019 Lecture 9 - Fluid Mechanics - Ch 8 - Spring 2011 - S
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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
8/7/2019 Lecture 9 - Fluid Mechanics - Ch 8 - Spring 2011 - S
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Buoyant Force
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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
8/7/2019 Lecture 9 - Fluid Mechanics - Ch 8 - Spring 2011 - S
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Human Buoyancy
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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?
8/7/2019 Lecture 9 - Fluid Mechanics - Ch 8 - Spring 2011 - S
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?WHY?
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8/7/2019 Lecture 9 - Fluid Mechanics - Ch 8 - Spring 2011 - S
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Dynamic Force
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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
8/7/2019 Lecture 9 - Fluid Mechanics - Ch 8 - Spring 2011 - S
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Dynamic Force
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Relative velocity
Difference of the absolute velocity of object and
absolute velocity of fluid
8/7/2019 Lecture 9 - Fluid Mechanics - Ch 8 - Spring 2011 - S
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Dynamic Force
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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
8/7/2019 Lecture 9 - Fluid Mechanics - Ch 8 - Spring 2011 - S
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Drag Equation
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8/7/2019 Lecture 9 - Fluid Mechanics - Ch 8 - Spring 2011 - S
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Surface Drag (skin friction, viscous drag)
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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?
8/7/2019 Lecture 9 - Fluid Mechanics - Ch 8 - Spring 2011 - S
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Form Drag (shape drag, profile drag, pressure drag)
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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
8/7/2019 Lecture 9 - Fluid Mechanics - Ch 8 - Spring 2011 - S
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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
8/7/2019 Lecture 9 - Fluid Mechanics - Ch 8 - Spring 2011 - S
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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
8/7/2019 Lecture 9 - Fluid Mechanics - Ch 8 - Spring 2011 - S
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Will rough surface always increase form drag?
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8/7/2019 Lecture 9 - Fluid Mechanics - Ch 8 - Spring 2011 - S
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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
8/7/2019 Lecture 9 - Fluid Mechanics - Ch 8 - Spring 2011 - S
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Dilemma: Choosing the correct shape
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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?
8/7/2019 Lecture 9 - Fluid Mechanics - Ch 8 - Spring 2011 - S
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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:
8/7/2019 Lecture 9 - Fluid Mechanics - Ch 8 - Spring 2011 - S
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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
8/7/2019 Lecture 9 - Fluid Mechanics - Ch 8 - Spring 2011 - S
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Lift Force
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Bernoulli’s Principle
Faster moving fluids produce less lateral force than
slower moving fluids
8/7/2019 Lecture 9 - Fluid Mechanics - Ch 8 - Spring 2011 - S
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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
8/7/2019 Lecture 9 - Fluid Mechanics - Ch 8 - Spring 2011 - S
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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: