Chapter 15 Human Movement in a Fluid Medium Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D. © 2012 The McGraw-Hill Companies, Inc. All rights.

Chapter 15

Human Movement in a Fluid Medium

Basic Biomechanics, 6th editionBy Susan J. Hall, Ph.D.

© 2012 The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

15-2

The Nature of Fluids

What is a fluid?• a substance that flows or continuously

deforms when subjected to a shear stress• both liquids and gases are fluids • air and water are fluids that commonly

exert forces on the human body


15-3


What is relative velocity?

(velocity of a body with respect to the velocity of something else, such as the surrounding fluid)


15-4


vc/w = vc- vw

Velocity of cyclist relative to wind (20 m/s)Cyclist’s velocity (15 m/s)

Head windvelocity(5 m/s)

Tail windvelocity(5 m/s)

Velocity of cyclist relative to wind (10 m/s)Cyclist’s velocity (15 m/s)


15-5


What is laminar flow?

Laminar flow is characterized by smooth, parallel layers of fluid.


15-6


What is turbulent flow?

Turbulent flow is characterized by mixing of adjacent fluid layers.

Region of turbulence

Motion of

sphere


15-7


What are relevant fluid properties?

• density - mass/volume• specific weight - weight/volume• viscosity - internal resistance of a fluid to flow


15-8

Buoyancy

What is buoyancy?

a fluid force with:• magnitude based on Archimedes’ principle,• direction always vertically upward,• and point of application being a

body’s center of volume.


15-9

Buoyancy

What is Archimedes’ principle?A physical law stating that the buoyant

force acting on a body is equal to the weight of the fluid displaced by the body: Fb = Vd

Where Fb = buoyant force, Vd = displaced fluid volume, = fluid specific weight


15-10

Buoyancy

What determines whether a body floats or sinks?

• Floating occurs when the buoyant force is greater than or equal to body weight.

• Sinking occurs when body weight is greater than the buoyant force.


15-11

Buoyancy

What determines whether a body floats or sinks?

The equation of static equilibrium for vertical force can be used to quantitatively answer this

question:Fv = 0

0 = V - wt


15-12

Buoyancy

A floating body at rest (position A) will

rotate until the buoyant force and weight force are vertically aligned

(position B) so that zero torque is

present.

A

B

Buoyantforce Center of

volume

WeightCenter of

gravity

Center ofvolume

Buoyantforce

Center ofgravity

Weight


15-13

Drag

What is drag?

• a force caused by the dynamic action of a fluid that acts in the direction of the freestream fluid flow

• generally a resistance force that tends to slow the motion of a body

moving through a fluid


15-14

Drag

What factors affect the total drag force?

Where: • FD = drag, • CD = the coefficient of drag - a unitless number;

an index of a body’s ability to generate fluid resistance• = fluid density• Ap = body surface area perpendicular to the fluid flow• v = relative velocity of the body with respect to the fluid

FD = ½CDApv2


15-15

Drag

From 0 to v1 drag increases approximately with velocity squared (v2.) At v1 there is sufficient relative velocity to generate a turbulent boundary layer, which is why, from v1 to v2, form drag decreases. After v2, total drag increases.

v1 v2

Relative velocity

Dra

g fo

rce

Laminar Turbulent

Pattern of change in drag force with increasing relative velocity.


15-16

Drag

What is skin friction?

• drag derived from friction in adjacent layers of fluid near a body moving through the fluid

• AKA surface drag and viscous drag


15-17

Drag

What is skin friction?

Side view of fluid flow around a flat thin plate. Skin friction is the form of drag that predominates when the flow is primarily laminar.

Laminar boundary layer

Turbulent boundary layer

Flu

id fl

ow


15-18

Drag

What factors affect the magnitude of skin friction?

Skin friction increases with:• the relative velocity of fluid flow• the surface area of the body over which the flow occurs• the roughness of the body surface• the viscosity of the fluid


15-19

Drag

What is form drag?

Form drag is derived from a pressure differential between the lead and rear sides of a body moving through a fluid. It is also known as profile drag and pressure drag.

Region of turbulence

Motion of

sphere


15-20

Drag

What is form drag?

A streamlined shape (A) reduces form drag by reducing the turbulence created at the trailing edge, (thus reducing the pressure differential present in B.)

A

B


15-21

Drag

What factors affect the magnitude of form drag?Form drag increases with:• the relative velocity of fluid flow• the magnitude of the pressure gradient

between the front and rear ends of the body

• the surface area of the body perpendicular to the fluid flow


15-22

Drag

What is wave drag?(drag derived from the generation of

waves at the interface between two different fluids, such as air and water)


15-23

Drag

What factors affect the magnitude of wave drag?

Wave drag increases with:• the vertical oscillation of the body with

respect to the fluid• the relative velocity of the body in the

fluid


15-24

Lift

What is lift?

• a force acting on a body in a fluid in a direction perpendicular to the fluid flow

• generally a resistance force that tends to slow the motion of a body moving through a fluid


15-25

Lift

What factors affect lift force?

Where: • FL = lift, • CL = the coefficient of lift - a unitless number; an

index of a body’s ability to generate lift• = fluid density• AP = body surface area perpendicular to the fluid

flow• v = relative velocity of the body with respect to the

fluid

FL = ½CLApv2


15-26

Lift

What factors affect the magnitude of lift?

Lift increases with:• the relative velocity of fluid flow• the surface area of the flat side of the

foil• the coefficient of lift• the density of the fluid


15-27

Lift

What is a foil?(a shape capable of generating lift in a fluid)

Lift generated by a foil is directed from

the region of relative high pressure on the

flat side of the foil toward the region of relative low pressure on the curved side of

the foil.

High velocity low pressure

Low velocity high pressure


15-28

Lift

What is the Bernouli principle?• an expression of the inverse relationship

between relative velocity and relative pressure in a fluid flow

• regions of low relative velocity are associated with relative high

pressure• regions of high relative velocity are

associated with relative low pressure Basic Biomechanics, 6th edition

By Susan J. Hall, Ph.D.

15-29

Lift

What is the Bernouli principle?

Where: • p = pressure, • = specific weight of the fluid,• z = elevation,• v = relative velocity,• g = acceleration of gravity, and• C = a constant

P v2

+ z + 2g = C


15-30

Lift

What is the angle of attack?

(angle between the longitudinal axis of a body and the direction of the fluid flow)


15-31

Lift

What is the Magnus effect?

• deviation in the trajectory of a spinning object toward the direction of spin

• results from the Magnus force


15-32

Lift

What is the Magnus force?

Magnus force results from a pressure differential created by a spinning body.

Relative low velocity flowRelative high pressure

Relative high velocity flowRelative low pressure

Magnusforce

Relative low velocity flowRelative high pressure

Relative high velocity flowRelative low pressure

Magnusforce

Topspin Backspin


Chapter 15 Human Movement in a Fluid Medium Basic Biomechanics, 6 th edition By Susan J. Hall, Ph.D. © 2012 The McGraw-Hill Companies, Inc. All rights.

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