Mechanics of Solids and Fluids

AP Physics Rapid Learning Series - 11
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 1
Rapid Learning Center
Chemistry :: Biology :: Physics :: Math
Rapid Learning Center Presents …Rapid Learning Center Presents …
Teach Yourself
AP Physics in 24 Hours
1/57 *AP is a registered trademark of the College Board, which does not endorse, nor is
affiliated in any way with the Rapid Learning courses.
Mechanics of Solidsec a cs o So ds
and Fluids
Physics Rapid Learning Series
www.RapidLearningCenter.com/
© Rapid Learning Inc. All rights reserved.
Wayne Huang, Ph.D.
Keith Duda, M.Ed.
Peddi Prasad, Ph.D.
Gary Zhou, Ph.D.
Michelle Wedemeyer, Ph.D.
Sarah Hedges, Ph.D.

Learning Objectives
By completing this tutorial, you will learn the
properties of two basic states of matter – solids and
fluids:
Classification of states
of matter
Elasticity of solids
Pressure variation of
fluids and buoyancy
3/57
y y
Fluids in motion
Surface tension and
viscosity.
Concept Map
Previous content
New content
States of
Matter
Includes Viscous
Flow
Solids Fluids
Elasticity
Pressure
Static
fluids
Surface
Viscosity
Non viscousNon-viscous
Flow
By
In motion
4/57
Variation
Buoyancy andBuoyancy and
Archimedes’
Principle
Leads to
Bernoulli’s
Equation
Work and Energy
Law of
Work and Energy
Tension
Yields
Capillary
Action
Leads to
Density
Expansion
Thermal
Expansion

States of Matter
Low temperature High temperature
Change of state with temperature
Solids GasesFluids (Liquid)
5/57
Strong inter-molecular
force
Loose inter-molecular
force
Fixed molecule
Definite shape
Wandering molecule
Indefinite shape
Solids and
Elasticity
Let’s start out by discussing solids.
6/57

Classification of Solids - 1
Crystalline
Ordered atomic
Two categories:
Ordered atomic
structure
Existence of melting
point
Amorphous solid
Randomly arranged
7/57
y g
atomic structure
No melting point
Example:
Nature Crystal
Crystalline
Ordered atomic
Two categories:
Ordered atomic
structure
point
Amorphous solid
Randomly arranged
8/57
y g
atomic structure
No melting point
Ordered atomic structure

Crystalline
Ordered atomic
Two categories:
Ordered atomic
structure
point
Amorphous solid
Randomly arranged
9/57
y g
atomic structure
No melting point
Melting curve
Crystalline
Ordered atomic
Two categories
Ordered atomic
structure
point
Amorphous solid
Randomly arranged
10/57
y g
atomic structure
No melting point
Example:
Candle

Crystalline
Ordered atomic
Two categories:
Ordered atomic
structure
point
Amorphous solid
Randomly arranged
11/57
y g
atomic structure
No melting point Randomly arranged
structure
Crystalline
Ordered atomic
Two categories:
Ordered atomic
structure
point
Amorphous solid
Randomly arranged
12/57
y g
atomic structure
No melting point
Melting curve

Density and Thermal Expansion - 1
Density
Mass per unit volume,
i ld h hi hi.e. gold has a higher
density than iron.
Thermal expansion
effect
Volume or length
increases with
temperature
13/57
temperature.
Thermal expansion effect
Density
Mass per unit volume, Thermal
expansioni.e. gold has a higher density
than iron.
Volume or length
increases with
temperature
( )00 TTαLL −=−
High
Temp.
Low
Length at
high Temp.
Length at
expansion
coefficient
14/57
Thermal expansion
coefficients
Low
Temp.
Length at
low temp.

Density
Mass per unit volume,
i e gold has a higher densityi.e. gold has a higher density
than iron
Volume increases
with temperature
Thermal expansion
ffi i t
15/57
coefficients
Applications
Used in Thermostat
Bimetallic strips
Deformation of Solids
Stress
Force causing
deformation
Strain
Degree of deformation
Elastic behavior
Proportional limit
Elastic limit
Proportional
limit
Elastic
limit
Elastic behavior
Plastic behavior
Breaking
point
16/57
Elastic limit
Plastic behavior
Breaking point
Stress-strain curve

Three Types of Elastic Modulus - 1
Young’s modulus
Definitions:
stresstensile
Y ≡
A
F
Force
Cross area
17/57
straintensile
Y ≡
0L
∆L
Length change
Original length
Shear modulus
Definitions:
A
F
Tangent force
Cross
area
stressShear
G =
18/57
h
∆x
area
Tangent
displacement
Original thickness
strainShear
G =

Bulk modulus
Definitions:
A
F
Normal force
Normal areastressVolume
B =
19/57
V
∆V
Volume change
Original Volume
strainVolume
B −=
Example: Squeezing a Sphere
A sphere, with volume of 0.50 m3 and bulk modulus of 8
GPa, is immersed in water deeply. The pressure on it is
20 MPa. What is the change in volume of the sphere?
Solution:
Step 1: By the definition of bulk modulus
Step 2: Finally we get
( )
( )∆V/V
F/A
B −=×
B
∆V
B
∆V
×
20/57
( )
B
F/AV
∆V −=
Step 3: Substituting the parameters, we get
Pressure
33
m101.25∆V −
×−=

Melting process
Question: States of Solids
What are the physical differences between
crystalline and amorphous?
Melting process
Definite shape and volume
Micro-structures
Transparency
21/57
Transparency
Conductivity
Melting process
Answer: States of Solids
What are the physical differences between
crystalline and amorphous?
Melting process
Definite shape and volume
Micro-structures
Transparency
22/57
Transparency
Conductivity
Crystalline solids have a fixed melting point and
defined micro-structures. Amorphous solids have
neither.

Static Fluids
The mechanical properties of static fluids
23/57
Pressure in Fluids
Equilibrium equation for
arbitrary portion in fluidsy p
Pressure in fluids
0APMgPA 0 =−−
ρAhM =
ρghPP 0 +=
24/57
The forces on a water volume

Pascal’s Principle
Pascal’s principle:
The pressure at a depth
of h below the surface
of a fluid open to the
atmosphere is greater
than atmospheric
pressure by the amount
ρgh
25/57
Same depth will have
the same pressure
PA = PB = PC = PD
Pressure is the same at all
points that have the
same elevation
Pressure Transmission - 1
Application of Pascal principle – Hydraulic jack
Fluid inside the jack is
compressed through a
pistol.
This pressure is
transmitted to the larger
output piston that
creates a great force to
26/57
Hydraulic jack
creates a great force to
lift objects.

Pressure Transmission -2
Pressure can be
transmitted in fluid.
Application of Pascal principle – Hydraulic jack
Pressures at A1 and A2
are the same.
PA1 = F1/A1 = F2/A2 = PA2
Force can be amplified
If A1 <<A2, F2 >>F1
27/57
Stroke is reduced by
energy conservation
law and continuity law
Illustration of operating
Mechanism for
hydraulic jack
Buoyancy - 1
What is buoyancy?
The lifting force for
objects in fluids
28/57
They are lifted by buoyancy

Buoyancy - 2
What is buoyancy?
The lifting force for
objects in fluids
What causes buoyancy?
Pressure difference on
objects
(1) Upper pressure
(2) Lower pressure
29/57
(2) Lower pressure
(3) Resultant force
imρgVB =
Buoyancy of an object
Immersed in fluids
Buoyant force, N
Archimedes’ Principle
Archimedes’ principle:
Any body completely orAny body completely or
partially submerged in a
fluid is buoyed up by a
force whose magnitude
is equal to the weight of
the fluid displaced by
the body.
30/57
imρgVB = Archimedes
287-212B.C.
Volume
immersed
m3
Acceleration
of gravity
9.8m/s2
Density of
material
Kg/m3

Question: Hot Air Balloon
Why can a hot air balloon fly in the sky?
___________
31/57
___________
Answer: Hot Air Balloon
Why can a hot air balloon fly in the sky?
Density of inner air
___________decreases
Buoyancy generated
32/57
___________y y g

Surface Tension
Questions:
Why insects can walk
on water?
Why can razor blades
float on water?
Why can water raise in
33/57
Why can water raise in
thin tubes?
Why does this happen?
Surface Tension- 2
Questions
-Why can insects walk on
water?
-Why can razor blades
float on water?
-Why can water raise in
thin tubes?
Surface tension
The tendency for the Reason
34/57
surface of a liquid to
contract in area.
Why does this happen?

Surface Tension- 3
Questions
-Why can insects walk on
water?
Why can razor blades-Why can razor blades
float on water?
-Why can water raise in
thin tubes?
Surface tension
The tendency for the
surface of a liquid to
t t i
35/57
Mathematical definition
2L
F
γ =
Apparatus for testing
Surface tension
Inside edge
and outside
edge
contract in area.
Capillary Action - 1
Two types of fluid-
surface interactions:
Mercury
vs Glass
Water
vs Glass
36/57
Left: unwettable
Right: wettable

Two types of fluid-
Unwettable
Wettable
Unwettable
(water vs paraffin)
Contact
angle
37/57
Wettable
(water vs glass)
Two types of fluid-
UnwettableUnwettable
Wettable
Water rise for wettable
fluid-surface interaction
( )cosφr2πγFv =
Balanced by:
38/57
hρgπrw 2
=
Balanced by:
Yields:
cos φ
ρgr
2γ
h =
Vertical
component
of surface
forceWeight of
the water
volume
Water rise due to
capillary action

Question: Water Goes Up or Down?
If a thin tube made of paraffin is inserted in water, the
level of water inside the tube will be than the
outside water. (water-paraffin is unwettable)
higher
lower
same
39/57
uncertain
Answer: Water goes up or down?
If a thin tube made of paraffin made is inserted in
water, the level of water inside the tube will be
than the outside water. (water-paraffin is unwettable)
higher
lower
same
40/57
uncertain

Fluids in Motion
Now we’ll study the properties of
fluids that are moving
41/57
fluids that are moving.
Fluid in Motion: A Preview
Properties of fluids:
Density, gravity,
viscosity
Continuity
Laminar and turbulent
flow
Bernoulli’s Equation for
steady ideal flow
42/57
steady ideal flow

Density and Gravity
Definition of density
Mass per unit volume (fluids take indefinite
shape but definite volume)p )
Gravity
The force between the earth and the matter.
It is governed by Newton’s law of gravitation.
This force is pointing “downwards” (toward
the earth) and is proportional to the mass
43/57
) p p
of the matter by the scaling factor of 9.8 m/s2,
which is denoted by g.
For fluids, the force per volume is used
instead of the force itself.
Viscosity
Definition
Internal friction of a fluid;
damping mechanism of
fluids
Coefficient of viscosity
Sv
Fl
ratestrainshear
stressshear
η ==
44/57
Viscous flow

Viscosity Applications
Definition
Internal friction of a fluid;
damping mechanism of
fluids
Coefficient of viscosity
Sv
Fl
ratestrainshear
stressshear
η ==
45/57
Applications
Dashpot or damper
Configuration and products
The Equation of Continuity
Continuity
The net rate of flow of
mass inward across any
closed surface is equal to
the rate of increase of the
mass within the surface
Mathematical expression
222111 vAρvAρ =
46/57
For non-compression fluid
222111
constantρρ 21 ≡=
Yields:
2211 vAvA =
Flow into and out of
a portion of a tube

Laminar and Turbulent Flow - 1
Laminar or streamline
Every particley p
passing a particular
point moves exactly
along the smooth
path followed by
particles passing that
point earlier.
Laminar
(Streamline)
47/57
Different streamlines
cannot intercross.
Velocity is low.
Smoke from a cigarette
Cigarette
Laminar and Turbulent Flow - 2
Turbulent flow
Motion is highly
Turbulent
flow
g y
irregular.
Vortices are
developed within the
fluid.
Resistance to the
flow is increased
Laminar
(Streamline)
48/57
flow is increased.
Velocity is high.
Smoke from a cigarette
Cigarette

Steady Ideal Flow
Ideal flow:
Non-viscous
& non-compressible
The work at lower end
The work at upper end
VP∆xFW 1111 ==
VPW 22 −=
Ideal flow in a pipe
49/57
Work and energy law
( )12
2
1
2
221 ρgVyρgVyρVv
2
1
ρVv
2
1
WW −+⎟
⎠
⎞
⎜
⎝
⎛
−=+
Kinetic energy Potential energy
Work
Bernoulli’s Equation
Mathematical expression
Bernoulli’s Equation
Physical meaning:
constantρgyvρ
2
1
P 2
=++
For an ideal flow, the sum of the pressure (P),
Ideal flow in a pipe
50/57
, p ( ),
the kinetic energy per unit volume (1/2ρv2) ,
and the potential energy per unit volume(ρgy)
has the same value at all points along a stream line.

Application for Bernoulli’s Equation
Velocity at “2” is zero
Velocity at “1” is to be measured
Pitot tube
Illustration of pitot tube
Velocity at 1 is to be measured
Heights of “1” and “2” are the same
By Bernoulli’s equation
1
2
112
2
22 ρgyρv
2
1
Pρgyρv
2
1
P ++=++
=0
51/57
111222 ρgyρ
2
ρgyρ
2
Same
3l12
2
1 ghρPPρv
2
1
=−=
Density of the
liquid in the tube
3
l
1 gh
ρ
ρ
2v =
yields
Example: Speed at a Drain Hole
Consider a tank with a drain hole at its bottom. The cross-
sectional area of the tank is large relative to that of the
hole. The water level drops slowly so that we assume
V2=0. Find the speed at which the water leaves the hole2 p
when the water level is 0.5m above the hole.
Solution:
Step 1: By Bernoulli’s Equation
2
2
201
2
10 ρgyvρ
2
1
Pρgyvρ
2
1
P ++=++
=0
52/57
Step 3: Substituting the parameters, we get
( )121 yy2gv −=
3.13m/sv 1 =

Question: Aerodynamic Force on Wings
Why can a fixed-wing aircraft fly?
Tip: Consider and apply Bernoulli’s equation
Air flow near the upper surface of the wing is
moving faster than that near its lower surface
An air flow blowing toward the wing
The pressure on the upper surface of the wing is
smaller than that near its lower surface
53/57
Other mechanism
Answer: Aerodynamic Force on Wings
Why can a fixed-wing aircraft fly?
Tip: Consider and apply Bernoulli’s equation
Air flow near the upper surface of the wing is
moving faster than that near its lower surface
An air flow blowing toward the wing
The pressure on the upper surface of the wing is
smaller than that near its lower surface
54/57
Other mechanism

Ideal flow:
Bernoulli’s
Ideal flow:
Bernoulli’s
States of
matter: Solid,
States of
matter: Solid, ApplicationsApplications
Learning Summary
Static behavior ofStatic behavior of
Bernoulli’s
equation
Bernoulli’s
equation
Liquid and
Gas
Liquid and
Gas
of fluid flowof fluid flow
55/57
Static behavior of
fluid: pressure,
buoyancy, and
surface tension
Static behavior of
fluid: pressure,
buoyancy, and
surface tension
Solids and
elasticity
Solids and
elasticity
Congratulations
You have successfully completed
the tutorial
Mechanics of Solids and
FluidsFluids

Wh t’ N t
Chemistry :: Biology :: Physics :: Math
What’s Next …
Step 1: Concepts – Core Tutorial (Just Completed)
Step 2: Practice – Interactive Problem Drill
Step 3: Recap – Super Review Cheat Sheet
57/57
Go for it!
http://www.RapidLearningCenter.com

Mechanics of Solids and Fluids

Recommended

Recommended

More Related Content

Viewers also liked

Viewers also liked (20)

Similar to Mechanics of Solids and Fluids

Similar to Mechanics of Solids and Fluids (20)

More from Timothy Welsh

More from Timothy Welsh (20)

Recently uploaded

Recently uploaded (20)

Mechanics of Solids and Fluids