普通物理－Lecture10－Solids & Waves

(1)

普通物理

Lecture 10

Solids & Fluids

固體與流體固體與流體

(2)



St t

f M tt

物質的型態物質的型態



State of Matter

物質的型態物質的型態



Deformation of Solids

固體的變形固體的變形



V i ti

f P

ith D th

壓力隨高度改變壓力隨高度改變



Density & Pressure

密度密度&&壓力壓力



Variation of Pressure with Depth

壓力隨高度改變壓力隨高度改變



Pressure Measurements

壓力量測壓力量測



Buoyant Forces & Archimedes’s Principle

浮力與阿基米得原理浮力與阿基米得原理浮力與阿基米得原理浮力與阿基米得原理



Fluid in Motion

運動中的流體運動中的流體



Applications of Fluid Dynamics

流體動力學的應用流體動力學的應用



Applications of Fluid Dynamics

流體動力學的應用流體動力學的應用



(3)

State of Matter

物質的型態

The Solid The Solid 固體固體 The Solid The Solid 固體固體 

 Has definiteHas definite volumevolume 

 Has definite Has definite volumevolume 

 Has definite Has definite shapeshape

M l l h ld i ifi



 Molecules are held in specific Molecules are held in specific

locations locations

–

– by by electrical forceselectrical forces 

 Vibrate about equilibrium Vibrate about equilibrium qq

positions positions

(4)

State of Matter

物質的型態



External forces can be applied to

the solid and compress the

material

I h d l h i ld b

–

– In the model, the springs would be In the model, the springs would be

compressed compressed



When the force is removed, the

solid returns to its original shape

and size

(5)

State of Matter

物質的型態

Crystalline Solidy



 Atoms have an ordered Atoms have an ordered

structure structure structure structure



 This example is saltThis example is salt

G h t N

G h t N ++ _ii

–

– Gray spheres represent NaGray spheres represent Na++ ionsions –

– Green spheres represent ClGreen spheres represent Cl-- ionsions

Amorphous Solid



 Atoms are arranged almostAtoms are arranged almost 

 Atoms are arranged almost Atoms are arranged almost

randomly randomly

(6)

State of Matter

物質的型態

The Liquid

The Liquid qq 液體液體 

 Has a definite volumeHas a definite volume 

 No definite shapeNo definite shape 

 Exists at a Exists at a higher temperaturehigher temperaturegg pp

than solids than solids



 The molecules “wander”The molecules “wander” 

 The molecules wander The molecules wander

through the liquid in a random through the liquid in a random fashion

fashion fashion fashion

–

(7)

State of Matter

物質的型態

The Gas

The Gas 氣體氣體



Has no definite volume



Has no definite shape

M l

l

i

t t

d

ti

M l

l

i

t t

d

ti



Molecules are in constant random motion



The molecules exert only weak forces on

yy

each other



Average distance between molecules is



(8)

State of Matter

物質的型態

The Plasma

The Plasma 游離氣體游離氣體、、電漿電漿、、等離子體等離子體



Matter heated to a

very high temperature

M

f h

l

f

d f

h

M

f h

l

f

d f

h



Many of the electrons are freed from the

nucleus



Result is a collection of free, electrically

charged ions

Plasmas exist inside stars

(9)

Deformation of Solids



 All objects are deformableAll objects are deformable 

 It is possible to change the shape or size (or It is possible to change the shape or size (or pp gg pp ((

both) of an object through the

both) of an object through the application of application of external forces

external forces



 when the forces are removed, the object tends when the forces are removed, the object tends

to its original shape to its original shape to its original shape to its original shape

–

– This is a deformation that exhibits This is a deformation that exhibits elastic elastic behavior

behavior behavior behavior

(10)

Deformation of Solids

Elastic Propertiesp



 StressStress is the is the force per unit areaforce per unit area causing the causing the

deformation deformation deformation deformation



 StrainStrain is a measure of the amount of is a measure of the amount of

deformation deformation deformation deformation



 The The elastic moduluselastic modulus is the constant of is the constant of

proportionality between stress and strain proportionality between stress and strain proportionality between stress and strain proportionality between stress and strain

–

– For sufficiently small stresses, the stress is directly For sufficiently small stresses, the stress is directly

proportional to the strain proportional to the strain proportional to the strain proportional to the strain

–

(11)

Deformation of Solids

Elastic Modulus



The elastic modulus can be thought of as

the

stiffness

of the material

–

– A material with a large elastic modulus isA material with a large elastic modulus isA material with a large elastic modulus is A material with a large elastic modulus is

very stiff and difficult to deform very stiff and difficult to deform

 Analogous to the spring constantAnalogous to the spring constantAnalogous to the spring constantAnalogous to the spring constant –

(12)

Deformation of Solids

Young’s Modulus: Elasticity in Lengthg y g



 Tensile stress is the ratio of Tensile stress is the ratio of

the external force to the the external force to the the external force to the the external force to the cross

cross--sectional areasectional area

Tensile is because the bar Tensile is because the bar

–

– Tensile is because the bar Tensile is because the bar

is under tension is under tension

i i



 The elastic modulus is called The elastic modulus is called

Young’s modulus Young’s modulus

(13)

Deformation of Solids



 SI units of stress are Pascals, PaSI units of stress are Pascals, Pa 

 SI units of stress are Pascals, PaSI units of stress are Pascals, Pa

–

– 1 Pa = 1 N/m1 Pa = 1 N/m22



 The tensile strain is the ratio of the change in length to theThe tensile strain is the ratio of the change in length to the 

 The tensile strain is the ratio of the change in length to the The tensile strain is the ratio of the change in length to the original length

original length

Strain is dimensionless

F



Y



L

–

– Strain is dimensionlessStrain is dimensionless

o

Y

A

L



 Young’s modulus applies to a stress of Young’s modulus applies to a stress of either

either tension tension oror compressioncompression



 It is possible to exceed the elastic limit of It is possible to exceed the elastic limit of the material

(14)

Deformation of Solids

Breakingg



 If stress continues, it surpasses its If stress continues, it surpasses its ultimate strengthultimate strength

Th lti t t th i th t t t th Th lti t t th i th t t t th

–

– The ultimate strength is the greatest stress the The ultimate strength is the greatest stress the

object can withstand without breaking object can withstand without breaking 

 The breaking pointThe breaking point 

 The breaking point The breaking point

–

– For a For a brittle materialbrittle material, the breaking point is just , the breaking point is just

beyond its ultimate strength beyond its ultimate strength beyond its ultimate strength beyond its ultimate strength

–

– For a For a ductile materialductile material, after passing the ultimate , after passing the ultimate

strength the material thins and stretches at a strength the material thins and stretches at a gg lower stress level before breaking

(15)

Deformation of Solids

Shear Modulus: Elasticity of Shape y p



 Forces may be Forces may be parallel parallel to one of to one of

th bj t’ f th bj t’ f

the object’s faces the object’s faces



 The stress is called a The stress is called a shear stressshear stress 

 The The _{shear strain}_{shear strain} is the ratio of the is the ratio of the

horizontal displacement and the horizontal displacement and the h i ht f th bj t

h i ht f th bj t height of the object height of the object



(16)

Deformation of Solids

 

_FF

shear stress

A



x

shear strain

h





h

F

x

S



 S

A



h



(17)

Deformation of Solids

Bulk Modulus: Volume Elasticityy



Bulk modulus characterizes the response

of an object to

uniform squeezing

–

– Suppose the forces are perpendicular to, and Suppose the forces are perpendicular to, and pppp p pp p ,,

act on, all the surfaces act on, all the surfaces

 Example: when an object is immersed in a fluidExample: when an object is immersed in a fluid



The object undergoes a change in volume

without a change in shape

g

p

(18)

Deformation of Solids



 Volume stress, ΔP, is theVolume stress, ΔP, is theVolume stress, ΔP, is the Volume stress, ΔP, is the

ratio of the force to the ratio of the force to the surface area

surface area

–

– This is also the PressureThis is also the Pressure



 The volume strain is equal The volume strain is equal qq

to the ratio of the change to the ratio of the change in volume to the original in volume to the original

ll volume volume V V P B V    

(19)

Deformation of Solids



 A material with a large bulk modulus is difficult A material with a large bulk modulus is difficult

to compress to compress



 The negative sign is included since an increase in The negative sign is included since an increase in

pressure will produce a decrease in volume pressure will produce a decrease in volume

–

– B is always positiveB is always positive



 The The _{compressibility}_{compressibility} is the reciprocal of the bulk is the reciprocal of the bulk

modulus modulus

C

1

(20)

Deformation of Solids



Solids

have Young’s, Bulk, and Shear

moduli



Liquids

have only

bulk moduli

, they will

not undergo a shearing or tensile stress

–

(21)

Deformation of Solids

(22)

Deformation of Solids

Ultimate Strength of Materials Ultimate Strength of Materials



The

ultimate strength

of a material is the



The

ultimate strength

of a material is the

maximum force per unit area the material

ith t d b f

it b

k

f

t

ith t d b f

it b

k

f

t

can withstand before it breaks or fractures



Some materials are stronger in compression

than in tension

(23)

Example 1

A vertical steel beam in a building supports a load of 6.0×104_{N. (a) If the length of the beam is 4.0 m and its}

cross-sectional area is 8.0×10-3 _m2_{, find the distance the beam is compressed along its length. (b) What}

maximum load in newtons could the steel beam support before failing? Assuming ultimate strength = 5×108kPa.

(24)

Example 2

A solid lead sphere of volume 0.50 m3_{, dropped in the ocean, sinks to a depth of 2.0×10}3_{m, where}

the pressure increases by 2.0×107_{Pa. Lead has a bulk modulus of 4.2×10}7 _{kPa. What is the change}

the pressure increases by 2.0×10 Pa. Lead has a bulk modulus of 4.2×10 kPa. What is the change in volume of the sphere?

(25)

Deformation of Solids

Post and Beam Arches



 A horizontal beam is A horizontal beam is

d b l

supported by two columns supported by two columns



 Used in Greek templesUsed in Greek temples 

 Columns are closely spacedColumns are closely spaced

–

– Limited length of available Limited length of available gg

stones stones

–

– Low ultimate tensile strength of Low ultimate tensile strength of

sagging stone beams sagging stone beams

(26)

Deformation of Solids

Semicircular Arch Semicircular Arch



 Developed by the RomansDeveloped by the Romans 

 Allows a wide roof span Allows a wide roof span

ti ti on narrow supporting on narrow supporting columns columns 

 Stability depends upon Stability depends upon

the compression of the the compression of the wedge

(27)

Deformation of Solids

Gothic Arch Gothic Arch



 First used in Europe in First used in Europe in

th 12

th 12thth _tt

the 12

the 12thth _century_century



 Extremely highExtremely high 

 The The flying buttressesflying buttresses飛扶飛扶壁

壁 are needed to prevent are needed to prevent

th di f th h

the spreading of the arch the spreading of the arch supported by the tall,

supported by the tall, narrow columns

narrow columns narrow columns narrow columns

(28)

Density & Pressure

y

Density



The density of a substance of uniform

Density



The density of a substance of uniform

composition is defined as its

mass per

unit volume

::

unit volume

::

_m

V







Units are kg/m

33

(SI) or g/cm

33

(cgs)

V

gg

( )

g

( g )



(29)

Density & Pressure

y



The densities of most

liquids and solids

vary

slightly

with changes in temperature and

slightly

with changes in temperature and

pressure

D

iti

f

D

iti

f

tl

ith h



Densities of

gases

vary

greatly

with changes

in temperature and pressure

(30)

Density & Pressure

y

Specific Gravity Specific Gravity

Th

ifi

it

f

b t

i th



The

specific gravity

of a substance is the

ratio of its density to the

density of water

at 4

at 4°° C

C

–

– The density of water at 4The density of water at 4°° C isThe density of water at 4The density of water at 4 C is C isC is 1000 kg/m1000 kg/m1000 kg/m1000 kg/m33



(31)

Density & Pressure

y

Pressure Pressure



 The force exerted by a The force exerted by a yy

fluid on a submerged fluid on a submerged object at any point if object at any point if jj y py p perpendicular to the perpendicular to the surface of the object surface of the objectjj

N F N Pa in F P  

(32)

Density & Pressure

y

Measuring Pressure Measuring Pressure



 ThTh ii ii lib t dlib t d 

 The spring is calibrated The spring is calibrated

by a known force by a known force



 The force the fluid exerts The force the fluid exerts

on the piston is then on the piston is then measured

(33)

Variation of Pressure with Depth

p



 If a fluid is at rest in a container, all portions of If a fluid is at rest in a container, all portions of

the fluid must be in static equilibrium the fluid must be in static equilibrium



 All points at the All points at the same depthsame depth must be at the must be at the

same pressure same pressure same pressure same pressure

–

– Otherwise, the fluid would not be in equilibriumOtherwise, the fluid would not be in equilibrium –

– The fluid would flow from the higher pressureThe fluid would flow from the higher pressureThe fluid would flow from the higher pressure The fluid would flow from the higher pressure

region to the lower pressure region region to the lower pressure region

(34)

Variation of Pressure with Depth

p



 Examine the darker region, Examine the darker region,

assumed to be a fluid assumed to be a fluidssu ed o bessu ed o be u du d

–

– It has a crossIt has a cross--sectional area Asectional area A –

– Extends to a depth h below theExtends to a depth h below theExtends to a depth h below the Extends to a depth h below the

surface surface 

 Three external forces act onThree external forces act on 

 Three external forces act on Three external forces act on

the region the region

(35)

Variation of Pressure with Depth

p

 

_P



_P





_gh

0   PP_oo is normal is normal atmospheric pressure atmospheric pressure

gh

P

₀





p p p p – – 1.013 x 101.013 x 105 5 Pa = 14.7 lb/inPa = 14.7 lb/in22 

 The pressure does not The pressure does not e p essu e does oe p essu e does o

depend upon the shape depend upon the shape of the container

(36)

Example 3

In a huge oil tanker, salt water has flooded an oil tank to a depth of 5.00 m. On top of th t i l f il 8 00 d i th ti l i f th t k Th il the water is a layer of oil 8.00 m deep, as in the cross-sectional view of the tank. The oil has a density of 0.700 g/cm3_{. Find the pressure at the bottom of the tank. (Take 1025} kg/m3 _{as the density of salt water.)}

(37)

Variation of Pressure with Depth

p

Pascal’s Principle Pascal s Principle

A h

i

li d t

A h

i

li d t

l

d



A change in pressure applied to an

enclosed

fluid

is transmitted undimished to every

point of the fluid and to the walls of the

container.

–

– First recognized by Blaise Pascal, a French First recognized by Blaise Pascal, a French

scientist (1623

scientist (1623 –– 1662)1662) scientist (1623

(38)

Variation of Pressure with Depth

p



 The hydraulic press is an The hydraulic press is an

important application of important application of P l’ P i i l P l’ P i i l Pascal’s Principle Pascal’s Principle 2 1 F F P 2 2 1 1 A A P   

 Also used in hydraulic Also used in hydraulic

brakes, forklifts, car lifts, brakes, forklifts, car lifts, etc

etc etc. etc.

(39)

Example 4

In a car lift used in a serveice station, compressed air exerts a force on a small piston of circular cross section having a radius of r1=5.00 cm. This pressure is transmitted by an incompressible liquid to a second piston of g p y p q p radius r2=15.0 cm. (a) What force must the compressed air exert on the small piston in order to lift a car weighting 13,300N? Neglect the weights of the pistons. (b) What air pressure will produce a force of that magnitude? (c) Show that the work done the by input and output pistons is the same.

(40)

Variation of Pressure with Depth

p

Ab l t G P

Absolute vs. Gauge Pressure



The pressure P is called the

The pressure P is called the absolute

absolute pressure

pressure

– – Remember, Remember,

_P



_P





_gh

0 ,,  

i th

錶壓錶壓

gh

P

₀





gh

P





(41)

Pressure Measurements

Manometer壓力計



 One end of the UOne end of the U--shaped shaped pp

tube is open to the tube is open to the atmosphere

atmospherepp



 The other end is connected The other end is connected

to the pressure to be to the pressure to be to the pressure to be to the pressure to be measured measured   Pressure at B is PPressure at B is P +ρgh+ρgh   Pressure at B is PPressure at B is P_oo+ρgh+ρgh

(42)

Pressure Measurements

Blood pressure



 Blood pressure is Blood pressure is

Blood pressure measured with a measured with a special type of special type of manometer called a manometer called a sphygmomano sphygmomano--metermeter 

 Pressure is measured Pressure is measured

in mm of mercury in mm of mercuryyy

(43)

Pressure Measurements

Barometer氣壓計



 Invented by TorricelliInvented by Torricelli 

 Invented by Torricelli Invented by Torricelli

(1608

(1608 –– 1647)1647)



 A long closed tube is filledA long closed tube is filled 

 A long closed tube is filled A long closed tube is filled

with

with mercurymercury and inverted and inverted in a dish of mercury

in a dish of mercury in a dish of mercury in a dish of mercury



 Measures atmospheric Measures atmospheric

h h pressure as ρgh pressure as ρgh

(44)

Pressure Measurements

Pressure Values in Various Units Pressure Values in Various Units



One atmosphere of pressure is defined as



One atmosphere of pressure is defined as

the pressure equivalent to a column of

mercury exactly

0 76 m

tall at 0

oo

_{C where g}

mercury exactly

0.76 m

tall at 0

oo

_{C where g}

= 9.81 m/s

22



One atmosphere (1 atm) =

–

– 76.0 cm of mercury76.0 cm of mercury –

(45)

Buoyant Forces & Archimedes’s Principle

Archimedes

y

p

y

p

Archimedes   287 287 –– 212 BC212 BC 

 Greek mathematicianGreek mathematician 

 Greek mathematician, Greek mathematician,

physicist, and engineer physicist, and engineer



 Buoyant forceBuoyant force 

(46)

Buoyant Forces & Archimedes’s Principle

y

p

Archimedes' Principle Archimedes Principle

A

bj t

l t l

ti ll

A

bj t

l t l

ti ll



Any object completely or partially

submerged in a fluid is

buoyed up by a

force

whose magnitude is equal to the

weight of the fluid displaced

(47)

Buoyant Forces & Archimedes’s Principle

y

p

Buoyant Force Buoyant Force



 The upward force is called The upward force is called pp

the

the buoyant forcebuoyant force



 The physical cause of theThe physical cause of the 

 The physical cause of the The physical cause of the

buoyant force is the buoyant force is the pressure difference pressure difference pressure difference pressure difference

between the top and the between the top and the bottom of the object

bottom of the object bottom of the object bottom of the object

(48)

Buoyant Forces & Archimedes’s Principle

y

p



The magnitude of the buoyant force always

equals the weight of the displaced fluid

B

V

g

Th b

t f

i th

f

Th b

t f

i th

f

t t ll

fluid fluid fluid

B





V

g w





The buoyant force is the same for a

totally

submerged

object of any size, shape, or density



The buoyant force is exerted by the fluid



(49)

Buoyant Forces & Archimedes’s Principle

y

p

Totally Submerged Object Totally Submerged Object



The upward buoyant force is

B ρ

B=ρ

B ρ

_fluid_fluid_fluid_fluid

gV

_obj_obj_obj_obj



The downward gravitational force is

w=mg=ρ

g ρ

gV

gg

Th

f

i

Th

f

i

B

((

) V



(50)

Buoyant Forces & Archimedes’s Principle

y

p



 ThTh bj t i lbj t i l dd 

 The object is less dense The object is less dense

than the fluid than the fluid



 The object experiences a The object experiences a

net upward force net upward force

(51)

Buoyant Forces & Archimedes’s Principle

y

p



 The object is more dense The object is more dense

h h fl id h h fl id than the fluid than the fluid



 The net force is downwardThe net force is downward 

 The object accelerates The object accelerates

downward downward

(52)

Example 5

A bargain hunter purchases a “gold “ crown at a flea market. After she gets home, she hangs it from a scale and finds its weight to be 7.84 N. She then , g g weights the crown while it is immersed in water, and now the scale reads 6.86 N. Is the crown made of pure gold?

(53)

Buoyant Forces & Archimedes’s Principle

y

p

Fl ti Obj t Floating Object



The object is in

static equilibrium



The object is in

static equilibrium



The upward buoyant force is balanced by

the downward force of gravity



Volume of the fluid displaced

corresponds to the volume of the object

beneath the fluid level

(54)

Buoyant Forces & Archimedes’s Principle

y

p



 The forces balanceThe forces balance  

V

obj fluid fluid obj

V





obj fluid



(55)

Example 6

A raft is constructed of wood having a density of 6.00 ×102 _kg/m3_{. Its surface area is} 5 70 2 _{d it} _l _{i 0 60} 3 _Wh _th _{ft i} _l _{d i f} _h _t _t _{h t} 5.70 m2_{, and its volume is 0.60 m}3_{. When the raft is placed in fresh water , to what} depth h is the bottom of the raft submerged?

(56)

Fluids in Motion

St li Fl 流線流

Streamline Flow流線流



 Streamline flowStreamline flow 

 Streamline flow Streamline flow

–

– Every particle that passes a particular point moves Every particle that passes a particular point moves

exactly along the smooth path followed by particles exactly along the smooth path followed by particles yy gg pp y py p that passed the point earlier

that passed the point earlier

–

– Also called Also called laminar flowlaminar flow層流層流



 Streamline is the pathStreamline is the path

–

– Different streamlines cannot cross each otherDifferent streamlines cannot cross each other

(57)

Fluids in Motion

(58)

Fluids in Motion

T b l t Fl 紊流湍流亂流

Turbulent Flow 紊流、湍流、亂流



The flow becomes irregular

–

– exceeds a certain velocityexceeds a certain velocityyy –

– any condition that causes abrupt changes in any condition that causes abrupt changes in

velocity velocity velocity velocity



Eddy currents

渦流渦流

are a characteristic of

b l

fl

b l

fl

turbulent flow

(59)

Fluids in Motion

Viscosity

Vi

it

Vi

it

i th d

f

i t

l f i ti



Viscosity

is the degree of

internal friction

in the fluid



The internal friction is associated with

the

resistance between two adjacent

the

resistance between two adjacent

layers

of the fluid moving relative to each

th

other

(60)

Fluids in Motion

Characteristics of an Ideal Fluid



 The fluid is nonviscousThe fluid is nonviscous

–

– There is no internal friction between adjacent layersThere is no internal friction between adjacent layers



 The fluid is incompressibleThe fluid is incompressible

–

– Its density is constantIts density is constant



 The fluid motion is steadyThe fluid motion is steady

–

– Its velocity, density, and pressure do not change in timeIts velocity, density, and pressure do not change in time



 The fluid moves without turbulenceThe fluid moves without turbulence

–

(61)

Fluids in Motion

Equation of Continuity _A_A _A_A Equation of Continuity __ _A_A 11vv11 = A= A22vv22 

 The product of the crossThe product of the

cross--i l f i

i l f i

sectional area of a pipe sectional area of a pipe and the fluid speed is a and the fluid speed is a constant

constant constant constant

–

– Speed is high where the Speed is high where the

pipe is narrow and speed is pipe is narrow and speed is pipe is narrow and speed is pipe is narrow and speed is low where the pipe has a low where the pipe has a large diameter

large diameter



(62)

Fluids in Motion



 The equation is a consequence of The equation is a consequence of conservation conservation

of mass

of mass and aand a steady flowsteady flow of mass

of mass and a and a steady flowsteady flow



 A v = constantA v = constant

i i i f

–

– This is equivalent to the fact that This is equivalent to the fact that the volumethe volume

of fluid that

of fluid that entersenters one end of the tube in a one end of the tube in a

i i i

i i i ff

given time interval equals

given time interval equals the volumethe volume of of fluid

fluid leavingleaving the tube in the same intervalthe tube in the same interval

(63)

Example 7

A water hose 2.50 cm in diameter is used by a gardener to fill a 30.0-liter bucket.( One liter =1000 cm3₎

The gardener notices that it take 1.00 min to fill the bucket. A nozzle with an opening of cross-sectional g p g area 0.500 cm2_{is then attached to the hose. The nozzle is held so that water is projected horizontally from}

(64)

Fluids in Motion

Daniel Bernoulli Daniel Bernoulli   1700 1700 –– 17821782 

 Swiss physicist and Swiss physicist and p yp y

mathematician mathematician



 Wrote Wrote Hydrodynamica_{Hydrodynamica}_y_y _y_y 

 Also did work that was Also did work that was

the beginning of the the beginning of the gg gg kinetic theory of gases kinetic theory of gases

(65)

Fluids in Motion

Bernoulli’s Equation Bernoulli s Equation



 Relates Relates pressurepressure to fluid to fluid speedspeed and and elevationelevation 

 Bernoulli’s equation is a consequence of Bernoulli’s equation is a consequence of Conservation of Conservation of

Energy

Energy applied to an applied to an ideal fluidideal fluid 

 Assumes the fluid is incompressible and nonviscous, and Assumes the fluid is incompressible and nonviscous, and flows in a nonturbulent, steady

flows in a nonturbulent, steady--state mannerstate manner 

 States that the States that the sum ofsum of the pressure, kinetic energy per the pressure, kinetic energy per unit volume, and the potential energy per unit volume unit volume, and the potential energy per unit volume has the same value at all points along a streamline

(66)

Fluids in Motion

Venturi Tube文氏管



 Shows fluid flowing through Shows fluid flowing through

a horizontal constricted pipe a horizontal constricted pipe



 Speed changes as diameter Speed changes as diameter

changes changes



 Can be used to measure the Can be used to measure the

speed of the fluid flow speed of the fluid flow



 Swiftly moving fluids exert Swiftly moving fluids exert

less pressure than do slowly less pressure than do slowly moving fluids

(67)

Example 8

A nearsighted sheriff fires at a cattle rustler with his trusty six-shooter. Fortunately for the rustler, the bullet misses him and penetrated the town water tank, causing a leak. (a) If the top of the tank is open to the

atmosphere, determine the speed at which the water leaves the hole when the water level is 0.500 m above the hole. (b) Where does the stream hit the ground if the hole is 3.00 m above the ground?

(68)

Fluids in Motion

An Object Moving Through a Fluid



 Many common phenomena can be explained by Many common phenomena can be explained by

An Object Moving Through a Fluid

y p p y

Bernoulli’s equation Bernoulli’s equation

–

– At least partiallyAt least partiallypp yy



 In general, an object moving through a fluid is In general, an object moving through a fluid is

acted upon by a net upward force as the result acted upon by a net upward force as the result acted upon by a net upward force as the result acted upon by a net upward force as the result of any effect that causes the fluid to change its of any effect that causes the fluid to change its direction as it flows past the object

direction as it flows past the object direction as it flows past the object direction as it flows past the object

(69)

Applications of Fluid Dynamics

pp

y



 The dimples in the golfThe dimples in the golf 

 The dimples in the golf The dimples in the golf

ball help move air along ball help move air along its surface

its surface



 The ball pushes the air The ball pushes the air

down down

N ’ Thi d L N ’ Thi d L



 Newton’s Third Law Newton’s Third Law

tells us the air must push tells us the air must push up on the ball

up on the ballpp



 The spinning ball travels The spinning ball travels

farther than if it were farther than if it were

i i i i not spinning not spinning

(70)

Applications of Fluid Dynamics

pp

y



 The air speed above the The air speed above the

wing is greater than the wing is greater than the

d b l d b l

speed below speed below



 The air pressure above The air pressure above

th i i l th th th i i l th th the wing is less than the the wing is less than the air pressure below

air pressure below

Th i t d



 There is a net upward There is a net upward

force force

C ll d

C ll d liftlift

–

– Called Called liftlift



(71)

Surface Tension, Capillary Action,

& Viscous Fluid Flow

Surface Tension



 Net force on molecule A Net force on molecule A

is zero is zero

–

– Pulled equally in all Pulled equally in all

di ti di ti

directions directions 

 Net force on B is not zeroNet force on B is not zero

N l l b

–

– No molecules above to act No molecules above to act

on it on it

–

– Pulled toward the centerPulled toward the centerPulled toward the center Pulled toward the center

of the fluid of the fluid

(72)

Surface Tension, Capillary Action,

& Viscous Fluid Flow



The net effect of this pull on all the

surface molecules is to make the surface

of the liquid contract



Makes the surface area of the liquid as



Makes the surface area of the liquid as

small as possible

E l W t d l t t k h i l

–

– Example: Water droplets take on a spherical Example: Water droplets take on a spherical

shape since a sphere has the smallest surface shape since a sphere has the smallest surface area for a given volume

area for a given volume area for a given volume area for a given volume

(73)

Surface Tension, Capillary Action,

& Viscous Fluid Flow

Surface Tension on a Needle



 Surface tension allows the Surface tension allows the

needle to float, even though the needle to float, even though the ,, gg density of the steel in the

density of the steel in the

needle is much higher than the needle is much higher than the density of the water

density of the water



 The needle actually rests in a The needle actually rests in a

small depression in the liquid small depression in the liquid surface

surface



(74)

Surface Tension, Capillary Action,

& Viscous Fluid Flow

Surface Tension, Equation



 The surface tension is defined as the ratio of the The surface tension is defined as the ratio of the

magnitude of the surface tension force to the magnitude of the surface tension force to the

Surface Tension, Equation

gg

length along which the force acts: length along which the force acts:

F



 SI units are N/mSI units are N/m

L F







 SI units are N/mSI units are N/m 

 In terms of energy, any equilibrium In terms of energy, any equilibrium

configuration of an object is one in which the configuration of an object is one in which the configuration of an object is one in which the configuration of an object is one in which the energy is a minimum

(75)

Surface Tension, Capillary Action,

& Viscous Fluid Flow

Measuring Surface Tension



 The force is measured The force is measured

j t th i b k j t th i b k

Measuring Surface Tension

just as the ring breaks just as the ring breaks free from the film

free from the film

  L F 2 



–

– The 2L is due to the force The 2L is due to the force

being exerted on the being exerted on the

L

2

inside and outside of the inside and outside of the

(76)

Surface Tension, Capillary Action,

& Viscous Fluid Flow



The surface tension of liquids decreases

i h

i

with

increasing temperature



Surface tension can be decreased by

yy

adding ingredients called

surfactants

to a

liquid

–

(77)

Surface Tension, Capillary Action,

& Viscous Fluid Flow



Cohesive forces

are forces between

like

molecules



Adhesive forces

are forces between

unlike

molecules



The shape of the surface depends upon the

relative size of the cohesive and adhesive forces

(78)

Surface Tension, Capillary Action,

& Viscous Fluid Flow

Liquids in Contact with a Solid Surface – Case 1q



 The adhesive forces areThe adhesive forces are 

 The adhesive forces are The adhesive forces are

greater than the cohesive greater than the cohesive forces

forces forces forces



 The liquid clings to the The liquid clings to the

walls of the container walls of the container walls of the container walls of the container



 The liquid “wets” the The liquid “wets” the

ff

surface surface

(79)

Surface Tension, Capillary Action,

& Viscous Fluid Flow

Liquids in Contact with a Solid Surface Case 2 Liquids in Contact with a Solid Surface – Case 2



 C h iC h i ff 

 Cohesive forces are Cohesive forces are

greater than the greater than the

dh i f dh i f

adhesive forces adhesive forces



 The liquid curves The liquid curves

downward downward



 The liquid does not “wet” The liquid does not “wet”

the surface the surface

(80)

Surface Tension, Capillary Action,

& Viscous Fluid Flow

Contact Angle Contact Angle



 In a, Φ > 90In a, Φ > 90°° and cohesive forces are greater and cohesive forces are greater

h dh i f

than adhesive forces than adhesive forces



 In b, Φ < 90In b, Φ < 90°° and adhesive forces are greater and adhesive forces are greater

than cohesive forces than cohesive forces

(81)

Surface Tension, Capillary Action,

& Viscous Fluid Flow

Capillary Actionp y



 Capillary action is the result Capillary action is the result pp yy

of surface tension and of surface tension and adhesive forces

adhesive forces



 The liquid The liquid risesrises in the tube in the tube

when adhesive forces are when adhesive forces are greater than cohesive forces greater than cohesive forces



 At the point of contact At the point of contact

between the liquid and the between the liquid and the

(82)

Surface Tension, Capillary Action,

& Viscous Fluid Flow



 Here, the cohesive Here, the cohesive

forces are greater forces are greater than the adhesive than the adhesive forces

forces



 The level of the fluid The level of the fluid

in the tube will be in the tube will be

b l th f f

below the surface of below the surface of the surrounding fluid the surrounding fluid

普通物理－Lecture10－Solids & Waves

普通物理

Lecture 10

Solids & Fluids

Contents





St t

St t

f M tt

f M tt





State of Matter

State of Matter





Deformation of Solids

Deformation of Solids





V i ti

V i ti

f P

f P

ith D th

ith D th





Density & Pressure

Density & Pressure





Variation of Pressure with Depth

Variation of Pressure with Depth





Pressure Measurements

Pressure Measurements





Buoyant Forces & Archimedes’s Principle

Buoyant Forces & Archimedes’s Principle





Fluid in Motion

Fluid in Motion





Applications of Fluid Dynamics

Applications of Fluid Dynamics





Applications of Fluid Dynamics

Applications of Fluid Dynamics



State of Matter

State of Matter

物質的型態

物質的型態

State of Matter

State of Matter

物質的型態

物質的型態

External forces can be applied to

External forces can be applied to

the solid and compress the

the solid and compress the

the solid and compress the

the solid and compress the

material

material

When the force is removed, the

When the force is removed, the

solid returns to its original shape

solid returns to its original shape

and size

State of Matter

State of Matter

物質的型態