Chapter 9Chapter 9

Solids and FluidsSolids and Fluids

SolidsSolids

Has definite volumeHas definite volume Has definite shapeHas definite shape Molecules are held in Molecules are held in

specific locationsspecific locations by electrical forcesby electrical forces

vibrate about vibrate about equilibrium positionsequilibrium positions

Can be modeled as Can be modeled as springs connecting springs connecting moleculesmolecules

LiquidLiquid Has a definite volumeHas a definite volume No definite shapeNo definite shape Exist at a higher Exist at a higher

temperature than temperature than solidssolids

The molecules The molecules “wander” through the “wander” through the liquid in a random liquid in a random fashionfashion The intermolecular The intermolecular

forces are not strong forces are not strong enough to keep the enough to keep the molecules in a fixed molecules in a fixed positionposition

GasGas

Has no definite volumeHas no definite volume Has no definite shapeHas no definite shape Molecules are in constant random Molecules are in constant random

motionmotion The molecules exert only weak The molecules exert only weak

forces on each otherforces on each other Average distance between Average distance between

molecules is large compared to the molecules is large compared to the size of the moleculessize of the molecules

Deformation of SolidsDeformation of Solids

All objects are deformableAll objects are deformable It is possible to change the shape It is possible to change the shape

or size (or both) of an object or size (or both) of an object through the application of external through the application of external forcesforces

when the forces are removed, the when the forces are removed, the object tends to its original shapeobject tends to its original shape elastic behaviorelastic behavior

Elastic PropertiesElastic Properties

StressStress is related to the force causing the is related to the force causing the deformationdeformation

StrainStrain is a measure of the degree of is a measure of the degree of deformationdeformation

The The elastic moduluselastic modulus is the constant of is the constant of proportionality between stress and proportionality between stress and strainstrain

strain

stressulusmodElastic

Young’s ModulusYoung’s Modulus Young’s modulus Young’s modulus

applies to a stress of applies to a stress of either tension or either tension or compressioncompression

It is possible to exceed It is possible to exceed the the elastic limitelastic limit of the of the materialmaterial No longer directly No longer directly

proportionalproportional Ordinarily does not Ordinarily does not

return to its original return to its original lengthlength

If stress continues, the If stress continues, the object may breakobject may break

Young’s Modulus: Young’s Modulus: Elasticity in LengthElasticity in Length

Tensile stress is Tensile stress is the ratio of the the ratio of the external force to external force to the cross-the cross-sectional areasectional area

The elastic The elastic modulus is called modulus is called Young’s modulusYoung’s modulus LA

LF

LLA

F

straintensile

stresstensileY o

o

Fig. P9.12, p. 295

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Shear ModulusShear Modulus

A material having A material having a large shear a large shear modulus is modulus is difficult to benddifficult to bend

hxA

F

strainshear

stressshearS

Bulk ModulusBulk Modulus

Volume stress, ΔP, is Volume stress, ΔP, is the ratio of the force the ratio of the force to the surface areato the surface area This is also the This is also the

PressurePressure The volume strain is The volume strain is

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

VVP

VVA

F

strainvolume

stressvolumeB

DensityDensity

The density of a substance of The density of a substance of uniform composition is defined as uniform composition is defined as its mass per unit volume:its mass per unit volume:

Units are kg/mUnits are kg/m33 (SI) or g/cm (SI) or g/cm33 (cgs) (cgs) 1 g/cm1 g/cm33 = 1000 kg/m = 1000 kg/m33

V

m

PressurePressure

The force exerted The force exerted by a fluid on a by a fluid on a submerged object submerged object at any point if at any point if perpendicular to perpendicular to the surface of the the surface of the objectobject

2m

NPain

A

FP

Measuring PressureMeasuring Pressure

The spring is The spring is calibrated by a calibrated by a known forceknown force

The force the fluid The force the fluid exerts on the exerts on the piston is then piston is then measuredmeasured

Pressure and DepthPressure and Depth Examine the darker Examine the darker

region, assumed to region, assumed to be a fluidbe a fluid It has a cross-It has a cross-

sectional area Asectional area A Extends to a depth Extends to a depth

h below the surfaceh below the surface Three external Three external

forces act on the forces act on the regionregion

Pressure and Depth Pressure and Depth equationequation

PPoo is normal is normal atmospheric atmospheric pressurepressure 1.013 x 101.013 x 1055 Pa = Pa =

14.7 lb/in14.7 lb/in22

The pressure does The pressure does not depend upon not depend upon the shape of the the shape of the containercontainer

ghPP o

Pascal’s PrinciplePascal’s Principle A change in pressure A change in pressure

applied to an enclosed applied to an enclosed fluid is transmitted fluid is transmitted undimished to every point undimished to every point of the fluid and to the of the fluid and to the walls of the container.walls of the container.

The hydraulic press is an The hydraulic press is an important application of important application of Pascal’s PrinciplePascal’s Principle

Also used in hydraulic Also used in hydraulic brakes, forklifts, car lifts, brakes, forklifts, car lifts, etc.etc.

2

2

1

1

A

F

A

FP

Pressure Measurements:Pressure Measurements:ManometerManometer

One end of the U-One end of the U-shaped tube is shaped tube is open to the open to the atmosphereatmosphere

The other end is The other end is connected to the connected to the pressure to be pressure to be measuredmeasured

Pressure at B is Pressure at B is PPoo+ρgh+ρgh

Pressure Measurements: Pressure Measurements: BarometerBarometer Invented by TorricelliInvented by Torricelli A long closed tube is filled A long closed tube is filled

with mercury and inverted with mercury and inverted in a dish of mercuryin a dish of mercury

Measures atmospheric Measures atmospheric pressure as ρghpressure as ρgh

One atmosphere (1 atm) =One atmosphere (1 atm) = 76.0 cm of mercury76.0 cm of mercury 1.013 x 101.013 x 1055 Pa Pa 14.7 lb/in14.7 lb/in22

Buoyant ForceBuoyant Force The magnitude of the The magnitude of the

buoyant force always buoyant force always equals the weight of the equals the weight of the displaced fluiddisplaced fluid

The buoyant force is the The buoyant force is the same for a totally same for a totally submerged object of any submerged object of any size, shape, or densitysize, shape, or density

fluidfluid wVgB

Archimedes’ Principle:Archimedes’ Principle:Floating ObjectFloating Object

The object is in static equilibriumThe object is in static equilibrium The upward buoyant force is The upward buoyant force is

balanced by the downward force of balanced by the downward force of gravitygravity

Volume of the fluid displaced Volume of the fluid displaced corresponds to the volume of the corresponds to the volume of the object beneath the fluid levelobject beneath the fluid level

obj

fluid

fluid

obj

V

V

Fig. P9.26, p. 297

Slide 70

Characteristics of an Ideal Characteristics of an Ideal FluidFluid

The fluid is nonviscousThe fluid is nonviscous There is no internal friction between There is no internal friction between

adjacent layersadjacent layers The fluid is incompressibleThe fluid is incompressible

Its density is constantIts density is constant The fluid is steadyThe fluid is steady

Its velocity, density and pressure do not Its velocity, density and pressure do not change in timechange in time

The fluid moves without turbulenceThe fluid moves without turbulence No eddy currents are presentNo eddy currents are present

Equation of ContinuityEquation of Continuity

AA11vv11 = A = A22vv22 The product of the The product of the

cross-sectional area cross-sectional area of a pipe and the fluid of a pipe and the fluid speed is a constantspeed is a constant Speed is high where Speed is high where

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

Av is called the Av is called the flow flow raterate

Bernoulli’s EquationBernoulli’s Equation

Relates pressure to fluid speed and Relates pressure to fluid speed and elevationelevation

Bernoulli’s equation is a consequence of Bernoulli’s equation is a consequence of Conservation of Energy applied to an Conservation of Energy applied to an ideal fluidideal fluid

Assumes the fluid is incompressible and Assumes the fluid is incompressible and nonviscous, and flows in a nonturbulent, nonviscous, and flows in a nonturbulent, steady-state mannersteady-state manner

constant gyv2

1P 2

Applications of Bernoulli’s Applications of Bernoulli’s Principle: Venturi MeterPrinciple: Venturi Meter Shows fluid flowing Shows fluid flowing

through a horizontal through a horizontal constricted pipeconstricted pipe

Speed changes as Speed changes as diameter changesdiameter changes

Can be used to measure Can be used to measure the speed of the fluid flowthe speed of the fluid flow

Swiftly moving fluids Swiftly moving fluids exert less pressure than exert less pressure than do slowly moving fluidsdo slowly moving fluids

22221

211 2

1

2

1gyvPgyvP

Fig. P9.45, p. 298

Slide 75