Chapter 11: Solids (part1 of chap 11)

Chapter 13: Fluids

Properties of Solids

Properties of Fluids (Liquids and Gases)

States of Matter

Solid fixed shape and volume

Liquid definite volume, but not a definite shape

Gas neither shapes nor fixed volumes

Plasma (Highly ionized substance of positive

and negative charges- stars)

http://intro.chem.okstate.edu/1225/Lecture/Chapter13/State.html

http://intro.chem.okstate.edu/1225/Lecture/Chapter13/Microstates.html

Deformation of Solids

Solids have definite shape and volume, but are deformable. To change the

shape or size, one can apply a force. When force is removed, the object tends

to return to its original shape and size: Elastic behavior

Stress: force causing the deformation

Strain: measure of the degree of deformation

For small stresses, stress and strain are proportional. The proportionality

constant is called the elastic modulus and measure the stiffness of a material.

strain

stress ModulusElastic

Elasticity in Length: Young’s Modulus:

2

0

0

22

N/m L/L

F/A Y

strain tensile

stress tensile Y Modulus sYoung'

less)(dimension units no L

L strain tensile

N/m 1 (pascal) 1Pa N/m A

F stress tensile

F (perpendicular to

cross section area)

Cross section = ALL0

Elasticity in Length: Young’s Modulus:

Pa20x10 Y Steel

Pa35x10 Y Tungsten :9.1 Table

stretch to difficult are Y large withmaterials

L/L

F/AY

10

10

0

Stress

(MPa)

strain

Elastic behavior

(straight line)

Elastic limit

Breaking point

Elasticity of Shape: Shear Modulus

Fixed point

h

xCross section = A

F (parallel to cross section area)

F

(Pa) x/h

F/AS

strain shear

stress shear S Modulus Shear

less)(dimension units no h

x strain shear

Pa)( A

F stress shear

Elasticity of Shape: Shear Modulus

Fixed point

h

xCross section = A

F (parallel to cross section area)

F

Pa 8.4x10 S Steel

Pa14x10 S Tungsten :9.1 Table

bend to difficult are S large withmaterials

x/h

F/AS

10

10

Volume Elasticity: Bulk Modulus

F (perpendicular to surfaces)

(Pa) V/V

PB

strain volume

stress volume B Modulus Bulk

less)(dimension units no V

V strain volume

(Pa) PA

F stress volume

Volume Elasticity: Bulk Modulus

ilitycompressib the called is B

1

easily compress not does modulus bulk large withMaterial

compressed be can liquids and Solids

0V so decreases V and 0P increases, P When

positive always is way this defined B

Pa V/V

PB

Density and Specific GravityOne of the most important property of materials.

If a mass m of a substance occupies a volume V, then the mass

density of the substance is the mass per unit volume

density = massvolume

ρ = m/VTypical Units: kg/m3 or g/cm3

1 kg /m3 = 0.001 g/cm3

Densities of some materials on page 262: (STP)

Water has a density of 1 g/cm3 (1000 kg/m3)

Another quantity that is commonly used is

weight density = weight weight per unit volume

volume

Specific density:

Specific density = density of substancedensity of water

Pressure

Pressure is defined as the force exerted

over a unit area

pressure = forcearea

P = F/A

Typical Units: pascal (Pa), 1 Pa = 1 N/m2.

Atmospheric PressureLike water, the atmosphere exerts a pressure. Just as water

pressure is caused by the weight of water, atmospheric

pressure is caused by the weight of air.

The pressure at sea level is about 15 lb/in2 (101.3 kPa). We

are not aware about the 15 lb force pushing every square

inch of our bodies, simply because the pressure inside our

bodies equals that of the surrounding air.

There is not net force on us.

Units: 1 atm = 1.013x103 N/m2 = 101.3 kPa

1 bar = 1.00x103 N/m2 = 100 kPa

Variation of Pressure with Depth

Fluid at rest in a container. Fluid exert force on object

(perpendicular to surface area)

F1 = F2

P1A = P2A

P1 = P2

All points at the same depth must be at the same

pressure

F1 F2

Small block of fluid

Small column of fluid

h

Mg

P0A

PA

3 forces on the column of fluid of height h

•P0A = force exerted by atmosphere

•Mg = force of gravity

•PA = force exerted by liquid below

Equilibrium: PA – Mg – P0A = 0

Since M = V= Ah, then Mg = gAh

P = P0 + gh

Variation of Pressure with DepthWhen you swim under water, you can feel the pressure acting

against your eardrums. The deeper you go, the greater the

pressure.

The pressure exerted by a liquid depends on the depth.

If you swam in a liquid denser than water, the pressure would

be greater also.

The pressure exerted by a liquid depends on depth and density

Liquid pressure = weight density x depth

P = ρg h

Pressure does not depend on amount of liquid!

Pressure gauges register the pressure over and above atmospheric

pressure

Absolute pressure = atmospheric pressure + gauge pressure

If a tire gauge registers 220 kPa, the absolute pressure within the tire is

220 kPa + 101 kPa = 321 kPa

P = P0 + ρgh

ρgh is the gauge pressure

Variation of Pressure with Depth

Pascal’s Principle

Since pressure depends on

depth and on the atmospheric

pressure P0, any increase in

pressure at the surface must be

transmitted in the fluid

Example 9.4

Example: Hydraulic lift

in

in

outout

out

out

in

in

outin

FA

AF

A

F

A

F

P P

Measuring Pressure

Atmospheric pressure are measured with

instruments called barometers.

A mercury barometer where the weight of the

mercury column is balanced by atmospheric

pressure.

1 atm = pressure equivalent of a column of

mercury 76 cm in height at 00C

Hg = 13.595x103 kg/m3

g = 9.806 m/s2

h = 0.76 m

P0 = gh = 1.013x105 Pa = 1 atm

Buoyancy in a Liquid

The pressure exerted by a liquid on the bottom of the

object produces an upward buoyant force. The buoyant

force is an upward force in the direction opposite the

direction of the gravitational force.

Buoyant force and volume of fluid displaced

Water

displaced

Archimedes’ PrincipleAny 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 by the object

FB

W =

mobjectg

Object completely immersed: Vobject = Vfluid = V

Weight of object: W = mobjectg = objectVg

Buoyant force: FB = weight of fluid displaced

FB = mfluid g = fluidVg

Fnet = FB – W = (fluid - object )Vg

fluid = object, equilibrium

fluid >object, net force up, accelerates up

fluid < object, net force down, accelerates down

Archimedes’ Principle

FB

W =

mobjectg

fluid >object, net force up, accelerates up

fluid < object, net force down, accelerates down

Watch the video. Why does diet Coke float?

https://youtu.be/5PHQJ4_lydc

Archimedes’ PrincipleFloating object

FB

W = mobjectg

Object partially immersed:

Vobject = total volume of object

Vfluid = volume of the part of the object submerged

Weight of object: W = mobjectg = objectVg

Buoyant force: FB = weight of fluid displaced

FB = mfluid g = fluidVg

Equilibrium: FB = W

fluidVfluid g = object Vobjectg

object

fluid

fluid

object

V

V

ρ

ρ

Fluids in Motion: Fluid Dynamics

Smooth flow: streamline or

laminar (layered) flow

Turbulent flow

Different kinds of flow

Fluids in Motion: Fluid Dynamics

IDEAL FLUID

fluid is non viscous. No internal friction force

between adjacent layers

fluid is incompressible: density is constant

fluid motion is steady: velocity, density and

pressure at each point in the fluid do not change in

time

fluid moves without turbulence

Fluids in Motion

Conservation of mass:

Region1: m1 = ρV1 = ρA1l1= ρA1v1 t

Region 2: m2 = ρV2 = ρA2l2= ρA2v2 t

Steady flow m1 = m2

Equation of Continuity: A1 v1 = A2 v2

The amount of fluid that enters one end of

the tube in a given time interval equals the

amount of fluid leaving the tube in the

same interval. Liquid is incompressible

ρ constant

Steady laminar flow

Bernoulli’s Equation

When the speed of a fluid

increases, pressure in the fluid

decreases.

Bernoulli's principle holds only

for steady flow. If the speed is

too great, the flow may become

turbulent.

Examples:

•Atmospheric pressure

decreases in a tornado or

hurricane.

•A spinning ball curves up

Airplane wingBall in jet of air

Low pressure

High pressure

lift

Bernoulli’s Equation: conservation

of energy applied to an ideal fluid

P1 + ½ ρv12 + ρgy1 = P2 + ½ ρv2

2 + ρgy2

P + ½ ρv2 + ρgy = constant

Kinetic energy

Potential energy