Transcript Chapter 9

Chapter 9
Solids and Fluids
States of matter
• Solid
• Liquid
• Gas
• Plasma
Solids
• Have definite volume and shape
• Molecules:
1) are held in specific locations by electrical forces
2) vibrate about equilibrium positions
3) can be modeled as springs connecting molecules
Solids
• Crystalline solid: atoms have an ordered structure
(e.g., diamond, salt)
• Amorphous solid: atoms are arranged almost
randomly (e.g., glass)
Fluids
• Fluids – substances that can flow (gases, liquids)
• Fluids conform with the boundaries of any container
in which they are placed
• Fluids lack orderly long-range arrangement of
atoms and molecules they consist of
• Fluids can be compressible and incompressible
Liquids
• Have a definite volume, but no definite shape
• Exists at a higher temperature than solids
• The molecules “wander” through the liquid in a
random fashion
• The intermolecular forces are not strong enough to
keep the molecules in a fixed position
Gases
• Have neither definite volume nor definite shape
• Molecules are in constant random motion
• The molecules exert only weak forces on each other
• Average distance between molecules is large
compared to the size of the molecules
Plasmas
• Matter heated to a very high temperature
• Many of the electrons are freed from the nucleus
• Result is a collection of free, electrically charged
ions
• Plasmas exist inside stars
Indeterminate structures
• Indeterminate systems cannot be solved by a simple
application of the equilibrium conditions
• In reality, physical objects are
not absolutely rigid bodies
• Concept of elasticity is employed
Elasticity
• All real “rigid” bodies can change their dimensions
as a result of pulling, pushing, twisting, or
compression
• This is due to the behavior of a microscopic
structure of the materials they are made of
• Atomic lattices can be approximated as
sphere/spring repetitive arrangements
Stress and strain
• All deformations result from a stress – deforming
force per unit area
• Deformations are described by a strain – unit
deformation
• Coefficient of proportionality between stress and
strain is called a modulus of elasticity
stress = modulus * strain
Tension and compression
• Strain is a dimensionless ratio – fractional change in
length of the specimen ΔL/Li
• The modulus for tensile and compressive strength
is called the Young’s modulus
F
L
Y
A
Li
Thomas Young
(1773 – 1829)
Tension and compression
• Strain is a dimensionless ratio – fractional change in
length of the specimen ΔL/Li
• The modulus for tensile and compressive strength
is called the Young’s modulus
Shearing
• For the stress, force vector lies in the plane of the
area
• Strain is a dimensionless ratio Δx/h
• The modulus for this case is called the shear
modulus
F
x
S
A
h
Hydraulic stress
• The stress is fluid pressure P
= F/A
• Strain is a dimensionless ratio ΔV/V
• The modulus is called the bulk modulus
F
V
B
A
Vi
Density and pressure
• Density
m
  lim
V  0  V
• SI unit of density: kg/m3
• Pressure
P  lim
A0
F
A
• SI unit of pressure: N/m2 = Pa (pascal)
Blaise Pascal
(1623 - 1662)
• Pressure is a scalar – at a given point in a fluid the
measured force is the same in all directions
• For a uniform force on a flat area
F
P
A
Atmospheric pressure
• Atmospheric pressure:
• P0 = 1.00 atm = 1.013 x 105 Pa
• Specific gravity of a substance is the ratio of its
density to the density of water at 4° C (1000 kg/m3)
• Specific gravity is a unitless ratio
Fluids at rest
• For a fluid at rest (static equilibrium) the pressure is
called hydrostatic
• For a horizontal-base cylindrical water sample in a
container
F2  F1  mg
P2 A  P1 A  A( y1  y2 ) g
P2  P1   ( y1  y2 ) g
P  P0  hg
Fluids at rest
• The hydrostatic pressure at a point in a fluid
depends on the depth of that point but not on any
horizontal dimension of the fluid or its container
• Difference between an absolute pressure and an
atmospheric pressure is called the gauge pressure
Pg  P  P0  hg
P  P0  hg
Measuring pressure
• Mercury barometer
P2  P1   ( y1  y2 ) g
y1  0; P1  P0
y2  h; P2  0
P0  hg
• Open-tube manometer
P2  P1   ( y1  y2 ) g
y1  0; P1  P0
y2  h; P2  P
Pg  P  P0  hg
Chapter 9
Problem 19
A collapsible plastic bag contains a glucose solution. If the average gauge
pressure in the vein is 1.33 × 103 Pa, what must be the minimum height h of the
bag in order to infuse glucose into the vein? Assume that the specific gravity of
the solution is 1.02.
Pascal’s principle
• Pascal’s principle: A change in the pressure applied
to an enclosed incompressible fluid is transmitted
undiminished to every portion of the fluid and to the
walls of its container
• Hydraulic lever
F1 F2
P 

V  A1x1  A2x2
A1 A2
A2
A1
x1  x2
F1  F2
A1
W  F1x1  F2 x2
A2
• With a hydraulic lever, a given force applied over a
given distance can be transformed to a greater force
applied over a smaller distance
Archimedes’ principle
• Buoyant force:
For imaginary void in a fluid
p at the bottom > p at the top
B  mf g
Archimedes
of Syracuse
(287-212 BCE)
• Archimedes’ principle: when a body is submerged in
a fluid, a buoyant force from the surrounding fluid
acts on the body. The force is directed upward and
has a magnitude equal to the weight of the fluid that
has been displaced by the body
Archimedes’ principle
• Sinking:
mg  B
• Floating:
mg  B
• Apparent weight:
weight apparent  mg  B
• If the object is floating at the surface of a fluid, the
magnitude of the buoyant force (equal to the weight
of the fluid displaced by the body) is equal to the
magnitude of the gravitational force on the body
Chapter 9
Problem 34
A light spring of force constant k = 160 N/m rests vertically on the bottom of a
large beaker of water. A 5.00-kg block of wood (density = 650 kg/m3) is
connected to the spring, and the block–spring system is allowed to come to
static equilibrium. What is the elongation ΔL of the spring?
Motion of ideal fluids
Flow of an ideal fluid:
• Steady (laminar) – the velocity of the moving fluid at
any fixed point does not change with time (either in
magnitude or direction)
• Incompressible – density is constant and uniform
• Nonviscous – the fluid experiences no drag force
• Irrotational – in this flow the test body will not rotate
about its center of mass
Equation of continuity
• For a steady flow of an ideal fluid through a tube
with varying cross-section
V  Ax  Avt  A1v1t  A2v2t
A1v1  A2v2
Av  const
Equation of continuity
Bernoulli’s equation
• For a steady flow of an ideal fluid:
Etot  K  U g  Eint
• Kinetic energy
mv 2 Vv 2
K

2
2
• Gravitational potential energy
U g  mgy  Vgy
• Internal (“pressure”) energy
Eint  VP
Daniel Bernoulli
(1700 - 1782)
Bernoulli’s equation
• Total energy
Etot  K  U g  Eint
Vv

 Vgy  VP
2
2
Etot v

 gy  P  const
V
2
2
v1
2
2
 gy1  P1 
v2
2
2
 gy2  P2
Chapter 9
Problem 43
A hypodermic syringe contains a medicine having the density of water. The
barrel of the syringe has a cross-sectional area A = 2.50 × 10-5 m2, and the
needle has a cross-sectional area a = 1.00 × 10-8 m2. In the absence of a force
on the plunger, the pressure everywhere is 1 atm. A force F of magnitude 2.00 N
acts on the plunger, making medicine squirt horizontally from the needle.
Determine the speed of the medicine as it leaves the needle’s tip.
Surface tension
• Net force on molecule A is zero, because it is pulled
equally in all directions
• Net force on B is not zero, because no molecules
above to act on it
• It is pulled toward the center of the fluid
Surface tension
• 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 small as
possible – surface tension
Surface tension
• Surface tension: the ratio of the magnitude of the
surface tension force to the length along which the
force acts:
F

L
• SI units are N/m
• Surface tension of liquids decreases with increasing
temperature
• Surface tension can be decreased by adding
ingredients called surfactants to a liquid (e.g., a
detergent)
Liquid surfaces
• Cohesive forces are forces between like molecules,
adhesive forces are forces between unlike molecules
• The shape of the surface depends upon the relative
strength of the cohesive and adhesive forces
• If adhesive forces are greater than cohesive forces,
the liquid clings to the walls of the container and
“wets” the surface
Liquid surfaces
• Cohesive forces are forces between like molecules,
adhesive forces are forces between unlike molecules
• The shape of the surface depends upon the relative
strength of the cohesive and adhesive forces
• If cohesive forces are greater than adhesive forces,
the liquid curves downward and does not “wet” the
surface
Contact angle
• If cohesive forces are greater than adhesive forces,
Φ > 90°
• If adhesive forces are greater than cohesive forces,
Φ < 90°
Capillary action
• Capillary action is the result of surface tension and
adhesive forces
• The liquid rises in the tube when adhesive forces
are greater than cohesive forces
Capillary action
• Capillary action is the result of surface tension and
adhesive forces
• The level of the fluid in the tube is below the surface
of the surrounding fluid if cohesive forces are greater
than adhesive forces
Viscous fluid flow
• Viscosity: friction between the layers of a fluid
• Layers in a viscous fluid have different velocities
• The velocity is greatest at the center
• Cohesive forces between the fluid and the walls
slow down the fluid on the outside
Questions?
Answers to the even-numbered problems
Chapter 9
Problem 14:
1.9 × 104 N
Answers to the even-numbered problems
Chapter 9
Problem 22:
10.5 m;
no, some alcohol and water evaporate
Answers to the even-numbered problems
Chapter 9
Problem 26:
0.611 kg