Solids and Fluids

1
Chapter 9

• Solids and Fluids

Conceptual questions 10,11,12,16,17 Quick
quizzes 2,6,7 Problems 17,22,28,47
2
Solids

• Has definite shape and volume
• Molecules or atoms are held in specific locations
  by electrical forces
• Atoms (molecules) vibrate about equilibrium
  positions

3
Crystalline Solids and Amorphous Solids

• Atoms are arranged randomly
• Examples include glass

• Atoms have an ordered structure
• Example below is salt

Cl-
Na
4
Liquid
Gas

• Has a definite volume but no definite shape
• Liquids exist 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

• Has no definite volume and 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

5
Plasma

• 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

6
Deformation of Solids

• All objects are deformable
• It is possible to change the shape or size (or
  both) of an object through the application of
  external forces
• when the forces are removed, the object tends to
  its original shape
• This is elastic behavior

• Stress is related to the force causing the
  deformation
• Strain is a measure of the degree of deformation
• The elastic modulus is the constant of
  proportionality between stress and strain

7
Youngs Modulus

• Tensile stress is the ratio of the external force
  to the cross-sectional area
• SI units of stress are Pascals, Pa
• 1 Pa 1 N/m2
• The tensile strain is the ratio of the change in
  length to the original length
• The elastic modulus is called Youngs modulus

8
Youngs Modulus, final

• Youngs modulus applies to a stress of either
  tension or compression
• It is possible to exceed the elastic limit of the
  material
• Ordinarily does not return to its original length
• If stress continues, the object may break

9
Shear ModulusElasticity of Shape

• Forces may be parallel to one of the objects
  faces
• The stress is called a shear stress
• The shear strain is the ratio of the horizontal
  displacement and the height of the object
• The shear modulus is S

10
Bulk ModulusVolume Elasticity

• Bulk modulus characterizes the response of an
  object to uniform squeezing
• The object undergoes a change in volume without a
  change in shape

11
Bulk Modulus

• A material with a large bulk modulus is difficult
  to compress
• The negative sign is included since an increase
  in pressure will produce a decrease in volume
• B is always positive
• The compressibility is the reciprocal of the bulk
  modulus

12
Ultimate Strength of Materials

• The ultimate strength of a material is the
  maximum force per unit area the material can
  withstand before it breaks or factures
• Some materials are stronger in compression than
  in tension (cement)

13
Post and Beam Arches
Semicircular Arch

• A horizontal beam is supported by two columns
• Used in Greek temples
• Columns are closely spaced
• Low ultimate tensile strength of sagging stone
  beams

• Developed by the Romans
• Allows a wide roof span on narrow supporting
  columns
• Stability depends upon the compression of the
  wedge-shaped stones

14
Gothic Arch

• First used in Europe in the 12th century
• Extremely high
• The flying buttresses are needed to prevent the
  spreading of the arch supported by the tall,
  narrow columns

15
Density Pressure

• The density of a substance of uniform composition
  is defined as its mass per unit volume
• Units are kg/m3 (SI) or g/cm3 (cgs)
• 1 g/cm3 1000 kg/m3
• The specific gravity of a substance is the ratio
  of its density to the density of water at 4 C
• The density of water at 4 C is 1000 kg/m3

The force exerted by a fluid on a submerged
object at any point if perpendicular to the
surface of the object
16
Problem 9-17

• If 1.0 m3 of concrete weighs 5.0 x 104 N, what
  is the height of the tallest cylindrical concrete
  pillar that will not collapse under its own
  weight? The compression strength of concrete (the
  maximum pressure that can be exerted on the base
  of the structure) is 1.7 x 107 Pa.

17
Pressure and Depth equation

• All points at the same depth must be at the same
  pressure

• Po is normal atmospheric pressure
• 1.013 x 105 Pa 14.7 lb/in2
• The pressure does not depend upon the shape of
  the container

18
Quick quiz 9-2
The pressure at the bottom of a glass filled with
water (? 1 000 kg/m3) is P. The water is poured
out and the glass is filled with ethyl alcohol (?
806 kg/m3). The pressure at the bottom of the
glass is now (a) smaller than P (b) equal to P
(c) larger than P (d) indeterminate.
19
Pascals Principle

• The hydraulic press is an important application
  of Pascals Principle
• Also used in hydraulic brakes, forklifts, car
  lifts, etc.

20
Pressure MeasurementsManometer

• One end of the U-shaped tube is open to the
  atmosphere
• The other end is connected to the pressure to be
  measured
• Pressure at B is Po?gh

21
Pressure Measurements Barometer

• Invented by Torricelli
• A long closed tube is filled with mercury and
  inverted in a dish of mercury
• Measures atmospheric pressure as p?gh
• One atmosphere (1 atm)
• 76.0 cm of mercury
• 1.013 x 105 Pa
• 14.7 lb/in2

22
Problem 9-22

• Blaise Pascal duplicated Torricellis barometer
  using a red Bordeaux wine, of density 984 kg/m3,
  as the working liquid (Fig. P9.22). What was the
  height h of the wine column for normal
  atmospheric pressure? Would you expect the vacuum
  above the column to be as good as for mercury?

23
Archimedes' Principle

• 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 by the
  object
• The upward force is called the buoyant force
• The physical cause of the buoyant force is the
  pressure difference between the top and the
  bottom of the object
• The magnitude of the buoyant force always equals
  the weight of the displaced fluid

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
24
Totally Submerged Object

• The object is more dense than the fluid
• The net force is downward
• The object accelerates downward

• The upward buoyant force is B?fluidgVobj
• The downward gravitational force is
  wmg?objgVobj
• The net force is B-w(?fluid-?obj)gVobj

25
Floating Object

• The object is less dense than the fluid
• The object experiences a net upward force

• 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

26
Quick quiz 9-6
Lead has a greater density than iron, and both
are denser than water. Is the buoyant force on a
solid lead object (a) greater than, (b) less
than, or (c) equal to the buoyant force on a
solid iron object of the same dimensions?
27
Problem 9-28

• The density of ice is 920 kg/m3, and that of sea
  water is 1 030 kg/m3. What fraction of the total
  volume of an iceberg is exposed?

28
Checking the battery
29
Fluids in MotionStreamline Flow

• Streamline flow, also called laminar flow
• every particle that passes a particular point
  moves exactly along the smooth path followed by
  particles that passed the point earlier
• different streamlines cannot cross each other
• the streamline at any point coincides with the
  direction of fluid velocity at that point

30
Fluids in MotionTurbulent Flow

• The flow becomes irregular
• After the flow exceeds a certain velocity
• Any condition that causes abrupt changes in
  velocity
• Eddy currents are a characteristic of turbulent
  flow

Characteristics of an Ideal Fluid

• The fluid is nonviscous (no friction)
• The fluid is incompressible
• Its density is constant
• The fluid is steady
• Its velocity, density and pressure do not change
  in time
• The fluid moves without turbulence
• No eddy currents are present

31
Fluid Flow Viscosity

• Viscosity is the degree of internal friction in
  the fluid
• The internal friction is associated with the
  resistance between two adjacent layers of the
  fluid moving relative to each other

32
Equation of Continuity

• A1v1 A2v2
• Speed is high where the pipe is narrow and speed
  is low where the pipe has a large diameter
• Av is called the flow rate

33
Bernoullis Equation

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

34
Problem 9-47
The inside diameters of the larger portions of
the horizontal pipe in Figure P9.47 are 2.50 cm.
Water flows to the right at a rate of 1.80 x 104
m3/s. Determine the inside diameter of the
constriction.
35
Venturi Meter

• Speed changes as diameter changes
• Pressure be used to measure the speed of the
  fluid flow
• Swiftly moving fluids exert less pressure than do
  slowly moving fluids

36
Lift on an airplane wing
Above the wing the air is moving faster than
below the wing. Pressure above the wing is less
than the pressure below the wing. There is an
upward lift force on the wing.
37
Quick quiz 9-7
You observe two helium balloons floating next to
each other at the ends of strings secured to a
table. The facing surfaces of the balloons are
separated by 1-2 cm. You blow through the
opening between the balloons. What happens to
the balloons? (a) They move toward each other.
(b) They move away from each other. (c) They
are unaffected.
38
Bernoullis law other applications
39
Surface Tension

• Net force on molecule A is zero
• Pulled equally in all directions
• Net force on B is not zero
• Pulled toward the center of the fluid

• Makes the surface area of
• the liquid as small as possible
• Example Water droplets take on a spherical
  shape since a sphere has the smallest surface
  area for a given volume

40
Surface Tension

• The surface tension is defined as the ratio of
  the magnitude of the surface tension force to the
  length along which the force acts
• SI units are N/m
• For the apparatus in the figure use

41
A Closer Look at the Surface of Liquids

• 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

42
Liquids in Contact with a Solid Surface

• The adhesive forces are greater than the cohesive
  forces
• The liquid clings to the walls of the container
• The liquid wets the surface
• Cohesive forces are greater than the adhesive
  forces
• The liquid curves downward
• The liquid does not wet the surface

43
Angle of Contact

• In a, F gt 90 and cohesive forces are greater
  than adhesive forces
• In b, F lt 90 and adhesive forces are greater
  than cohesive forces

44
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
• The upward force
• The vertical force
• Equilibrium

45
Capillary Action, cont.

• Here, the cohesive forces are greater than the
  adhesive forces
• The level of the fluid in the tube will be below
  the surface of the surrounding fluid

46
Viscous Fluid Flow

• Viscosity refers to friction between the layers
• 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

47
Coefficient of Viscosity

• Assume a fluid between two solid surfaces
• A force is required to move the upper surface
• ? is the coefficient
• SI units are Ns/m2
• cgs units are Poise
• 1 Poise 0.1 Ns/m2

48
Poiseuilles Law

• Gives the rate of flow of a fluid in a tube with
  pressure differences

49
Reynolds Number

• At sufficiently high velocity, a fluid flow can
  change from streamline to turbulent flow
• The onset of turbulence can be found by a factor
  called the Reynolds Number, RN
• If RN 2000 or below, flow is streamline
• If 2000 ltRNlt3000, the flow is unstable
• If RN 3000 or above, the flow is turbulent

50
Motion in a ViscousMedium

• As the object falls, three forces act on the
  object
• As its speed increases, so does the resistive
  force
• The resistive force on a small, spherical object
  of radius r falling through a viscous fluid is
  given by Stokes Law
• Fr6phrv
• At a particular speed, called the terminal speed,
  the net force is zero

51
Diffusion and Ficks Law

• Molecules move from a region of high
  concentration to a region of low concentration
• Basic equation for diffusion is given by Ficks
  Law
• D is the diffusion coefficient

52
Diffusion Osmosis

• Concentration on the left is higher than on the
  right of the imaginary barrier
• Many of the molecules on the left can pass to the
  right, but few can pass from right to left
• There is a net movement from the higher
  concentration to the lower concentration

Osmosis is the movement of water from a region
where its concentration is high, across a
selectively permeable membrane, into a region
where its concentration is lower A selectively
permeable membrane is one that allows passage of
some molecules, but not others
53
Conceptual questions

• Will an ice cube flow higher in water or in an
  alcohol beverage?
• A pound of Styrofoam and a pound of lead have the
  same weight. If they are placed on a sensitive
  equal arm balance, will it balance?
• An ice cube is placed in a glass of water. What
  happens to the level of water as the ice melts?

54
Conceptual questions

• 16. A barge is carrying a load of gravel along a
  river. It approaches a low bridge, and the
  captain realizes that the top of the pile of
  gravel is not going to make it under the bridge.
  He orders the crew to shovel gravel from the pile
  into the water. Is it a good decision?
• 17. Tornadoes often lift the roofs of houses.
  Use the Bernoulli equation to explain why.
• Why should you keep your windows open under
  these conditions?