Solid

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Solid Fluid Dynamics

• Physics

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Solids Fluids Contents

• Overview of the four physical states of Matter
• Solids, liquids, and gases
• Solid Mechanics
• Deformation of Solids
• Fluid Mechanics
• Density Pressure
• Buoyant Forces Archimedes Principle
• Fluids in Motion
• Bernoulli Equation
• Application of Fluid Dynamics

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Intermolecular Forces hold molecules together

• Instantaneous Dipoles that are created by
  constantly moving electrons.

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Comparisons of the Three States of Matter
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Three States of MatterShape

• Gases have no shape because of little attractive
  forces and independent movement. Liquids take the
  shape of their container but do not expand
  readily because of attractive forces. Solid
  molecules have definite shape and are held in
  fixed position.

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States of Matter Density
Section 4 Changes of State

• Density is mass per unit volume and indicates the
  closeness of particles in a sample of matter.
• Gas Liquid
  Solid
• Low High
  High

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Three States of MatterParticle Energy

• Differences in attractive forces slow down
  particle movement.
• Gases- high kinetic energy because of low
  attraction between particles.
• Liquids- moderate kinetic energy and attraction
• Solids- low kinetic energy and high attractive
  forces.

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Factors that effect a GAS

1. The quantity of a gas, n, in moles
2. The temperature of a gas, T, in Kelvin (Celsius
   degrees 273)
3. The pressure of a gas, P, in pascals
4. The volume of a gas, V, in cubic meters

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Gas Law 1 Boyles Law(complete TREE MAP)

• The pressure of a gas is inverse related to the
  volume
• Moles and Temperature are constant

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Gas Law 2 Charles Law

• The volume of a gas is directly related to the
  temperature
• Pressure and Moles are constant

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Gas Law 3 Gay-Lussacs Law

• The pressure of a gas is directly related to the
  temperature
• Moles and Volume are constant

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Gas Law 4 Avogadros Law

• The volume of a gas is directly related to the
  of moles of a gas
• Pressure and Temperature are constant

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Gas Law 5 The Combined Gas Law

• You basically take Boyles Charles and
  Gay-Lussacs Law and combine them together.
• Moles are constant

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Solids Fluids Contents

• Solid Mechanics
• Deformation of Solids
• Stress, strain, and
• Youngs Modulus Elasticity of Length
• Shear modulus Elasticity of Shape
• Bulk Modulus Volume Elasticity

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Atomic Arrangement of a solid

• Crystalline Solid
• Very structured atomic arrangement.
• Ex sodium chloride (salt)

• Amorphous Solid
• Randomly arranged atoms
• Ex glass

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Solids vibrating atoms
Temperature is related to the average kinetic
energy of the particles in a substance. Vibration
is slight, essentially fixed Atomic attraction is
electrical Solids are elastic
KE mv2 2
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Deformation of a Solid

• Solids are elastic
• Application of a external force can
• Deform a solid
• Break a solid
• Removal of external force
• Solid returns to original shape
• Unless you surpass the elastic limit.
• Video

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Stress Strain
Demo
Stress strain are the terms used to discuss the
elastic properties of a solid.

• Stress (s)- is the force per unit area causing
  deformation

• Strain (s)- is a measure of the amount of the
  deformation

Hookes Law K springness ?x displacement
Elastic modulus Y proportionality constant. It
is analogous to the spring constant k.
Y is the stiffness of a material. It is
determined experimentally A material having a
large is very stiff, therefore difficult to
deform.
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Elastic Modulus

• Elastic modulus Y is like the spring constant.
• stiffness of a material.
• Large elastic modulus very stiff
• Small elastic modulus not stiff
• Three types of stress related to this expression
• Tensile Y - pulling apart, force is
  perpendicular to cross-section
• Shear S- pushing apart, force is parallel to
  cross-section
• Bulk -B- squeezing force

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Elastic Modulus Values
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Overview
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Stress Strain
Elastic Modulus Y is determine in the lab and is
unique to the material.
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Tensile Stress Youngs Modulus

• Elasticity of length
• A- is cross-sectional area
• F- force perpendicular to cross-section
• Y- youngs modulus
• Lo- original length
• ?L change in length
• Units

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Tensile Stress Youngs Modulus

• Elasticity of length
• Strain
• Consider the metal bar. When an external force is
  applied perpendicular cross-sectional area the
  atomic bonds of the metal, by their nature,
  resist the distortion (stretching).
• The bar is said to experience tensile
  stress.(pulling)
• Strain is the ratio of change in length and
  original length.

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Tensile Strength Breaking Point
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Pause for a Cause

• A vertical steel beam in a building supports a
  load of 6.0 X 104 N.
• A) If the length of the beam is 4.0 m and its
  cross-sectional area is 8.0 X 10-3 m2, find the
  distance the beam is compressed along its length.
  
• B) Find the maximum load that the beam can
  support.

F 6.0 X 104 N A 8.0 X 10-3 m2 Lo 4.0 m Y
20 X 1010 Pa ?L ?
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Pause for a Cause

• A vertical steel beam in a building supports a
  load of 6.0 X 104 N.
• A) If the length of the beam is 4.0 m and its
  cross-sectional area is
• 8.0 X 10-3 m2, find the distance the beam is
  compressed along its length.
• B) Find the maximum load that the beam can
  support.

Look up Tensile Strength limit from chart for
steel
F 6.0 X 104 N A 8.0 X 10-3 m2 Lo 4.0 m Y
20 X 1010 Pa ?L ?
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Pause for a Cause

• Determine the elongation of the metal rod if it
  is under a tension of 5.8 X 103 N.

F 5.8 X 103 N A p r2 LoCu 2.6 m LoAl 1.3
m Ycu 11 X 1010 Pa YAl 7.0 X 1010 Pa ?L ?
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Shear Modulus rigidness

• Elasticity of shape
• A- is cross-sectional area
• F- force parallel to cross-section
• S- Shear modulus
• h- height of object
• ?x distance displaced
• Units

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Shear Modulus rigidness

• Elasticity of shape
• When a force is applied parallel to one its faces
  while the other is held fixed.
• Ex A rectangular block under shear stress would
  become a parallelogram.
• Force must be parallel to the cross-sectional
  area.
• Ex book

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Shear Modulus Pause for a Cause

• A 125 kg linebacker of makes a flying tackle at
  vi 4.00m/s on a stationary quarterback of mass
  85 kg. The linebackers helmet makes solid contact
  with the quarterbacks femur.
• a) What is the speed vf of the two athletes
  immediately after contact? Assume this is a
  Perfectly inelastic collision from the point of
  impact.
• b) If the collision last for 0.100 s, estimate
  the average force exerted on the quarterbacks
  femur.
• c) If the cross-sectional area of the
  quarterbacks femur is 5.0 x 10-4 m2, calculate
  the shear stress exerted on the bone in the
  collision.

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Shear Modulus Practice

• A 125 kg linebacker of makes a flying tackle at
  vi 4.00m/s on a stationary quarterback of mass
  85 kg. The linebackers helmet makes solid contact
  with the quarterbacks femur.
• a) What is the speed vf of the two athletes
  immediately after contact? Assume this is a
  Perfectly inelastic collision from the point of
  impact.

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Shear Modulus Practice

• A 125 kg linebacker of makes a flying tackle at
  vi 4.00m/s on a stationary quarterback of mass
  85 kg. The linebackers helmet makes solid contact
  with the quarterbacks femur.
• b) If the collision last for 0.100 s, estimate
  the average force exerted on the quarterbacks
  femur.

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Shear Modulus Practice

• A 125 kg linebacker of makes a flying tackle at
  vi 4.00m/s on a stationary quarterback of mass
  85 kg. The linebackers helmet makes solid contact
  with the quarterbacks femur.
• c) If the cross-sectional area of the
  quarterbacks femur is 5.0 x 10-4 m2, calculate
  the shear stress exerted on the bone in the
  collision.

The average shear stress of an athletes femur is
7x107 Pa, so his did not leg break?
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Bulk Modulus compressibility

• Elasticity of volume
• ?P- volume stress
• F/A
• B- Bulk modulus, always -
• V- original volume
• ?V- change in volume
• Units

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Bulk Modulus compressibility

• Elasticity of volume
• This is a deformation due to uniform squeezing.
• All the external forces are perpendicular to
  every surface and are evenly distributed.
• Ex Deep sea diving
• An object under this stress will experience a
  deformation of volume.

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Bulk Modulus Pause for a Cause

• A solid lead sphere of volume 0.50 m3, dropped in
  the ocean, sinks to a depth of 2.0 x 103 m (1
  mile), where the pressure increases by 2.0 x 107
  Pa. Lead has a bulk modulus of
• 4.2 x 1010 Pa. What change is the change in
  volume of the lead sphere?

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Fluid Mechanics - Hydrostatics
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Fluids Contents

• Fluid Mechanics
• Density Pressure
• Pressure with Depth
• Pressure Measurements
• Buoyant Forces Archimedes Principle
• Fluids in Motion

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Density Quick Quiz

• Suppose you have one cubic meter of gold, two
  cubic meters of silver, and six cubic meters of
  aluminum.
• Rank each of them by mass, from smallest to
  largest.

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Density

• The 3 primary states have a distinct density,
  which is defined as mass per unit of volume.

Density is represented by the Greek letter,
RHO, r
Specific gravity- is the ratio of an objects
density to the density of water at 4 C (1.0 X
103 kg/m3)
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Common Densities
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Pause for a Cause

• A water bed is 2.0 m on each side an 30.0 cm
  deep.
• (a) Find its weight if the density of water is
  1000 kg/m3.
• (b) Find the pressure the that the water bed
  exerts on the floor. Assume that the entire lower
  surface of the bed makes contact with the floor.

1.2 m3
1200 kg
11760 N
2940 N/m2
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Why fluids are useful in physics?

• Typically, liquids are considered to be
  incompressible.
• That is once you place a liquid in a sealed
  container you can DO WORK on the FLUID as if it
  were an object.
• The PRESSURE you apply is transmitted throughout
  the liquid and over the entire length of the
  fluid itself.

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What is a Fluid?

• By definition, a fluid is any material that is
  unable to withstand a static shear stress. Unlike
  an elastic solid which responds to a shear stress
  with a recoverable deformation, a fluid responds
  with an irrecoverable flow.
• The only stress a fluid can exert is compression
  on a submerged object.
• What kind of stress is that?
• The stress experienced on a submerged object is
  always perpendicular to all surfaces.

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Hydrostatic Pressure Video1 Video2

• Suppose a Fluid (such as a liquid) is at REST, we
  call this HYDROSTATIC PRESSURE
• Two important points
• A fluid will exert a pressure in all directions
• A fluid will exert a pressure perpendicular to
  any surface it compacts

The only stress a fluid can exert on a submerged
object is compression.
Notice that the arrows on TOP of the objects are
smaller than at the BOTTOM. This is because
pressure is greatly affected by the DEPTH of the
object. Since the bottom of each object is deeper
than the top the pressure is greater at the
bottom.
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Pressure

• One of most important applications of a fluid is
  it's pressure- defined as a Force per unit Area

Atmospheric pressure Is defined as the amount of
pressure exert on an object due to the weight of
the air from the object to outer space.
The boiling point of liquids is dependant on the
atmospheric pressure.
English PSI pound/inch2
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Pressure

• One of most important applications of a fluid is
  it's pressure- defined as a Force per unit Area

Blood Pressure is the measure of how much
pressure one heart beat exerts on the walls of
your vascular system How is it measured?
English PSI pound/inch2
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Pressure Example

• If you tried to support your total weight (Fmg),
  on a bed of one nail. Your weight would be
  divided by the tiny area of the tip of the nail.

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Pressure vs. Depth

• Key Points
• All portions of the fluid must be in static
  equilibrium
• All points at the same depth must be at the same
  pressure
• Since P F/A if the pressure was greater on the
  left of the container so the force would be
  greater.
• If the Force was greater left of the block, the
  block would accelerate to the right.

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Pressure vs. Depth
Fabove

• Suppose we had an object submerged in water. If
  we were to draw an FBD for this object we would
  have three forces
• The weight of the object mg
• The force of the water above
• The force of the water pressing up
• If the object does not move then the sum of all
  forces is zero.
• What would that equation look like?

mg
Fwater
Fwater -Fabove mg 0
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Pressure vs. Depth
FATM

• Suppose we had an object submerged in water with
  the top exposed to the atmosphere. If we were to
  draw an FBD for this object we would have three
  forces
• The weight of the object mg
• The force of the atmosphere pushing down
• The force of the water pressing up
• If the object does not move then the sum of all
  forces is zero.
• What would that equation look like?

mg
Fwater
Fwater -Fatm mg 0
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Pressure vs. Depth

• But recall, pressure is force per unit area. So
  if we solve for force we can insert our new
  equation in.

Note Solving pressure for force gives us
Note Now consider mass m. solving density for
mass gives
Note Now consider volume V. Solving volume for
height gives.
Note Dived out all of the areas A
Note The initial pressure in this case is
atmospheric pressure, which is a CONSTANT. Po
1x105 N/m2
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A closer look at Pressure vs. Depth
Depth below surface
Initial Pressure May or MAY NOT be atmospheric
pressure
ABSOLUTE PRESSURE
Gauge Pressure CHANGE in pressure or the
DIFFERENCE in the initial and absolute pressure
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Pause for Cause

• a) Calculate the absolute pressure at an ocean
  depth of 1000 m. Assume that the density of water
  is 1000 kg/m3 and that Po 1.01 x 105 Pa (N/m2).
• b) Calculate the total force exerted on the
  outside of a 30.0 cm diameter circular submarine
  window at this depth.

9.9x106 N/m2
2.80 x 106 N
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Pause for Cause

• In a huge oil tanker, salt water has flooded an
  oil tank to a depth of 5.00 m. On top of the
  water is a layer of oil 8.00m deep. The oil has a
  density of 0.700 g/cm3. Find the pressure at the
  bottom of the tank if the density of salt water
  is 1025 kg/m3.

(1 m)3 (100 cm)3 106 cm3
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A closed system

• If you take a liquid and place it in a system
  that is CLOSED like plumbing for example or a
  cars brake line, the PRESSURE is the same
  everywhere.
• Since this is true, if you apply a force at one
  part of the system the pressure is the same at
  the other end of the system. The force, on the
  other hand MAY or MAY NOT equal the initial force
  applied. It depends on the AREA.
• You can take advantage of the fact that the
  pressure is the same in a closed system as it has
  MANY applications.
• The idea behind this is called PASCALS
• PRINCIPLE
• -thank you for hydraulics Pascal

Pascals Principle A change in the pressure
applied to an enclosed fluid is transmitted
undiminished to every point of the fluid and to
the walls of the container.
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Pascals Principle
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Another Example - Brakes
In the case of a car's brake pads, you have a
small initial force applied by you on the brake
pedal. This transfers via a brake line, which had
a small cylindrical area. The brake fluid then
enters a chamber with more AREA allowing a LARGE
FORCE to be applied on the brake shoes, which in
turn slow the car down.
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Pause for a Cause Pascals Principle
What force must the small piston of radius 5.00
cm exert on the large piston of radius 15.0 cm to
lift a 13,300 N car?
r1 5.00 cm r2 15.0 cm F2 13,300 N
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Buoyancy Demo
The principle affecting objects submerged in
fluids was discovers by Greek mathematician and
natural philosopher Archimedes.
Principle Any object immersed completely or
partially in a fluid it is buoyed UPWARD by a
force with a magnitude equal to the weight of the
fluid displaced by the object.
When the object is placed in fluid it DISPLACES a
certain amount of fluid. If the object is
completely submerged, the VOLUME of the OBJECT is
EQUAL to the VOLUME of FLUID it displaces.
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Archimedes's Principle

• " An object is buoyed up by a force equal to the
  weight of the fluid displaced."

In the figure, we see that the difference between
the weight in AIR and the weight in WATER is 3
lbs. This is the buoyant force that acts upward
to cancel out part of the force. If you were to
weight the water displaced it also would weigh 3
lbs.
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Archimedes's Principle Eureka!

• The bathtub epiphany!
• -According to legend, Archimedes was asked by
  King Hieron to determine whether the kings crown
  was made of only pure gold, or merely a gold
  alloy (mix).

• It had to be done without damaging the crown.
• -The solution came while taking a bath.
  Archimedes realized he felt lighter when
  submerged in water. As the story goes he was so
  excited he ran naked through the streets yelling
  Eureka! Eureka! -Greek for, I have found it.

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Archimedes's Principle
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Pause for a Cause

• 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 in air to be
  7.84 N. She then weighs the crown while it is
  immersed in water (density of water is 1000
  kg/m3) and now the scale reads 6.86 N. Is the
  crown made of pure gold if the density of gold is
  19.3 x 103 kg/m3?

Sub (1) into (2) in terms of mg
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Pause for a Cause Archimedes
The weight in air 7.84 N The weight in water
6.86 N ?water 1000 kg/m3
The density of pure Gold is known to be 19.3 X
103 kg/m3
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Fluid Flow

• Up till now, we have pretty much focused on
  fluids at rest. Now let's look at fluids in
  motion
• It is important that you understand that an IDEAL
  FLUID
• Is non viscous (meaning there is NO internal
  friction)
• Is incompressible (meaning its Density is
  constant)
• Its motion is steady and NON TURBULENT

A fluid's motion can be said to be STREAMLINE, or
LAMINAR. The path itself is called the
streamline. By Laminar, we mean that every
particle moves exactly along the smooth path as
every particle that follows it. If the fluid
DOES NOT have Laminar Flow it has TURBULENT FLOW
in which the paths are irregular and called EDDY
CURRENTS (angular momentum).
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Mass Flow Rate
Consider a pipe with a fluid moving within it.
The volume of the blue region is the AREA times
the length. Length is velocity times
time Density is mass per volume Putting it all
together you have MASS FLOW RATE.
A
v
L
A
v
L
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What happens if the Area changes?
The first thing you MUST understand is that MASS
is NOT CREATED OR DESTROYED! IT IS CONSERVED.
v2
A2
L1v1t
L2v2t
The MASS that flows into a region The MASS that
flows out of a region.
A1
v1
Using the Mass Flow rate equation and the idea
that a certain mass of water is constant as it
moves to a new pipe section
example The pipe delivery your house hold water
supply from the meter to the house a 1 inch pipe.
However the pipe delivery the water from your hot
water heater is usually a ½ pipe.
If the fluid is incompressible then the density
wont change
We have the Fluid Flow Continuity equation
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Equation of Continuity

• What do we mean by good water pressure.
• The mass of the fluid is conserved

• How would you expect the velocity of flow to
  change according to the cross-sectional area of
  the pipe?

Pause for CauseWhat is the initial velocity of
the fluid at A1 if?
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Pause for a Cause

• The speed of blood in the aorta is 50 cm/s and
  this vessel has a radius of 1.0 cm. If the
  capillaries have a total cross sectional area of
  3000 cm2, what is the speed of the blood in them?

0.052 cm/s
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Volume Flow Rate
Consider a pipe with a fluid moving within it.
The product of area velocity (m3/s) is called
flow rate Important Since fluids are not
compressible the volume of fluid the enters a
tube in a given time interval is equal to the
amount of fluid that leaves the tube over the
same time interval.
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Pause for a Cause

• 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 is takes
  1.00 min to fill the bucket. A nozzle with an
  opening of cross-sectional area 0.500 cm3 is then
  attached. The nozzle is held so that water is
  projected horizontally from a point 1.00 m above
  the ground. Over what horizontal distance can the
  water be projected?

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Bernoulli's Principle

• The Swiss Physicist Daniel Bernoulli, was
  interested in how the velocity changes as the
  fluid moves through a pipe of different area. He
  especially wanted to incorporate pressure into
  his idea as well. Conceptually, his principle is
  stated as " If the velocity of a fluid
  increases, the pressure decreases and vice
  versa."

The velocity can be increased by pushing the air
over or through a CONSTRICTION
A change in pressure results in a NET FORCE
towards the low pressure region.
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Bernoulli's Principle
Funnel
Ping pong Ball
Constriction
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Bernoulli's Principle
The constriction in the Subclavian artery causes
the blood in the region to speed up and thus
produces low pressure. The blood moving UP the
LVA is then pushed DOWN instead of up causing a
lack of blood flow to the brain. This condition
is called TIA (transient ischemic attack) or
Subclavian Steal Syndrome.
One end of a gopher hole is higher than the other
causing a constriction and low pressure region.
Thus the air is constantly sucked out of the
higher hole by the wind. The air enters the lower
hole providing a sort of air re-circulating
system effect to prevent suffocation.
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Bernoulli's Equation
Lets look at this principle mathematically.
X L
F1 on 2
-F2 on 1
Work is done by the blue section of water
applying a force on the red section. Formula for
work is?
According to Newtons 3rd law, the red section of
water applies an equal and opposite force back on
the first.
Consequence of energy conservation as applied to
an ideal fluid
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Bernoulli's Equation
v2
A2
y2
L1v1t
L2v2t
y1
A1
v1
ground
Work is also done by GRAVITY as the water travels
a vertical displacement UPWARD. As the water
moves UP the force due to gravity is DOWN. So the
work is NEGATIVE (Potential Energy).
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Bernoulli's Equation

• Part of the work goes into changing the velocity.
  Ex the volume that passes through A1 in a time
  interval ?t equals the volume that passes through
  A2 in the same time interval.

Change in velocity is?
KINETIC ENERGY!
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Bernoulli's Equation
Put it all together now.
Mass ?V
Divided out volume
Rearrange like terms
Swiftly moving fluids exert less pressure than do
slowly moving fluids
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Bernoulli's Equation
Moving everything related to one side results in
What this basically shows is that Conservation of
Energy holds true within a fluid and that if you
add the PRESSURE, the KINETIC ENERGY (in terms of
density) and POTENTIAL ENERGY (in terms of
density) you get the SAME VALUE anywhere along a
streamline.
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Pause for a Cause

• Water circulates throughout the house in a
  hot-water heating system. If the water is pumped
  at a speed of 0.50 m/s through a 4.0 cm diameter
  pipe in the basement under a pressure of 3.0 atm,
  what will be the flow speed and pressure in a 2.6
  cm-diameter pipe on the second floor 5.0 m above?

1 atm 1x105 Pa
1.183 m/s
2.5x105 Pa(N/m2) or 2.5 atm
84
Pause for a Cause
Consider what we know

• A large pipe with cross-sectional area of 1.00 m2
  descends 5.00 m and narrows to 0.500m2, where it
  terminates in a valve at point (1). If the
  pressure at (2) is atmospheric pressure, and the
  valve is opened wide and water allowed to flow
  freely, find the speed of the water leaving the
  pipe.

1 atm 1x105 Pa
Sub for V2
Both pressures are ATM
Solve for V1
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Pause for a Cause
Consider what we know

• A large pipe with cross-sectional area of 1.00 m2
  descends 5.00 m and narrows to 0.500m2, where it
  terminates in a valve at point (1). If the
  pressure at (2) is atmospheric pressure, and the
  valve is opened wide and water allowed to flow
  freely, find the speed of the water leaving the
  pipe.

1 atm 1x105 Pa
Subtract Po out
Multiply the 2 out divide the ? out
Get V1 together
Factor V1 out
11.4m/s
Solve for V1
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Note
The denominator goes away if the ratio of A1 and
A2 is very large Ex A1 0.5 m2 A2 1000 m2
General Relativity
87
Pause for a Cause
1 atm 1x105 Pa

• A nearsighted sheriff fires at a cattle rustler
  with his trusty six-shooter. Fortunately for the
  rustler, the bullet misses him and penetrates the
  town water tank, causing a leak. a) If the top of
  the tank is open to the atmosphere, determine the
  speed at which 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?

Assume the ratio between A1/A2 1
Solve for v1
3.13 m/s
88
Pause for a Cause
1 atm 1x105 Pa

• A nearsighted sheriff fires at a cattle rustler
  with his trusty six-shooter. Fortunately for the
  rustler, the bullet misses him and penetrates the
  town water tank, causing a leak. a) If the top of
  the tank is open to the atmosphere, determine the
  speed at which 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?

3.13 m/s
b) Projectile motion
2.45 m
89
Cohesion Adhesion
The force of attraction between unlike charges in
the atoms or molecules of substances are
responsible for cohesion and adhesion.
Cohesion is the clinging together of
molecules/atoms within a substance. Ever wonder
why rain falls in drops rather than individual
water molecules? Its because water molecules
cling together to form drops. Adhesion is the
clinging together of molecules/atoms of two
different substances. Adhesive tape gets its
name from the adhesion between the tape and other
objects. Water molecules cling to many other
materials besides clinging to themselves.
continued
90
Cohesion Adhesion (cont.)
The meniscus in a graduated cylinder of water is
due to the adhesion between water molecules the
sides of the tube. The adhesion is greater than
the cohesion between the water molecules. The
reverse is true about a column of mercury
Mercury atoms are attracted to each other more
strongly than they are attracted to the sides of
the tube. This causes a sort of reverse
meniscus.
91
Why molecules cling

To understand why molecules cling to each other
or to other molecules, lets take a closer look at
water. Each blue line represents a single
covalent bond (one shared pair of electrons).
Two other pairs of electrons also surround the
central oxygen atom. The four electron pairs want
to spread out as much as possible, which
_
gives H2O its bent shape. It is this shape that
account for waters unusual property of expanding
upon freezing. The shared electrons are not
shared equally. Oxygen is more electronegative
than hydrogen, meaning this is an unequal
tug-o-war, where the big, strong oxygen keeps the
shared electrons closer to itself than to
hydrogen. The unequal sharing, along with the
electron pairs not involved in sharing, make
water a polar molecule. Water is neutral, but it
has a positive side and a negative side. This
accounts for waters cohesive and adhesive nature
as well as its ability to dissolve so many other
substances.
92
Why moleculescling (cont.)
The dashed lines represent weak, temporary bonds
between molecules. Water molecules can cling to
other polar molecules besides them-selves, which
is why water is a good solvent. Water wont
dissolve nonpolar molecules, like grease, though.
(Detergent molecules have polar ends to attract
water and nonpolar ends to mix with the grease.)
Nonpolar molecules can attract each other to some
extent, otherwise they couldnt exist in a liquid
or solid state. This attraction is due to random
asymmetries in the electron clouds around the
nuclei of atoms.
93
Capillary Action
How do trees pump water hundreds of feet from the
ground to their highest leaves? Why do paper
towels soak up spills? Why does liquid wax rise
to the tip of a candle wick to be burned? Why
must liquids on the space shuttle be kept covered
to prevent them from crawling right out of their
containers?! These are all examples of capillary
action--the movement of a liquid up through a
thin tube. It is due to adhesion and cohesion.
Capillary action is a result of adhesion and
cohesion. A liquid that adheres to the material
that makes up a tube will be drawn inside.
Cohesive forces between the molecules of the
liquid will connect the molecules that arent
in direct contact with the inside of the tube.
In this way liquids can crawl up a tube. In a
pseudo-weightless environment like in the space
shuttle, the weightless fluid could crawl right
out of its container.
continued
94
Capillary Action (cont.)
The setups below looks just like barometers,
except the tubes are open to the air. Since the
pressure is the same at the base and inside the
tube, there is no pressure difference to support
the column of fluid. The column exists because
of capillarity. (Barometers must compen-sate for
this effect.) The effect is greater in thin
tubes because there is more surface area of tube
per unit of weight of fluid The force
supporting fluid is proportional to the surface
area of the tube, 2 ? r h, where h is the fluid
height. The weight of the fluid in the tube is
proportional to its volume, ? r 2 h. If the
radius of the tube is doubled,
the surface area doubles (and so does the force
supporting the fluid), but the volume quadruples
(as does the weight). Note if the fluid were
mercury, rather than rise it be depressed by the
tube.
95
Surface Tension
Ever wonder why water beads up on a car, or how
some insects can walk on water, or how bubbles
hold themselves together? The answer is surface
tension Because of cohesion between its
molecules, a substance
tends to contract to the smallest area possible.
Water on a waxed surface, for example, forms
round beads because in this shape, more weak
bounds can be formed between molecules than if
they were arranged in one flat layer. The drops
of water are flattened, however, due to their
weight. Cohesive forces are greater in mercury
than in water, so it forms a more spherical
shape. Cohesive forces are weaker in alcohol
than in water, so it forms a more flattened shape.
continued
mercury
water
alcohol
96
Surface Tension (cont.)
Below the surface a molecule in fluid is pulled
in all directions by its neighbors with
approximately equal strength, so the net force on
it is about zero. This is not the case at the
surface. Here the net force on a molecule is
downward. Thus, the layer of molecules at the
surface are slightly compressed. This surface
tension is strong enough in water to support
objects denser than the itself, like water bugs
and even razorblades (so long as the blade is
laid flat on the water so that more water
molecules can help support its weight).
Surface tension can be defined as the force per
unit length holding a surface together. Imagine
youre in a water balloon fight. You have one
last balloon, but its got a slash in it, so you
tape it up and fill it
with water. The surface tension is the force per
unit length the tape must exert on the balloon to
hold it together. A bubble is similar to the
water balloon. Rather than tape, the bubble is
held together by the cohesive forces in the
bubble.