Fluids

1

• Fluids

2
Question
What is a fluid? 1. A liquid 2. A gas 3.
Anything that flows 4. Anything that can be made
to change shape.
3
States of matter Phase Transitions
ICE
WATER
STEAM
Add heat
Add heat
These are three states of matter (plasma is
another one)
4
States of Matter

• Solid
• Liquid
• Gas
• Plasma

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States of Matter

• Solid
• Liquid
• Gas
• Plasma

• Has definite volume
• Has definite shape
• Molecules are held in specific location by
  electrical forces and vibrate about equilibrium
  positions
• Can be modeled as springs connecting molecules

6
States of Matter

• Solid
• Liquid
• Gas
• Plasma

• Crystalline solid
• Atoms have an ordered structure
• Example is salt (red spheres are Na ions, blue
  spheres represent Cl- ions)
• Amorphous Solid
• Atoms are arranged randomly
• Examples include glass

7
States of Matter

• Solid
• Liquid
• Gas
• Plasma

• Has a definite volume
• No definite shape
• 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

8
States of Matter

• Solid
• Liquid
• Gas
• Plasma

• Has no definite volume
• Has no 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

9
States of Matter

• Solid
• Liquid
• Gas
• 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 or experimental
  reactors or fluorescent light bulbs!

For more information http//fusedweb.pppl.gov/CPE
P/Chart_Pages/4.CreatingConditions.html
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Is there a concept that helps to distinguish
between those states of matter?
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Density

• The density of a substance of uniform composition
  is defined as its mass per unit volume
• some examples
• The densities of most liquids and solids vary
  slightly with changes in temperature and pressure
• Densities of gases vary greatly with changes in
  temperature and pressure (and generally 1000
  smaller)

12
Sometimes Specific Gravity

• 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
• Specific gravity is a unitless ratio

13
Pressure

• Pressure of fluid is the ratio of the force
  exerted by a fluid on a submerged object to area

Example 100 N over 1 m2 is P(100 N)/(1 m2)100
N/m2100 Pa.
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Pressure and Depth

• If a fluid is at rest in a container, all
  portions of the fluid must be in static
  equilibrium
• All points at the same depth must be at the same
  pressure (otherwise, the fluid would not be in
  equilibrium)
• Three external forces act on the region of a
  cross-sectional area A

External forces atmospheric, weight, normal
15
ConcepTest 1
You are measuring the pressure at the depth of 10
cm in three different containers. Rank the values
of pressure from the greatest to the
smallest 1. 1-2-3 2. 2-1-3 3. 3-2-1 4.
Its the same in all three
10 cm
Please fill your answer as question 1 of
General Purpose Answer Sheet
1 2 3
16
Pressure and Depth equation

• 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

• Other units of pressure
• 76.0 cm of mercury
• One atmosphere 1 atm 1.013 x 105 Pa
• 14.7 lb/in2

17
Example
Find pressure at 100 m below ocean surface.
Given masses h100 m Find P ?

18
Pascals Principle

• A change in pressure applied to an enclosed fluid
  is transmitted undiminished to every point of the
  fluid and to the walls of the container.
• The hydraulic press is an important application
  of Pascals Principle
• Also used in hydraulic brakes, forklifts, car
  lifts, etc.

Since A2gtA1, then F2gtF1 !!!
19
Measuring Pressure

• 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

• A long closed tube is filled with mercury and
  inverted in a dish of mercury
• Measures atmospheric pressure as ?gh

• The spring is calibrated by a known force
• The force the fluid exerts on the piston is then
  measured

20
How would you measure blood pressure?
Has to be (a) accurate (b) non-invasive (c)
simple
sphygmomanometer
21
Question
Suppose that you placed an extended object in the
water. How does the pressure at the top of this
object relate to the pressure at the bottom? 1.
Its the same. 2. The pressure is greater at the
top. 3. The pressure is greater at the bottom. 4.
Whatever
22
Buoyant Force

• This force is called the buoyant force.
• What is the magnitude of that force?

P1A
mg
P2A
23
Buoyant Force

• 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
• Whether an object sinks or floats depends on the
  relationship between the buoyant force and the
  weight

24
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.

This force is buoyant force. Physical cause
pressure difference between the top and the
bottom of the object
25
Archimedes PrincipleTotally Submerged Object

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

Depending on the direction of the net force, the
object will either float up or sink!
26
The net force is B-w(?fluid-?obj)gVobj

• The object is more dense than the fluid
  ?fluidgt?obj
• The net force is downward, so the object
  accelerates downward

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

27
Archimedes PrincipleFloating Object

• 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

28
Question 1
Suppose that you have a steel bar. Will it float
on water? Why?
29
Question 2
Suppose that you have a steel bar. Will it float
on water? Why? How come that ships (which are
made of steel) can float?
30
Question 3
Suppose that your friend gave you a necklace
(crown, piece of yellow metal, ). He claims that
this object is made of pure gold. How can you
check his statement (without going through his
credit history)?
31
Question 3
Suppose that your friend gave you a necklace
(crown, piece of yellow metal, ). He claims that
this object is made of pure gold. How can you
check his statement (without going through his
credit history)?
Idea determine density! Lets weight the object
in and outside the water container
Out In
If r is not the same as rgold, your friend is
lying
32
ConcepTest 2
Two identical glasses are filled to the same
level with water. One of the two glasses has ice
cubes floating in it.Which weighs more? 1. The
glass without ice cubes. 2. The glass with ice
cubes. 3. The two weigh the same.
Please fill your answer as question 3 of
General Purpose Answer Sheet
33
ConcepTest 3
Two identical glasses are filled to the same
level with water. One of the two glasses has ice
cubes floating in it.When the ice cubes melt, in
which glass is the level of the
water higher? 1. The glass without ice
cubes. 2. The glass with ice cubes. 3. It is the
same in both.
Please fill your answer as question 5 of
General Purpose Answer Sheet
34
Fluids in MotionStreamline Flow

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

35
Fluids in MotionTurbulent Flow

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

36
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

37
Characteristics of an Ideal Fluid

• The fluid is nonviscous
• There is no internal friction between adjacent
  layers
• 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

38
Equation of Continuity

• A1v1 A2v2
• The product of the cross-sectional area of a pipe
  and the fluid speed is a constant
• 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

39
Bernoullis Equation

• Relates pressure to fluid speed and elevation
• Bernoullis equation is a consequence of
  Conservation of Energy applied to an ideal fluid
• Assumes the fluid is incompressible and
  nonviscous, and flows in a nonturbulent,
  steady-state manner
• 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

40
How to measure the speed of the fluid flow
Venturi Meter

• Shows fluid flowing through a horizontal
  constricted pipe
• Speed changes as diameter changes
• Swiftly moving fluids exert less pressure than do
  slowly moving fluids

41
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.

This force is buoyant force. Physical cause
pressure difference between the top and the
bottom of the object
42
Question 3 (from last lecture)
Suppose that your friend gave you a necklace
(crown, piece of yellow metal, ). He claims that
this object is made of pure gold. How can you
check this statement (without going through your
friends credit history)?
43
Question 3
Suppose that your friend gave you a necklace
(crown, piece of yellow metal, ). He claims that
this object is made of pure gold. How can you
check his statement (without going through his
credit history)?
Idea determine density! Lets weight the object
in and outside the water container
Out In
If r is not the same as rgold, your friend is
lying
44
ConcepTest 2
Two identical glasses are filled to the same
level with water. One of the two glasses has ice
cubes floating in it.Which weighs more? 1. The
glass without ice cubes. 2. The glass with ice
cubes. 3. The two weigh the same.
Please fill your answer as question 39 of
General Purpose Answer Sheet
45
ConcepTest 2
Two identical glasses are filled to the same
level with water. One of the two glasses has ice
cubes floating in it.Which weighs more? 1. The
glass without ice cubes. 2. The glass with ice
cubes. 3. The two weight the same.
Convince your neighbor!
Please fill your answer as question 40 of
General Purpose Answer Sheet
46
ConcepTest 2
Two identical glasses are filled to the same
level with water. One of the two glasses has ice
cubes floating in it.Which weighs more? 1. The
glass without ice cubes. 2. The glass with ice
cubes. 3. The two weigh the same.
Ice cubes displace exactly their own weight in
water.
47
ConcepTest 3
Two identical glasses are filled to the same
level with water. One of the two glasses has ice
cubes floating in it.When the ice cubes melt, in
which glass is the level of the
water higher? 1. The glass without ice
cubes. 2. The glass with ice cubes. 3. It is the
same in both.
Please fill your answer as question 41 of
General Purpose Answer Sheet
48
ConcepTest 3
Two identical glasses are filled to the same
level with water. One of the two glasses has ice
cubes floating in it.When the ice cubes melt, in
which glass is the level of the
water higher? 1. The glass without ice
cubes. 2. The glass with ice cubes. 3. It is the
same in both.
Convince your neighbor!
Please fill your answer as question 42 of
General Purpose Answer Sheet
49
ConcepTest 3
Two identical glasses are filled to the same
level with water. One of the two glasses has ice
cubes floating in it.When the ice cubes melt, in
which glass is the level of the
water higher? 1. The glass without ice
cubes. 2. The glass with ice cubes. 3. It is the
same in both.
Previous problem weight was the same. Since
density is also the same, the volumes are going
to be the same as well.
50
Fluids in MotionStreamline/Turbulent Flow

• Streamline flow
• every particle that passes a particular point
  moves exactly along the smooth path followed by
  particles that passed the point earlier
• also called laminar flow
• Streamline is the path
• different streamlines cannot cross each other
• the streamline at any point coincides with the
  direction of fluid velocity at that point
• The flow becomes irregular
• exceeds a certain velocity
• any condition that causes abrupt changes in
  velocity
• The flow becomes turbulent

51
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

52
Characteristics of an Ideal Fluid

• The fluid is nonviscous
• There is no internal friction between adjacent
  layers
• 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

53
Equation of Continuity

• A1v1 A2v2
• The product of the cross-sectional area of a pipe
  and the fluid speed is a constant
• 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

54
Bernoullis Equation

• Relates pressure to fluid speed and elevation
• Bernoullis equation is a consequence of
  Conservation of Energy applied to an ideal fluid
• Assumes the fluid is incompressible and
  nonviscous, and flows in a nonturbulent,
  steady-state manner
• 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

55
How to measure the speed of the fluid flow
Venturi Meter

• Shows fluid flowing through a horizontal
  constricted pipe
• Speed changes as diameter changes
• Swiftly moving fluids exert less pressure than do
  slowly moving fluids

56
Example breathing
When a person inhales, air moves down the
bronchus (windpipe) at 15 cm/s. The average flow
speed of the air doubles through a constriction
in the bronchus. Assuming incompressible flow,
determine the pressure drop in the constriction.