Chapter 13
Fluids
Introduction
• Our Perspective on Fluids
– An application of Classical Mechanics
– The form of the objects are not solid as they
have been studied so far
– There is a need to introduce new complexity,
which produces some surprising results
– More hard work, but enjoy!
http://www.youtube.com/watch?v=UkmfmosZ
ONc
Introduction …
• Our approach
– In addition to mass, add volume and density
– In addition to force, add pressure
– Encounter new definitions and phenomena:
specific gravity, gauge pressure, Pascal’s
principle, buoyancy, Archimedes’ Principle,
fluid flow
– Conservation of energy leads to Bernoulli’s
equation and Bernoulli's principle
– A look at other interesting phenomena to gain
familiarity
Phases of matter
• A wide variety of phases
– Well beyond those listed in text
• Our interest in two: liquids and gasses
– Their macroscopic and microscopic properties
– Both in the general category of fluids
Density and specific gravity
• We will focus on volumes of substances
– Therefore need to know and use density
– Distinguish mass and volume (old joke)
– Data analysis activity (handout)
• Comparison of a substance’s density to
the density of water
– through “specific gravity”
Pressure …
• General definition of pressure
• Pressure in fluids acts in all directions
– Demonstration
• Direction of pressure on a volume in a fluid
– Question for discussion
• Tutorial on Pressure in a Liquid (handout)
– With demonstration or video
http://www.youtube.com/watch?v=E_hci9vrvfw
Pressure (cont’d) …
• Effect of elevation on atmospheric
pressure
– Simple model
– Guess & check a solution
• Absolute and gauge pressure
Pressure (cont’d)
• Pascal’s Principle
– Demonstration
– Statement and proof
– Understanding hydraulic devices
• Measurement of pressure
– Understanding devices, units
• Examples
• Question
Buoyancy & Archimedes’
Principle
• Demonstration question
• Buoyancy ILD (handout)
• Clarifying discussion
– Source of buoyancy; question
– Archimedes’ principle
– Static fluid ILD (handout, if time available)
– Questions from Buoyancy ILD 1 2 3 4 5
– Canal bridge question
– Balloon in car question
Fluids in Motion; Flow rate and
continuity equation
• Two main types of fluid flow: streamline
(laminar) and turbulent flow
– Character of each
– Mechanical energy loss in each
• Equation of continuity
– Derivation
– For incompressible fluids
– Examples
Bernoulli’s Equation
• Derivation exercise (on whiteboards)
– Draw the iconic diagram and label the
elements needed for the derivation.
– Why are the end sections singled out?
– What is the work done on the fluid in the time
Δt?
– What is the change in mechanical energy
during the time Δt?
– What is implied by the conservation of
mechanical energy?
Bernoulli’s Equation (cont’d)
• What is assumed in the derivation of
Bernoulli’s equation?
• Jeopardy questions (handouts)
Bernoulli’s Principle
• Special cases of Bernoulli’s equation
– Torricelli's’ theorem – jeopardy question
– Bernoulli’s principle – jeopardy question
• Applications
– Mini-experiments in small groups
– Atomizer
– Ball in air stream
– Sail
– Curve ball
– Cylindrical sail
More…(comments)
• Viscosity
• Flow in tubes; Poiseuille’s Equation
– Surface tension and Capillarity
– Scaling comment on both
• Capillarity: up or down
• Pumps
The end
Is the load on the canal bridge (in Germany)
increased when (1) people walk across?
(2) barges move across? or (3) both?
back
When I put my finger into the water in the
beaker on the scale, what will happen to
the reading?
A. It will go up.
B. It will go down.
C. It will stay the same.
back
If there were no gravity, would there be
buoyancy in a fluid (at rest in an inertial
frame of reference)?
A. Yes
B. No
Why or why not?
back
A boat sits at a particular height in the water.
What is true just at the level the boat sits
that determines how high it sits?
Next
back
Will a boat sit higher in the ocean or a fresh
water lake? Why?
A. Higher
B. Lower
C. Same
Next
back
When a large ice cube melts in a large glass
of water, what happens to the level of the
water? Why?
A. It would rise.
B. It would fall.
C. It would stay the same.
Next
back
If a boat in a sealed channel were to dump a
load of iron in the water, what would
happen to the water level of the channel?
A. It would rise.
B. It would fall.
C. It would stay the same.
Next
back
What are the two quantities which are equal
in Archimedes’ Principle?
back
•
Suppose you have a Helium-filled
balloon in your car and you come to a
stop. What happens to the balloon?
A. It moves forward.
B. It moves backward.
C. It stays in the same relative position in
the car.
back
Does the solution of the following form
work?
P = AeBy
If not, why not?
If so, what values of A and B make it work?
back
A suggestion is made to equip astronauts
with suction cups on their boots to stick to
the outside of their space station.
What do you think about this idea?
back