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=UkmfmosZONc

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?

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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.

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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?

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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

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Will a boat sit higher in the ocean or a fresh water lake? Why?

A. Higher

B. Lower

C. Same

Next

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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

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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.

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What are the two quantities which are equal in Archimedes’ Principle?

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• 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.

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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?

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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?

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