26-Sep-10

Pascal’s Principle(Chap. 13)

GasesAtmospheric Pressure

(Chapter 14)

Lecture 14

Midterm Exam 1 on Mon. October 4(Chapters 2-8,10-14; Lectures 1-15)

26-Sep-10

Floating & Liquid Density

The greater the density of a liquid, the greater the buoyant force on objects floating or immersed in the liquid. Floating in Great Salt Lake,

Utah is easy because the lake water is dense due to high concentration of salt.

Iceberg: ρ(ice)<ρ(water)An Iceberg is floating in the ocean. As the iceberg melts, does the ocean level 1) rise, 2) sink, or 3) stay the same.

h

As ice, the iceberg displaces a volume of water equal in mass to the iceberg’s mass. Once it is melted, the iceberg still displaces a volume of water equal in mass to the original iceberg (melting doesn’t change the iceberg mass).

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Demo: Hydrometer

Hydrometer is a calibrated float; denser the liquid, the higher the hydrometer floats.

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Density & WinemakingDiagram A represents a test jar full of grape juice before the yeast is pitched. The hydrometer is floating high because the liquid is "heavy" with all the sugar... the hydrometer is pushed up because of the high fluid density.

As yeast turns sugar into alcohol and carbon dioxide, the wine becomes lighter (alcohol weighs less per unit volume) and the hydrometer doesn't float as high. Diagram B represents wine that has fermented to dryness and is lighter than water.”

www.grapestompers.com

AB

Pascal’s PrincipleIf an external pressure is applied to a confinedfluid, pressure at every point within the fluid increases by that amount. This principle is used, for example, in hydraulic lifts:

Pascal’s Principle: Work-Energy

Need pressure P2 = 5000N/4m2 = P1 = F1/(0.04m2)Thus F1 = (0.04m2/4m2)(5000N)=50N

Force F1 needed on piston of area A1 = 0.04m2 to lift 5000N car on piston of area A2= 4 m2?

GasesGases are the easiest state of matter to describe, as all ideal gases exhibit similar behavior.

An ideal gas is one that has low enough density, and is far enough away from condensing to liquid, that the interactions between molecules can be ignored.

Gas atoms or molecules move independently, with speed that depends on temperature.

26-Sep-10

AirMost common example of a gas is air, which

is mixture of nitrogen and oxygen gasesDensity of water = 1000 kg/m3

(1 gram per cubic centimeter)

Density of air = 1 kg/m3

(0.001 gram per cubic centimeter)

Water is about 1000 times denser than airWeight of air is small but not negligible. For example, weight of air in this room is comparable to your weight (volume of room about 1000x your volume).

26-Sep-10

Atmosphere

Density of air in the atmosphere decreases with increasing altitude.

Most of atmosphere in the first 10 km (about 6 miles) of altitude.

We live at the bottom of an ocean of fluid—the fluid is air & “ocean” is the atmosphere.

26-Sep-10

Atmospheric PressureAtmospheric column of airBase: 1 square meterHeight: 10 km (10,000 m)Volume: 10,000 cubic metersMass: 10,000 kilogramsWeight: 100,000 Newtons

(= 22,000 lb = 11 tons)Pressure: 100,000 Pascals

(= 15 lb per sq. inch)

Atmospheric PressureAtmospheric pressure is due to the weight of the atmosphere above us.

This is standard atmospheric pressure at sea level. It declines with altitude above sea level.

Location Pat (kPa) San Francisco 101Denver, Co 84Mt. Whitney 60Mt. Everest 35

Pa = 101 kPa

Atmospheric PressureThere are a number of different ways to describe atmospheric pressure.

In pascals:

In pounds per square inch:

In bars:

In inches of mercury: 29.9 in Hg

Weather Report Barometer

• Apparent 52°• Dew Point 44°• Humidity 76%• Wind S/5 mph• Visibility 10 mi• Barometer 30.03 in Hg (slightly high)

Sensitivity to Pressure• Atmospheric pressure does

not crush us, as our cells maintain an internal pressure that balances it.

• Since atmospheric pressure acts uniformly in all directions, we don’t usually notice it.

• We notice when internal and external pressures are different - pressure difference on ear when descending in airplane, etc.

Plastic bottle closed at 2,000 m altitude & brought to sea level.

Example - Tire Pressure Gauge

Expert Quality, handy-size tyre pressure gauge - range 2.0-99.5 PSI (15-700 kPa)Reads gauge pressure of air in tires. Actual pressure would be Pg+Patm.

Typical tires: Pg= 30 PSI = 205 kPa

P = 44.7 PSI = 305 kPa

26-Sep-10

Demo: Magdeburg Hemispheres

Pair of hemispheres fit together with air-tight seal

Most of the air is pumped out from the interior.

Air pressure holds the two pieces tightly together.

A A

AA

L

A

L

- Atmospheric pressure

- Low pressure

26-Sep-10

Check YourselfThe surface area of a Magdeburg hemisphere is

about 1/100th of a square meter. If we evacuate the air from inside a pair, how large is the force holding them together (Atmospheric pressure is 100,000 Newtons per square meter)?

What if only 90% of the air is removed?

26-Sep-10

Crush the Rail Tanker CarInterior of tank car was washed out & cleaned with steam. Then all outlet valves were shut and tank car was sealed. Workers went home; when they returned, this is what they found. Apparently as tank car cooled, it collapsed. The shell on these tank cars is 7/16th inch thick steel.

26-Sep-10

Demo: Drinking Straw

L

A A

With lungs, you reduce pressure in your mouth and in the straw.The higher pressure on the outside pushes the liquid up the straw.Force due to the pressure difference must match or exceed the weight.

Weight

NO “SUCKING” FORCE

26-Sep-10

Boyle’s Law

Density of a gas increases as it is compressed (volume decreased)

As the density of a gas increases, the pressure in the gas also increases. Compress the gas by

pushing in the syringe. Dial gauge shows increase in pressure.

SyringeGauge

Tank

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Breathing & Boyle’s Law

L

AA

H

26-Sep-10

Demo: Stop the Funnel

Water will not enter an air-tight container.

H

A

Weight

A

Weight

A

ABlock exit hole

26-Sep-10

Buoyancy in AirObjects can float in air, just as they float in

water, if the objects’ average density is less than the density of air.

Hot Air Balloon Helium-filled Blimp

Fluids in Motion: Flow and ContinuityIf the flow of a fluid is smooth, it is called streamline or laminar flow (a). We will work with laminar flow.

Above a certain speed, the flow becomes turbulent (b). Turbulent flow has eddies; the viscosity (friction) of the fluid is much greater when eddies are present.

Look at fluid flowing in a tube or pipe.

The mass of fluid that passes any two points in a pipe or tube must be equal.

“What goes in must come out”

We call this principle “continuity of flow.”

Flow Rate and the Equation of Continuity

Flow Rate and the Equation of ContinuityIf the density doesn’t change – typical for liquids – continuity requireswhere A is area and v is speed. Where the pipe is wider, the flow is slower.

Equation of Continuity for Liquids.

Four-lane highway merges to two-lane. Officer in police car observes 8 cars passing per second, at 30 mph. How many cars does officer on motorcycle observe passing per second? A) 4 B) 8 C) 16How fast must cars in two-lane section be going?A) 15 mph B) 30 mph C) 60 mph

Water PipeWater is flowing continuously in the pipe shown below.

Where is the velocity of the water greatest? A) B) C) D) equal everywhere

A CB

ExampleA horizontal pipe contains water at a pressure of

110 kPa flowing with a speed of 1.4 m/s. When the pipe narrows to one-half its original radius, what is the speed?

vf Af = vi Aivf = vi Ai/Af = vi[πri

2]/[π(ri/2)2] = 4vi

vf = 5.6 m/s

Key Points of Lecture 14Key Points of Lecture 14

Before next lecture, read Hewitt Chap. 14, first 2/3.

Homework Assignment #10 is due before 11:00 PM on Tuesday, Sept. 26.

Homework Assignment #11 is due before 11:00 PM on Friday, Oct. 1.

• Pascal’s Principle• Gases• Atmospheric Pressure and Related Effects• Buoyancy in Gases• Fluid in Motion - Continuity