III. Behavior of Fluids III. Behavior of Fluids

Learning Goals – Students will be able toLearning Goals – Students will be able to

• explain the concept of fluid pressure.• summarize Boyle’s Law.• summarize Charle’s Law.• give Archimedes’ Principle in their own words.• define Pascal’s Principle.• demonstrate Bernoulli’s Principle.• explain surface tension.

MATTER

There is no such thing as still air. The air molecules are constantly moving at an average of 1,000 miles per hour.

A. PressureA. Pressure

area

forcepressure

Which shoes create the most pressure?

A. PressureA. Pressure

• Key Units at Sea Level

101.325 kPa (kilopascal)

1 atm

760 mm Hg

14.7 psi2m

NkPa

This much air weighs about 30 grams, or about the same as 6 nickels.

A. PressureA. Pressure

Barometer

Atm

osph

eric

Pre

ssur

e

Manometer

Con

tain

ed P

ress

ure

sphygmomanometersphygmomanometer• sphygmometer• Greek sphygmos meaning

pulse

Measures to 300mm Hg

This is the inner mechanisms of certain pressure gauges.

A. PressureA. Pressure• Effect on Boiling Point

– When atmospheric pressure increases, the boiling point of a liquid increases.

– EX: high altitude cooking, boiling cold water

9

0

18

9 hits9 sec

1 hitsec

=

18 hits9 sec

2 hitssec

=

00010203040506070809

Seconds

½ volume Pressure comes from the gas molecules hitting the side of the container.

Hits

So we saw that as volume decreases the pressure increases.

B. Boyle’s LawB. Boyle’s Law

• When the volume of a gas decreases, its pressure increases (at constant temp).

P

VINVERSE

B. Boyle’s LawB. Boyle’s Law

9

0

18

9 hits4.5 sec

2 hitssec

=

00010203040506070809

Seconds

27 ºC = 300 K

327 ºC = 600 K

327 ºC = 600 K

0 K

We are going from room temperature 27 ºC = 300 K to double that temperature, which is 600 Kelvin. We get twice the number of collisions and therefore twice the pressure.

15 psi, 300 K

30 psi

3 psi

600 K

60 K

So we just saw that when temperature goes up, so does the pressure. This makes sense because higher temperature means the gas molecules are going faster, colliding more often, and hitting harder.

V

T

C. Charles’ LawC. Charles’ Law• When the temperature of a gas

increases, its volume also increases (at constant pressure).

DIRECT

C. Charles’ LawC. Charles’ Law

C. Charles’ LawC. Charles’ Law• Absolute Zero - Temp at which...

– all particle motion would stop.

-273°Cor

0 K

Another way to increase pressure is to increase the number of gas molecules.

This is also a safety problem. Any closed container that has gas in and gets heated will likely increase pressure dramatically until the container bursts.

Let’s review what we learned. If the volume decreases the pressure will increase. Then the reverse happens if the volume increases. The pressure drops as gas molecules are farther apart.

As we also learned, we can increase pressure by introducing more molecules of the gas into the volume.

We also learned that if temperature doubles, the pressure doubles if volume is fixed. Or if the container is flexible, the volume will double with pressure staying constant. Or both can increase such that the product of the two doubles.

To make these quantities equal, we need a conversion constant. We call it R (the Universal Gas Constant)

When a pressure cooker is used, whatWhen a pressure cooker is used, what

causes the increased pressure?causes the increased pressure?

PV=nRTPV=nRT

Temperature goes from 25Temperature goes from 25ooC to 100C to 100ooCC

In 1984 in a village in the African nation of Cameroon….

On the night of the apocalypse, Ephriam Che was in his mud brick house on a cliff above Nyos. Around 9 P.M., Che heard a rumbling that sounded like a rockslide. Then a strange white mist rose from the lake. He went to bed, feeling ill.

There is a lake known as Nyos. It’s a beautiful lake that fills the cauldron of a ancient volcano. Nothing about it gives clues to the danger that rests in its deep waters.

At first light, Che headed downhill. Nyos had turned a dull red. He noticed the silence; the morning sounds of songbirds and insects were absent. He also saw dead animals. Frightened, he ran farther along the lake and downhill to the village. There, nearly every one of the village's 1,000 residents was dead, including his parents, siblings, aunts and uncles. It was the end of the world, or so Che believed.

Eye witnesses said they saw an invisible river coming down the hill knocking down brush and small trees. It traveled at about 50 mph but could not be seen.

All told, some 1,800 people perished around Lake Nyos. Later the killer was found to be carbon dioxide, which is not considered toxic, but its high density keeps it close to the ground causing asphyxiation. Density also caused it to flow down the hillsides asphyxiating more people.

Scientists found the carbon dioxide had been building up over time at the bottom layer of the lake. Magma vents were pumping CO2 into the lake forming carbonic acid (H2CO3) which essentially is carbonated water. The water pressure kept it from decomposing in to CO2 gas which would float and dissipate. However, a rock slide or small earthquake triggered the carbonic acid to decompose into CO2 causing the lake to explode.

To prevent build up of CO2 scientists installed pipes that reach down to the depths and trigger a release of CO2. This huge fountain is only powered by the release of CO2.

V. Forces in Fluids V. Forces in Fluids Archimedes’ Principle Pascal’s Principle Bernoulli’s Principle Surface tension

A. Archimedes’ PrincipleA. Archimedes’ Principle• Fluid

– matter that flows– liquids and gases

• Buoyancy– the ability of a fluid to exert

an upward force on an object immersed in it

Archimedes principleArchimedes principle• Archimede’s

principle: The buoyant force on an object in a fluid is equal to the weight of the fluid displaced by the object

• This force keeps objects afloat.

• How do boats that are loaded appear different then empty boats?

A. Archimedes’ PrincipleA. Archimedes’ Principle• Bouyant Force

– upward force exerted by a fluid on an immersed object

– bouyant force > weight

– bouyant force = weight

– bouyant force < weightballoon rises

balloon sinks

balloon floats

A. Archimedes’ PrincipleA. Archimedes’ Principle

A. Archimedes’ PrincipleA. Archimedes’ Principle

More water needs to be displaced in order to cancel weight ball floats lower in the water.

Not enough water is displaced in order to cancel weight ball sinks.

A. Archimedes’ PrincipleA. Archimedes’ Principle

Very little water needs to be displaced in order to cancel weight ball floats on surface.

B. Pascal’s PrincipleB. Pascal’s Principle•Pascal’s

Principle– pressure

applied to a fluid is transmitted unchanged throughout the fluid

B. Pascal’s PrincipleB. Pascal’s Principle

The car on the hydraulic lift in has a weight of 16,000 N. The large piston has a surface area of 4,000 cm3; The small piston has an area of 65 cm3. What force must be applied to piston A to lift the car?

C. Bernoulli’s PrincipleC. Bernoulli’s Principle• Bernoulli’s

Principle

– as the velocity of a fluid increases, the pressure exerted by the fluid decreases

– EX:airplane lift, curve balls

C. Bernoulli’s PrincipleC. Bernoulli’s Principle

Airplane lift Curve Ball

C. Bernoulli’s PrincipleC. Bernoulli’s Principle

Funnel Demos

C. Bernoulli’s PrincipleC. Bernoulli’s Principle• Venturi Effect

– fluids flow faster through narrow spaces causing reduced pressure

– EX: garden sprayer, atomizer, carburetor

VenturiVenturi• Venturi effect:

Fluids flow faster through narrow spaces

• Fluid- any material that flows

Water is always trying to Water is always trying to pull itself into a tight ball. pull itself into a tight ball.

D. Surface Tension

We see the same effect on waxy leaves.

Water pulls on itself so much that it forms a “skin.” It’s called surface tension.

SURFACETENSION

SURFACETENSION

What’s going onat the surfaceof a liquid?

What’s going onat the surfaceof a liquid?

Let’s takea look!

Particles that make up a liquid are in constant random motion; they are randomly arranged.

You might expect the particles at the surface,at the micro level, to form a random surface,as shown below.

You might expect the particles at the surface,at the micro level, to form a random surface,as shown below.

= intermolecularattractions

Under the surface, intermolecular attractions pull onindividual molecules in all directions

= intermolecularattractions

= intermolecularattractions

= intermolecularattractions

At the surface the net force on surface molecules is downward.

Surface molecules are compressedmore tightly together,forming a sort of skin on the surface.

This explains the characteristic roundedshape that liquids form when droppingthrough the air: The molecules are all being pulled toward the center.

This explains the characteristic roundedshape that liquids form when droppingthrough the air: The molecules are all being pulled toward the center.

Water in particularhas a very highsurface tension. Surface tension is caused bythe attraction between water molecules. This is called cohesion.

This is the water strider insect.

How is this possible?

We are lucky that water has this strong attraction force otherwise we’d never see raindrops. The water would just breakup into a mist as it fell. Very few liquids would remain as drops if they fell from a large height.