What variables affect liquid pressure?

What direction is liquid pressure? Why?

Which person experiences a greater FORCE?

Which person touches the tack with a lesser AREA?

Which person experiences a greater PRESSURE?

SAME

A

A

B

A

DENSITY�The RATIO of Mass to Volume.�(How much matter is compacted into a certain volume)

Learning Goal

Understand the source of�liquid pressure.

Develop an equation to�calculate liquid pressure.

Relate liquid pressure�to buoyancy.

A

B

Which block puts more FORCE on the surface?

Which block puts more PRESSURE on the surface?

5 pounds

5 pounds

Pressure

Pressure

The “deeper” you go,�the greater the pressure.

DOG PILE

Pressure

Pressure

The greater the density,�the greater the pressure.

Pressure

Derive an equation for Pressure as a function of Density, Gravity, and Height

Force = Mass·Gravity

= Pressure

= Density·Gravity·Height

Pressure = ρ·g·h

Force = Mass·Gravity

Mass

Force

Volume

Pressure = ρ·g·h

h = height (depth)� meters

ρ = Density � kg/m³

g = acceleration of gravity� m/s²

m

=

Pascals =

P = P₀ + ρ·g·h

ρ·g·h

P₀

P = P₀ + ρ·g·h

Absolute Pressure

P = ρ·g·h

Relative (Gauge) Pressure

http://4.bp.blogspot.com/_TIvZEoqhTSE/TS9S2k-0_RI/AAAAAAAAIwU/qeGkvr91lPs/s1600/otter%2Bchecking%2Bme%2Bout%2Bthru%2Bthe%2Bplastic.JPG

This is too much,�I can’t handle the ρ·g·h!

1 cm³

1,000 cm³

1 milliliter

1,000 milliliters

1 liter

Volume

1 cm³

1,000 cm³

1 milliliter

1,000 milliliters

1 liter

Volume

1,000 liters

1 meter³

1,000 kilograms

9,800 Newtons

1,000 liters

1 meter³

Pressure = ρ·g·h

M.K.S. UNITS!

FLUID�Pressure is in ALL directions

Liquid

Gas

FLUID�Pressure is in ALL directions

http://catalinaphysics.freeservers.com/photo.html

Solids

Liquids

How does this picture illustrate�pressure as a function of depth?

Pressure = ρ·g·h

y = k·x + 0

Pressure = ρ·g·h

www.dotpattern.com/dotpat/gLog/mizu/pages/ocean-large.html

http://www.overtons.com/cgi-bin/overtons/order/large.cgi?21571

Learning Objective

Understand the source of�liquid pressure.

Develop an equation to�calculate liquid pressure.

Relate liquid pressure�to buoyancy.

Why do these two objects have the same buoyant force?

Force = Pressure · Area

Buoyant Force = ΔP · A

ΔP·A

ΔP·A

Archimedes Principle

(287-212 BCE)

http://www-groups.dcs.st-and.ac.uk/~history/PictDisplay/Archimedes.html

The Story of

Archimedes Principle

​

​

​

Retold by James Baldwin

“I know of no way,” was the answer.

But Archimedes was not the man to say that anything was impossible. He took great delight in working out hard problems, and when any question puzzled him he would keep studying until he found some sort of answer to it. And so, day after day, he thought about the gold and tried to find some way by which it could be tested without doing harm to the crown.

One morning he was thinking of this question while he was getting ready for a bath. The tub was full to the very edge, and as he stepped into it a quantity of water flowed out upon the stone floor. A similar thing had happened a hundred times before, but this was the first time that Archimedes had thought about it.

“How much water did I displace by getting into the tub?” he asked himself. “Anybody can see that I displaced a volume of water equal to the volume of my body. A man half my size would displace half as much.

​

“Now suppose, instead of putting myself into the tub, I had put Hiero’s crown into it, it would have displaced a volume of water equal to its own volume. Ah, let me see! Gold is much denser than silver. Ten pounds of pure gold would not make so great a volume as say seven pounds of gold mixed with three pounds of silver. If Hiero’s crown is pure gold it will displace the same volume of water as any other ten pounds of pure gold. But if it is part gold and part silver it will displace a larger volume. I have it at last! Eureka! Eureka!

Forgetful of everything else he leaped from the bath. Without stopping to dress himself, he ran through the streets to the king’s palace shouting, “Eureka! Eureka! Eureka! Which is in English means, “I have found it! I have found it! I have found it!”

​

The crown was tested . It was found to displace much more water than ten pounds of pure gold displaced.

The guilt of the goldsmith was proved beyond a doubt. But whether he was punished or not, I do not know, neither does it matter. The simple discovery which Archimedes made in the his bathtub was worth far more to the world than Hiero’s crown.

TITLE:

OBJECTIVE:���

APPARATUS:

Archimedes Principle

Determine the relationship between the buoyant force, and the weight of the water displaced

PART 1 PART 2

​

Buoyant Force�EQUALS�Weight of Water Displaced

​

OUT of Water = 20 N

IN water = 13 N

Weight of Water Displaced = 7 N

Buoyant Force = 7 N

?

Buoyant Force = ?

Archimedes Principle

(287-212 BCE)

http://www-groups.dcs.st-and.ac.uk/~history/PictDisplay/Archimedes.html

ρ_gold = 19,320 kg/m³

ρ_silver = 10,490 kg/m³

Assume Gold had a mass of 2.00 kg.

= 8.799 x 10^-5 m³

= 2.860 x 10^-5 m³

= 10.352 x 10^-5 m³

Assume Crown had 1.70 kg of Gold and 0.30 kg of Silver.

= 11.659 x 10^-5 m³

= 103.52 cm³

= 87.99 cm³

= 28.60 cm³

= 116.59 cm³

10 lbs Pure Gold

10 lbs Pure Gold

10 lbs Gold Mixed with Silver

10 lbs Pure Gold

The Death of Archimedes

(287-212 BCE)

http://www-groups.dcs.st-and.ac.uk/~history/PictDisplay/Archimedes.html

The Roman invader, Marcus Marcellus, captured Syracuse. Having heard of Archimedes, he forbade harm to him. �Not recognizing Archimedes, an ignorant soldier killed him.

http://www.fineartsources.com/lithos_normal/lithos_death%20of%20archimedes.html

Archimedes Principle

Buoyant Force�EQUALS�Weight of Fluid Displaced

Find the buoyant�force on the ball.

Weigh the ball in water AND out of water.

OR��Calculate the�weight of the�water displaced!

Volume_ball = 4/3·π·Radius³

Volume_ball = 4/3·π·2.8³

Volume_ball = 92 cm³

V_{water displaced} = 92 cm³

m = ρ ·V

mass = 92 g

buoyant force =.092(9.8) = .90 N

Calculate the buoyant�force on the ball.

http://www.cotedazur-holiday.com/Photos/Swimming%20Pool.jpg

Is it hard to push an empty five gallon bucket under water?

How hard?

http://i.ehow.com/images/GlobalPhoto/Articles/2101895/nano-5g-bucket_Full.jpg

5.0 gal

=

42 lbs

Just as hard as it would be to lift the same bucket filled with water.

http://www.thecarycompany.com/containers/drums.html

≈200 gallons of water displaced.

Density_water = 8.3 lbs/gal

1700 pounds of water displaced.

1700 pounds of buoyant force.

“Pirates of the Caribbean” - Disney

Which object experiences a larger Buoyant Force?

Which object displaces a�greater Weight of Fluid?

Buoyant Force�EQUALS�Weight of Fluid Displaced

Archimedes Principle

Which object experiences a larger Buoyant Force?�

Which object displaces a�greater Weight of Fluid?

Which object experiences a larger Buoyant Force?�

Which object displaces a�greater Weight of Fluid?

SAME!

Which object experiences a larger Buoyant Force?�

Which object displaces a�greater Weight of Fluid?

Buoyant Force

Weight

1 kg Lead or 1 kg of Aluminum

Which object experiences a larger Buoyant Force?�

Which object displaces a�greater Weight of Fluid?

Pb

1 kg

Al

1 kg

1 liter of Lead or 1 liter of Aluminum

Which object experiences a larger Buoyant Force?�

Which object displaces a�greater Weight of Fluid?

SAME!

Archimedes Principle

Buoyant Force�EQUALS�Weight of Fluid Displaced

When FLOATING, Weight of Fluid Displaced �EQUALS weight of the object.

When FLOATING, Buoyant Force�Equals weight of the object.

Floating

Submerged

Equal WEIGHT

Equal VOLUME

Did this bridge have to be designed to withstand the�additional weight of ship and barge traffic, or just the weight of the water?

Falkirk Wheel

Scotland