Physics Part 1MECHANICSPhysics 1700

FLUIDS

W. Pezzaglia

Updated: 2013Jul23

Fluids (Hydrostatics)

A. Pressure & Pascal’s Laws

B. Archimedes Principle

C. Surface Tension

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A. Pressure & Pascal’s Laws

Pascal’s Laws (1647)

1. Pressure defined

2. Hydraulics: Law of Transmitted Pressure

3. Law of Depth

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Blaise Pascal1623-1662

1. Pressure

(a) Definition: Force per area

(b) Units:– SI: Pascal=Newton/m2

– cgs: barye=Dyne/cm2

– Imperial: psi=pound/inch2

– Other: Torr=mm of Hg– Other: inches of Hg– Bar: millibar=100 Pascals

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2. Pascal’s Law of Pressure

• Transmitted Pressure: if the weight of a fluid is neglected the pressure throughout an enclosed volume will be the same

• the static pressure in a fluid acts equally in all directions

• the static pressure acts at right angles to any surface in contact with the fluid

• Major application is Hydraulics

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Demo Breaking Bottle: http://www.youtube.com/watch?v=epOwdGIDzlY

3. Law of Depth

• Pressure increases with (vertical) depth in a fluid of density :

P0 is atmospheric pressure at top of fluid, g is acceleration of gravity

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ghPP 0

Water is shooting at faster at bigger depths due to more pressure

3b. Pascal’s Vases7

Pressure is same at points A, B, C, D as the are at equal height

Pressure is same at bottom of these vases

3c. Pascal’s Barrel

• Pascal's barrel was a hydrostatics experiment performed by Blaise Pascal in 1646. In the experiment, Pascal inserted a 10 m long (32.8 ft) vertical tube into a barrel filled with water. When water was poured into the vertical tube, Pascal found that the increase in pressure caused the barrel to burst.

• (Wikipedia)

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B. Archimedes Principle

287-212 BC

Discuss “the story of the crown”

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1. Buoyancy Force

• Objects weigh less in water

• Hence, there is an upward “Buoyant Force” on the object inside the fluid.

• If the Buoyant force is big enough, an object will “float”

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2. Archimedes's Principle (212 BC)

• “Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object.”

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3. The Crown

• Can show ratio of (dry) weight “W” to Buoyant force “B” is equal to the specific gravity of the object.

• Compare “fake” crown with equal weight of real gold.

• Since “fake” crown has less density than real gold, its buoyant force is greater so they have different weights underwater

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B

W

w

4. Floating• Archimedes: “Any floating object

displaces its own weight of fluid.“

• If density of object is less than water, the buoyancy will exceed the weight and the object will rise to the surface.

• At the surface, the object will float such that the % of volume underwater equals its specific gravity.

• For example, specific gravity of ice is 0.917 so the ice cube in ordinary water will be 92% underwater and only 8% above. However, an iceberg relative to salty seawater (s.g. 1.025) will have: 0.917/1.025=0.895 or 89.5% underwater

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C. Surface Tension

1. Molecular Forces

2. Capillary Action

3. Surface Tension

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1. Molecular Forces

(a) Cohesion: tendency of similar or identical particles/surfaces to cling to one another

(b) Adhesion: the tendency of dissimilar particles or surfaces to cling to one another

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2. Capillary Action

(a) Capillary Rise whenadhesion>cohesion[water in glass tube]

(b) Capillary Depression whenadhesion<cohesion[mercury in glass tube]

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2c. Capillary Action

Capillary rise is greater in smaller diameter tube

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3. Surface Tension

(a) Cohesion makes surface of water behave like elastic membrane

(b) Objects with adhesion<cohesioncan float on surface

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3c. Surface Tension

• x

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https://upload.wikimedia.org/wikipedia/commons/f/f8/Cutting_a_water_droplet_using_a_superhydrophobic_knife_on_superhydrophobic_surfaces.ogv

Notes/Demos

• PHET: Pascal's law of depth http://phet.colorado.edu/en/simulation/under-pressure

• PHET Density http://phet.colorado.edu/en/simulation/density

• PHET Buoyancy http://phet.colorado.edu/en/simulation/buoyancy

• PHET Buoyancy and Balloons http://phet.colorado.edu/en/simulation/balloons-and-buoyancy

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