Fluids and Pressure

PHYS 1090 Unit 5

Balloon Mash

• Greater force makes larger contact area

Pressure

• Force applied per unit area

p = F/A

• If pressure is constant, force and area change together

Pressure within Fluids

• Pascal’s Principle: fluids exert pressure evenly in all directions

Balloon Mash

• Upward force (pressure area) on plate exactly cancelled plate’s weight

• As weight increased, contact area did too

• (pressure may have increased as well)

Fountain

• Water shoots farther from lower holes

• Streams weaken as water drains

Static Fluids

• Pressure counteracts weight of fluid above (Pascal’s principle)

Supports weight above

• Pressure increases with depth

Liquid Pressure Formula

p = hg

• p = pressure

• = density of liquid

• h = depth under top of liquid

h

p = pressure here

Pressure within a Liquid

• Shape of the container does not matter!

• All that matters are depth h, fluid density , and gravitational field g.

p = hg

Fountain

• Stream velocity depends on pressure

• Pressure depends on depth

• Rocks in the can have no effect

Sinking and Floating

• Objects displace a volume of water equal to their submerged volume

• A floating boat displaces an additional volume of air

What forces are present?

What forces are present?

What forces are present?

What forces are present?

Pressure in a fluid

• Pressure increases with depth

• Greater pressure at bottom than top of an immersed object

• Results in upward buoyancy force that is the (vector) sum of all pA forces

Buoyancy Force

• Buoyancy force = weight of fluid displaced(Principle of Archimedes)

F = Vg

= density of fluid V = volume of fluid displaced = volume of

object submerged g = 9.8 N/kg

Sinking and Floating

• All objects are lighter under water

• Difference is buoyancy force• If buoyancy > weight, object rises to

surface and floats (so buoyancy = weight)

• if buoyancy < weight, object sinks

Clay Lump

• Weight of the lump was constant

• Making a boat increased the volume of water displaced

• That increased the buoyancy force

• A great enough buoyancy floated the boat

Expanding and Contracting

• The same amount of gas occupies more volume at a higher temperature.

Convection

• Warm fluids expand, becoming less dense

• Circulation is driven by buoyancy forces

• Much faster than conduction

“Ideal Gas” Law

• p = pressure

• V = volume

• N = number of gas molecules

• kB = 1.3806610–23 J/K

• T = absolute (Kelvin) temperature

pV = NkBT

Gas Pressure and Volume

• At a constant temperature, pV is constant• Increasing p decreases V and vice versa

p

V

pV = NkBT

Balloon Mash

• Pressure may have increased with greater force because air was compressed (volume became less)

Diver

• Diver’s weight = weight of (glass + air)

• Buoyancy = weight of excluded water

• Increasing pressure decreases air volume

• Buoyancy decreases

• Weight is unchanged

Neutral Buoyancy

• Air doesn’t weigh much

• Glass weight doesn’t change

• At neutral buoyancy F = 0, buoyancy↑ = glass weight↓

• Neutral buoyancy air volume is the same for all initial bubble sizes