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) Pressure increases with depth Supports weight above

Liquid Pressure Formula p = rhg h p = pressure r = density of liquid h = depth under top of liquid p = pressure here

Pressure within a Liquid p = rhg Shape of the container does not matter! All that matters are depth h, fluid density r, and gravitational field g.

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 = rVg r = 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 pV = NkBT p = pressure V = volume N = number of gas molecules kB = 1.3806610–23 J/K T = absolute (Kelvin) temperature

Gas Pressure and Volume pV = NkBT At a constant temperature, pV is constant Increasing p decreases V and vice versa p V

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 SF = 0, buoyancy↑ = glass weight↓ Neutral buoyancy air volume is the same for all initial bubble sizes