Fluid Mechanics• Liquids and gases have the ability to flow• They are called fluids• There are a variety of “LAWS” that fluidsobey• Need some definitions
Density• Regardless of form (solid, liquid, gas) wecan define how much mass is squeezed intoa particular spacedensity =massvolume
Pressure• A measure of the amount of force exertedon a surface areapressure =forcearea
Pressure in a Fluid• The pressure is just the weight of all thefluid above you• Atmospheric pressure is just the weight ofall the air above on area on the surface ofthe earth• In a swimming pool the pressure on yourbody surface is just the weight of the waterabove you (plus the air pressure above thewater)
Pressure in a Fluid• So, the only thing that counts in fluidpressure is the gravitational force acting onthe mass ABOVE you• The deeper you go, the more weight aboveyou and the more pressure• Go to a mountaintop and the air pressure islower
Pressure in a FluidPressure actsperpendicularto the surfaceand increasesat greaterdepth.
BuoyancyNet upwardforce iscalled thebuoyantforce!!!Easier tolift a rockin water!!
Displacement of WaterThe amount ofwater displaced isequal to thevolume of therock.
Archimedes’ Principle• An immersed body is buoyed up by a forceequal to the weight of the fluid it displaces.• If the buoyant force on an object is greaterthan the force of gravity acting on theobject, the object will float• The apparent weight of an object in a liquidis gravitational force (weight) minus thebuoyant force
Flotation• A floating object displaces a weight of fluidequal to its own weight.
Gases• The primary difference between a liquidand a gas is the distance between themolecules• In a gas, the molecules are so widelyseparated, that there is little interactionbetween the individual moledules• IDEAL GAS• Independent of what the molecules are
Boyle’s Law• Pressure depends on density of the gas• Pressure is just the force per unit areaexerted by the molecules as they collidewith the walls of the container• Double the density, double the number ofcollisions with the wall and this doubles thepressure
Boyle’s LawDensity is massdivided byvolume.Halve thevolume and youdouble thedensity and thusthe pressure.
Boyle’s Law• At a given temperature for a given quantityof gas, the product of the pressure and thevolume is a constantP1V1 = P2V2
Atmospheric Pressure• Just the weight of the air above you• Unlike water, the density of the airdecreases with altitude since air iscompressible and liquids are only veryslightly compressible• Air pressure at sea level is about 105newtons/meter2
Buoyancy in a Gas• An object surrounded by air is buoyed upby a force equal to the weight of the airdisplace.• Exactly the same concept as buoyancy inwater. Just substitute air for water in thestatement• If the buoyant force is greater than theweight of the object, it will rise in the air
Buoyancy in a GasSince air gets lessdense with altitude,the buoyant forcedecreases withaltitude. So heliumballoons don’t riseforever!!!
Bernoulli’s Principle• Flow is faster when the pipe is narrower• Put your thumb over the end of a gardenhose• Energy conservation requires that thepressure be lower in a gas that is movingfaster• Has to do with the work necessary tocompress a gas (PV is energy, more later)
Bernoulli’s Principle• When the speed of a fluid increases,internal pressure in the fluid decreases.