Fluid Mechanics Liquids and gases have the ability to flow Liquids and gases have the ability to...

Fluid MechanicsFluid Mechanics

Liquids and gases have the ability to Liquids and gases have the ability to flowflow

They are called fluidsThey are called fluids There are a variety of “LAWS” that There are a variety of “LAWS” that

fluids obeyfluids obey Need some definitionsNeed some definitions

DensityDensity

Regardless of form (solid, liquid, Regardless of form (solid, liquid, gas) we can define how much mass gas) we can define how much mass is squeezed into a particular spaceis squeezed into a particular space

density massvolume

PressurePressure

A measure of the amount of A measure of the amount of force exerted on a surface force exerted on a surface areaarea

pressure forcearea

PressurePressure

area

forcepressure

Which shoes create the most pressure?

Pressure in a FluidPressure in a Fluid

The pressure is just the weight of all The pressure is just the weight of all the fluid above youthe fluid above you

Atmospheric pressure is just the Atmospheric pressure is just the weight of all the air above on area weight of all the air above on area on the surface of the earthon the surface of the earth

In a swimming pool the pressure on In a swimming pool the pressure on your body surface is just the weight your body surface is just the weight of the water above you (plus the air of the water above you (plus the air pressure above the water)pressure above the water)

Pressure in a FluidPressure in a Fluid

So, the only thing that counts in So, the only thing that counts in fluid pressure is the gravitational fluid pressure is the gravitational force acting on the mass ABOVE force acting on the mass ABOVE youyou

The deeper you go, the more The deeper you go, the more weight above you and the more weight above you and the more pressurepressure

Go to a mountaintop and the air Go to a mountaintop and the air pressure is lowerpressure is lower

Pressure in a FluidPressure in a Fluid

Pressure acts perpendicular to the surface and increases at greater depth.

Pressure in a FluidPressure in a Fluid

Pascal’s PrinciplePascal’s Principle Pascal’s PrinciplePascal’s Principle

pressure applied to a fluid is pressure applied to a fluid is transmitted unchanged transmitted unchanged throughout the fluidthroughout the fluid

A

FP

2

2

1

1

A

F

A

F

BuoyancyBuoyancy

Net upward force is called the buoyant force!!!

Easier to lift a rock in water!!

Displacement of WaterDisplacement of Water

The amount of water displaced is equal to the volume of the rock.

Archimedes’ PrincipleArchimedes’ Principle

An immersed body is buoyed An immersed body is buoyed up by a force equal to the up by a force equal to the weight of the fluid it displaces.weight of the fluid it displaces.

If the buoyant force on an object is If the buoyant force on an object is greater than the force of gravity greater than the force of gravity acting on the object, the object will acting on the object, the object will floatfloat

The apparent weight of an object in a The apparent weight of an object in a liquid is gravitational force (weight) liquid is gravitational force (weight) minus the buoyant forceminus the buoyant force

A. Archimedes’ A. Archimedes’ PrinciplePrinciple

Bouyant ForceBouyant Force upward force exerted by a fluid on upward force exerted by a fluid on

an immersed objectan immersed object bouyant force > weightbouyant force > weight

bouyant force = weightbouyant force = weight

bouyant force < weightbouyant force < weight

balloon rises

balloon sinks

balloon floats

FlotationFlotation

A floating object displaces a A floating object displaces a weight of fluid equal to its own weight of fluid equal to its own weight.weight.

FlotationFlotation

GasesGases

The primary difference between a liquid The primary difference between a liquid and a gas is the distance between the and a gas is the distance between the moleculesmolecules

In a gas, the molecules are so widely In a gas, the molecules are so widely separated, that there is little interaction separated, that there is little interaction between the individual moleculesbetween the individual molecules

IDEAL GASIDEAL GAS Independent of what the molecules areIndependent of what the molecules are

Boyle’s LawBoyle’s Law

Boyle’s LawBoyle’s Law

Pressure depends on density of the Pressure depends on density of the gasgas

Pressure is just the force per unit Pressure is just the force per unit area exerted by the molecules as area exerted by the molecules as they collide with the walls of the they collide with the walls of the containercontainer

Double the density, double the Double the density, double the number of collisions with the wall number of collisions with the wall and this doubles the pressureand this doubles the pressure

Boyle’s LawBoyle’s Law

Density is mass divided by volume.

Halve the volume and you double the density and thus the pressure.

Boyle’s LawBoyle’s Law

At a given temperature for a given At a given temperature for a given quantity of gas, the product of the quantity of gas, the product of the pressure and the volume is a pressure and the volume is a constantconstant

P1V1 P2V2

Atmospheric PressureAtmospheric Pressure

Just the weight of the air above youJust the weight of the air above you Unlike water, the density of the air Unlike water, the density of the air

decreases with altitude since air is decreases with altitude since air is compressible and liquids are only compressible and liquids are only very slightly compressiblevery slightly compressible

Air pressure at sea level is about 10Air pressure at sea level is about 1055 newtons/meternewtons/meter22

Measuring PressureMeasuring Pressure

Barometer

Atm

osph

eric

Pre

ssur

e

Manometer

Con

tain

ed P

ress

ure

Effect on Boiling PointEffect on Boiling Point

When atmospheric pressure When atmospheric pressure increases, the boiling point of a increases, the boiling point of a liquid increases.liquid increases.

When atmospheric pressure When atmospheric pressure decreases, the boiling point of a decreases, the boiling point of a liquid decreases.liquid decreases.

EXEX: high altitude cooking, : high altitude cooking, boiling cold waterboiling cold water

Buoyancy in a GasBuoyancy in a Gas

An object surrounded by air is An object surrounded by air is buoyed up by a force equal to buoyed up by a force equal to the weight of the air displacedthe weight of the air displaced..

Exactly the same concept as buoyancy Exactly the same concept as buoyancy in water. Just substitute air for water in water. Just substitute air for water in the statementin the statement

If the buoyant force is greater than the If the buoyant force is greater than the weight of the object, it will rise in the weight of the object, it will rise in the airair

Buoyancy in a GasBuoyancy in a Gas

Since air gets less dense with altitude, the buoyant force decreases with altitude. So helium balloons don’t rise forever!!!

High Altitude BalloonHigh Altitude Balloon

Bernoulli’s PrincipleBernoulli’s Principle

Bernoulli’s PrincipleBernoulli’s Principle

Flow is faster when the pipe Flow is faster when the pipe is narroweris narrower

Put your thumb over the end Put your thumb over the end of a garden hoseof a garden hose

Energy conservation requires Energy conservation requires that the pressure be lower in that the pressure be lower in a gas that is moving fastera gas that is moving faster

Bernoulli’s PrincipleBernoulli’s Principle

When the speed of a fluid When the speed of a fluid increases, internal pressure in increases, internal pressure in the fluid decreases.the fluid decreases.

Bernoulli’s PrincipleBernoulli’s Principle

Bernoulli’s PrincipleBernoulli’s Principle

Bernoulli’s PrincipleBernoulli’s Principle