Lecture_6_1-29-2004 ـــــ

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Fluid Mechanics

Liquids and gases have the ability to flow

They are called fluids

There are a variety of LAWS that fluids

obey

Need some definitions


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Density

Regardless of form (solid, liquid, gas) we

can define how much mass is squeezed into

a particular space


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Pressure

A measure of the amount of force exerted

on a surface area


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Pressure in a Fluid

The pressure is just the weight of all the fluid

above you

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

In a swimming pool the pressure on your body

surface is just the weight of the water above you

(plus the air pressure above the water)


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Pressure in a Fluid

So, the only thing that counts in fluid

pressure is the gravitational force acting on

the mass ABOVE you

The deeper you go, the more weight above

you and the more pressure

Go to a mountaintop and the air pressure is

lower


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Pressure in a Fluid

Pressure acts

perpendicular

to the surfaceand increases

at greater

depth.


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Pressure in a Fluid


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BuoyancyNet upward

force is

called the

buoyantforce!!!

Easier to

lift a rock

in water!!


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Displacement of Water

The amount of

water displaced is

equal to thevolume of the

rock.


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Archimedes Principle

An immersed body is buoyed up by a force

equal to the weight of the fluid it displaces.

If the buoyant force on an object is greater

than the force of gravity acting on the object,

the object will float

The apparent weight of an object in a liquidis gravitational force (weight) minus the

buoyant force


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Flotation

A floating object displaces a weight of fluid

equal to its own weight.


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Flotation


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Gases

The primary difference between a liquid and a

gas is the distance between the molecules

In a gas, the molecules are so widelyseparated, that there is little interaction

between the individual moledules

IDEAL GAS Independent of what the molecules are


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Boyles Law


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Boyles Law

Pressure depends on density of the gas

Pressure is just the force per unit area

exerted by the molecules as they collide

with the walls of the container

Double the density, double the number of

collisions with the wall and this doubles thepressure


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Boyles Law

Density is mass

divided by

volume.

Halve the

volume and you

double thedensity and thus

the pressure.


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Boyles Law

At a given temperature for a given quantity

of gas, the product of the pressure and the

volume is a constant


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Atmospheric Pressure

Just the weight of the air above you

Unlike water, the density of the air

decreases with altitude since air is

compressible and liquids are only very

slightly compressible

Air pressure at sea level is about 105newtons/meter2


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Barometers


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Buoyancy in a Gas

An object surrounded by air is buoyed up by

a force equal to the weight of the air

displace. Exactly the same concept as buoyancy in

water. Just substitute air for water in the

statement If the buoyant force is greater than the

weight of the object, it will rise in the air


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Buoyancy in a Gas

Since air gets less

dense with altitude,the buoyant force

decreases with

altitude. So heliumballoons dont rise

forever!!!


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Bernoullis Principle


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Flow is faster when the pipe is narrower

Put your thumb over the end of a garden hose

Energy conservation requires that the pressure

be lower in a gas that is moving faster

Has to do with the work necessary to compress

a gas (PV is energy, more later)


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When the speed of a fluid increases,

internal pressure in the fluid decreases.


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Why the streamlines are compressed isquite complicated and relates to the air

boundary layer, friction and turbulence.


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