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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

Density

- Regardless of form (solid, liquid, gas) we can

define how much mass is squeezed into a

particular space

Pressure

- A measure of the amount of force exerted on a

surface area

Pressure in a Fluid

- The pressure is just the weight of all the fluid

above you - Atmospheric pressure is just the weight of all

the air 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)

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

Pressure in a Fluid

Pressure acts perpendicular to the surface and

increases at greater depth.

Pressure in a Fluid

Buoyancy

Net upward force is called the buoyant

force!!! Easier to lift a rock in water!!

Displacement of Water

The amount of water displaced is equal to the

volume of the rock.

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 liquid is

gravitational force (weight) minus the buoyant

force

Flotation

- A floating object displaces a weight of fluid

equal to its own weight.

Flotation

Gases

- The primary difference between a liquid and a gas

is the distance between the molecules - In a gas, the molecules are so widely separated,

that there is little interaction between the

individual moledules - IDEAL GAS
- Independent of what the molecules are

Boyles Law

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 the

pressure

Boyles Law

Density is mass divided by volume. Halve the

volume and you double the density and thus the

pressure.

Boyles Law

- At a given temperature for a given quantity of

gas, the product of the pressure and the volume

is a constant

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 105

newtons/meter2

Barometers

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

Buoyancy in a Gas

Since air gets less dense with altitude, the

buoyant force decreases with altitude. So helium

balloons dont rise forever!!!

Bernoullis Principle

Bernoullis Principle

- 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)

Bernoullis Principle

- When the speed of a fluid increases, internal

pressure in the fluid decreases.

Bernoullis Principle

Bernoullis Principle

Why the streamlines are compressed is quite

complicated and relates to the air boundary

layer, friction and turbulence.

Bernoullis Principle