Fluid mechanics

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

density mass

volume

Pressure

• A measure of the amount of force exerted on a surface area

pressure forcearea

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

BuoyancyNet 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

Boyle’s Law

Boyle’s 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

Boyle’s Law

Density is mass divided by volume.

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

Boyle’s Law

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

P1V1 P2V2

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 don’t rise forever!!!

Bernoulli’s Principle

Bernoulli’s 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)

Bernoulli’s Principle

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

Bernoulli’s Principle

Bernoulli’s Principle

Why the streamlines are compressed is quite complicated and relates to the air boundary layer, friction and turbulence.

Bernoulli’s Principle