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 Units of g/mL or g/cm 3

Pressure A measure of the amount of force exerted on a surface area Units of Pa, atm, mmHg, Torr, bar

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 molecules Independent of what the molecules are

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 10 5 newtons/meter 2 or 100,000 N/m 2

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

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

Bernoulli’s Principle When the speed of a fluid increases, internal pressure in the fluid decreases.

Bernoulli’s Principle

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

Bernoulli’s Principle