Goal: To understand liquids and gasses

Objectives:

1) To understand Pressure

2) To understand Buoyancy

3) To understand Archimedes Principal

4) To learn about Hydraulics

5) To learn about Surface Tension

6) To learn about how pressure is affected when a fluid moves

Pressure

• When understanding fluids one of the keys is Pressure.

• Pressure is a measure of the force a fluid exerts per area.

• Pressure = Force / Area

• Or, Force = Pressure * Area

Earth example

• On the surface of the earth the atmosphere exerts a pressure of 14 pounds per square inch.

• Why aren’t we crushed by this pressure?

What causes pressure?

• Atmospheric Pressure in reality is the weight of the stuff above you pressing down on you.

• So, if you weighed a segment of air 1 inch by 1 inch which went to the top of the atmosphere that air would weigh 14 pounds.

Summer door

• In the summer the outside pressure on a door with an area of 2 square meters is 1.01 * 105 Pascals

• On the inside of the air conditioned house the force is 1.00 * 105 Pascals

• A) What is the air pressure force pushing out?• B) What is the air pressure force pushing in?• C) What is the net force on the door and would

you be able to open this door?

Off the Deep End

• You dive into the bottom of the deep end of a swimming pool.

• What happens and why?

Pressure underwater

• Liquid Pressure = the pressure on the surface of the liquid + weight density * depth

• What about for water?

• The surface has about 1 bar of pressure (the air pressure at sea level).

• Every 10 meters is about 1 more bar of pressure.

• So, Pressure = 1.0 * 105 Pascal + Density * Depth * g

Deep sea dive

• You dive to a depth of 240 m.

• A) What is the pressure at this depth?

• B) If a mini submarine with a surface area of 0.4 square meters were at this depth then what would be the inwards crushing force on the sub due to the water pressure?

Buoyancy

• Each side of the object will have a force on it.

• However, the pressure on the bottom of an object will be higher than the pressure on the top.

• This means more force pushing up than down.

• This creates a net pressure force.• This force is called Buoyancy.

Depends on

• Volume of object• Density of medium you are in

• F = density * Volume * g (i.e. the weight that is displaced)

• NOTICE: the mass of the object is NOT a dependency.

• So, a cubic meter of ice and rock have the same Buoyancy force!

• What is the buoyancy force on an object with a volume of 1 cubic meter in water with a density of 1000 kg/cubic meter?

Um, wait a minute

• hold the phones – stop the presses!• How can a rock and ice for the same volume have the

same buoyancy force?• Clearly they have different masses and therefore

different weights.• How can this be?

• Well, look at the net force of everything (add the gravity force and the buoyancy force).

• The mass of a cubic meter of ice is about 700 kg. • For rock it is about 3000 kg.

• What direction will this net force be for ice vs. rock?

Sink like a rock?

• If the force of buoyancy is less than the gravitational force, the object will sink.

• However, it won’t fall as fast as if you dropped it. Its acceleration will be slowed.

• If the force of buoyancy is exactly the SAME, you will just float where you are at.

• At what density do you think this will be the case?

Floatation Device

• If buoyancy exceeds gravity you go UP!

• However, what happens when part of the crate exits the water.

• That is, how does the upwards and downwards pressure forces change (if at all) as the crate pushes up?

Some change ends change

• The force on the top stays the same – pretty much.

• It is moving into air, which is far less dense than water, so the pressure barely changes.

• The bottom pressure decreases, so that force decreases.

• So, your buoyancy decreases.

• When will the buoyancy stop decreasing – and when does that occur?

Archimedes’ Principle

• The buoyancy stabilizes once the buoyancy force equals the weight of the object.

• At this point, it is good to note that the buoyancy force is the weight of the liquid you are displacing (i.e. the weight of the water for the volume that the object takes up of the water).

• So, the amount of water displaced is equal to the weight of the crate.

Float vs sink

• If you float, you move water equal to your weight.

• If the object sinks, it moves water equal to its volume.

Your ship is in a lock.

• Your ship has an iron anchor.

• You toss the anchor into the water.

• Will the level of water in the lock rise or fall?

Iceberg

• An iceberg with a mass of 7200 kg floats in the water. Assume the ice berg is a cube which is 2 meters to a side. Assume the water has a density of 1000 kg/m3.

• A) Find the buoyancy force on the iceberg• B) What is the volume of water displaced

by the iceberg?• C) How far below the water does the

bottom of the iceberg reach?

Hydraulics

• Image from wikipedia• The pressures for each

side are the same.• F1 / A1 = F2 / A2• So, a force over a big

area can be held up by a small force over a small area.

• Note though that the works are the same.

Surface tension

• In an infinite liquid at every point you have liquid pushing against you from every direction.

• However, when you have a surface, you press the liquid against that surface, but nothing pushes back, or liquid doesn’t.

• This causes the surface to become more adhesive or film like.

Atmosphere

• Air is like a fluid – but one that is not very dense.

• As you get higher, the air gets thinner (less dense).

• For every 5.6 km you go up, the atmospheric pressure decreases by half (meaning that half of the air is below you).

Buoyancy

• Works the same way, but now it is based off of the density of local air instead of water.

• If you are less dense than air, your buoyancy is greater than weight, so you fly!

• This is how hot air balloons work.

Tire pressure

• If you have a closed surface, you can add a lot more of a gas.

• This makes it have a higher pressure (pressure is stuff running into you, so if you have more of it, then you have more pressure).

Boyle’s Law

• P1V1 = P2V2

• Meaning that if you have air inside a closed object and you make it bigger, the pressure inside that object decreases.

• If you shrink it, the pressure increases.

Pressure of moving fluids

• This applies to either air or water.

• If it moves, the pressure decreases.

• So, the pressure of the water in a moving river is less than the pressure of water that is not moving.

• Note this leads to a problem for swimmers…

Bernoulli’s Equation

• Pmoving = Prest – ½ density * v2

• Also, if the area of a tube or pipe changes:

• A1V1 = A2V2

• So, smaller area means faster moving fluid.

Don’t swim in moving water…• Imagine the typical river.

• Lets say the water is flowing at 5 m/s in the center. What is the velocity of water at the edge?

• Because of this, imagine you were trying to swim to shore from the center of the river. Since things get pulled to the region of lowest pressure, how will this affect you getting to shore?

Airplanes!

• Airplanes are set up such that the air velocity on the top of the wing is much higher than the bottom.

• How do the pressures of air on the top wing and bottom wing compare?

Tale of two pipes

Conclusion

• Today we have seem how fluids (liquids and gasses) affect the world around us.

• We have examined Buoyancy and pressure.