Fluids and Pressure

Lecturer: Professor Stephen T. Thornton

Reading Quiz:While snorkeling in the oceanyou exhale air that formsbubbles. As the bubbles rise towards the surface, does the diameter of the bubbles

A) increase?B) decrease?C) stay the same?

Answer: A

As the bubble rises, the pressure in the water decreases, which allows the air to expand and occupy a larger volume. LOOK AT THE PICTURE!

Last Lecture

Elasticity, stress, and strain

Fracture: compression and tension

Trusses and bridges

Arches and domes

Today

Density, fluids

Pressure

Pressure gauges and barometers

Pascal’s Principle

States of Matter

Matter has three states: solid, liquid, and gas.

In a solid, the molecules are very close together, and the form of the solid depends on the details of the forces between them; that form is often a lattice. Solids resist changes in shape.

In a gas, the molecules are far apart and the forces between them are very small.

In a liquid, the molecules are also close together and resist changes in density, but not in shape.

Qualitative behavior of the force between a pair of molecules as a function of their separation, r:

A substance with no resistance to shear is called a fluid (it flows). This includes gases and liquids.

Fluids take the shape of the container they are in. They are liquids and gases.

Density: 3

3 3water

3air

units are kg/m

1.00 g/cm 1000 kg/m

= 1.29 kg/m

M

V

Densities go up to 2,700 kg/m3 for Al, 11,000 -19,000 for heavy metals (iron, gold).

What is pressure?

We all understand what pressure means. Imagine three large defensive lineman piling on top. That is pressure! (Studying for physics exams is a different kind of pressure.) Pressure is related to force. In physics, we have to define it (think of force per unit area):

2 scalar, units N/mF

PA

Atmospheric pressure is the pressure of the air around us. It is due to the weight of the air above us, so it is greater at sea level, less on mountains.

Patm = 1.013 x 105 N/m2

1 Pa 1 N/m2 (pascal) SI unit

Patm = 101.3 kPa (kilopascal)

Patm = 14.7 lb/in2 common unit in U.S.

1 bar = 105 Pa 1 Patm

Gauge pressure is what we use to check the pressure in our tires. It refers to the pressure above atmospheric pressure.

gauge g atm

2

2

So when your tire gauge reads 20 lb/in ,

the actual pressure is 20 + 14.7 = 35 lb/in .

P P P P

Show pressure gauges.

Bed of Nails demo

Do chair demo.

Pressure is the same in every direction in a static fluid at a given depth; if it were not, the fluid would flow.

For a fluid at rest, there is also no component of force parallel to any solid surface—once again, if there were, the fluid would flow.

Pressure as a function of depth in liquid

top atm

bottom top atm

bottom atmbottom

atm

atm

At the bottom we add the weight of the fluid.

( )

at any depth

F P A

W Mg Vg hA g

F F W P A hAg

F P A hAgP

A AP hg

P P gy y

y

Pressure in FluidsIf there is external pressure in addition to the weight of the fluid itself, or if the density of the fluid is not constant, we calculate the pressure at a height y in the fluid; the negative sign indicates that the pressure decreases with height (increases with depth):

( up)dP g ydy

atm ( down)P P gy y

We then integrate to find the pressure:

2

1

2

1

2 1 2 1

1 2 2 1

0

P

P

y

ydP g dy

P P g y y

P P g y y

P P gh

Easy to integrate for contant density ρ.

Pressure Variation with Depth

y

Do some demos

Crush soda can - start early, do later

Hydrostatic pressureMagdeburg hemispheresAir has weight

A Simple Barometer

atmP gh

Many barometers we use today in meteorology contain mercury, because of its high density.Calculate the height h of a mercury column of the simple barometer we just saw.

atm

5atm

4 3 2

atm

1.013 10 Pa760 mm

g 1.3595 10 kg/m 9.81 m/s

1 atmosphere = 760 mm (of mercury) =29.92 in =

P gh

Ph

P

Hurricane Wilma set record: 26.4 in

Height of water towerWe just showed that a mercury barometer can at most be 760 mm tall due to atmospheric pressure.

How high can a water barometer be? We still use

atm

5atm

3 3 2

atm

1.013 10 Pa10.3 m

g 1.00 10 kg/m 9.81 m/s

1 atmosphere = 10.3 m (of water) =

P gh

Ph

P

Vacuum

Vacuum is the absence of matter. There will be no pressure when there is a vacuum. P = 0.

What happens when we have atmospheric pressure and a vacuum across an interface?

Do soda can demo.

Lots of demos to do here

Tanker car collapse

Workers steam cleaned tanker car, then closed all the valves and left for the night.

When we have unequal water levels, the pressure is different at the bottom. Fluid will flow (due to the force) to make the levels equal.

Oil and water have different densities. Oil will float on the water. The pressure at the bottom is equal on both sides.

You are walking out on a frozen lake and you begin to hear the ice cracking beneath you. What is your best strategy for getting off the ice safely?

A) stand absolutely still and don’t move a muscle

B) jump up and down to lessen your contact time with the ice

C) try to leap in one bound to the bank of the lake

D) shuffle your feet (without lifting them) to move towards shore

E) lie down flat on the ice and crawl toward shore

Conceptual QuizConceptual Quiz

You are walking out on a frozen lake and you begin to hear the ice cracking beneath you. What is your best strategy for getting off the ice safely?

A) stand absolutely still and don’t move a muscle

B) jump up and down to lessen your contact time with the ice

C) try to leap in one bound to the bank of the lake

D) shuffle your feet (without lifting them) to move towards shore

E) lie down flat on the ice and crawl toward shore

As long as you are on the ice, your weight is pushing down. What is important is not the net force on the ice, but the force exerted on a given small area of ice (i.e., the pressure!). By lying down flat, you distribute your weight over the widest possible area, thus reducing the force per unit area.

Conceptual QuizConceptual Quiz

Consider what happens when you push both a pin and the blunt end of a pen against your skin with the same force. What will determine whether your skin will be punctured?

A) the pressure on your skin

B) the net applied force on your skin

C) both pressure and net applied force are equivalent

D) neither pressure nor net applied force are relevant here

Conceptual QuizConceptual Quiz

Consider what happens when you push both a pin and the blunt end of a pen against your skin with the same force. What will determine whether your skin will be punctured?

A) the pressure on your skin

B) the net applied force on your skin

C) both pressure and net applied force are equivalent

D) neither pressure nor net applied force are relevant here

The net force is the same in both cases. However, in the case of the pin, that force is concentrated over a much smaller area of contact with the skin, such that the pressure is much greater. Because the force per unit area (i.e., pressure) is greater, the pin is more likely to puncture the skin for that reason.

Conceptual QuizConceptual Quiz