Fluids include both Liquids & Gases

What you absolutely have to know aboutFluids to pass the AP Physics B test!

Gases and Liquids dont seem very much alikeGasesLiquids

Molecular behaviorThe molecules are not connected to each other and are far apart compared to their size. Each molecule flies around free. The molecules only interact with each other when they collide. The molecules are very close together and exert weak bonding on each other. The bonding is strong enough to hold the fluid together but is not strong enough to hold a definite shape.

Volume & ShapeGases expand to fill the volume of their container. They do not have a defined surface.Liquids have a definite volume and a defined surface

CompressibilityDue to the empty space between the molecules, the volume of a gas can easily be changed. (Gases are said to be compressible) Since the molecules are close together, a liquid can not really be compressed. Due to the bonding between the molecules, liquids cant be expanded. (Liquids are incompressible.)

For all their differences, gases and liquids actually have a great deal in common.

1) Both gases and liquids flow.

2) Since they flow, neither gases nor liquids have a definite shape.

3) Both gases and liquids exert pressure on the containers that confine them.

Due to their similarities, gases and liquids have common properties and are lumped into a group called Fluids. A Fluid is any material or substance that flows. Thus both gases and liquids are fluids.Everything that is discussed in the study of fluids applies to both liquids & gases. The study of fluids is broken down into two sections:

1. Fluid Statics(Stationary Fluids)

2. Fluid Dynamics (Moving Fluids)

(Note: Since gases have the ability to expand and contract, they have some unique properties that liquids do not have. These unique properties of gases will be discussed in a separate study dedicated just to gases.)

Before we start into Fluids we need to know three things:

Volume:

Volume is the amount of space a fluid takes up. In physics we measure volume in m3.

Not liters.

Not cm3.

It has to be m3.

Caution: While 1 m = 100 cm.

1 m3 100 cm3.

Remember:Mass Density:

Mass to volume ratio is called mass density or just density for short: ( = m/V. Units are kg/ m3.

Density is designated by the Greek letter rho: (. Below is a table of densities for common fluids.LiquidsDensity (kg/ m)Gases Density (kg/ m3)

Gasoline680Helium 0.179

Ethyl Alcohol790Steam (Water 100 C)0.598

Oil (Average)900Air 1.29

Water (at 4 C)1000Carbon Dioxide1.98

Sea Water1025

Blood1050Unless otherwise noted all gas densities are listed for standard temperature and pressure of 0 C and 1 atm.

Glycerin1260

Mercury13600

Note: The density of a substance is the same no mater how much of the material you have. A small glass of water and a swimming pool of water both have the same density.

Pressure:

First of all Pressure is not a force! We like to say things like: When I dove to the bottom of the pool the pressure hurt my ears. or The air pressure blows up a balloon. Technically it is the water that exerts a force on your ear drums that hurts your ear. And, it is the force from the air that inflates a balloon.

So, what exactly is pressure? Pressure is a ratio of the force to area: p = F/A The units are newton/meter2 which we call a pascal or Pa for short. 1 pascal = 1 Pa = 1N / 1m2. Pressure is a scalar. Pressure is everywhere in a fluid. At any one point in a fluid the pressure is the same in all directions! If you take a pressure gauge (a device that measures pressure) and submerge it in a fluid, the gauge will measure the exact same pressure no matter which direction you point the device.Question 1: Is it possible to produce a large force from a small pressure?

Answer 1: Look at the end of this study guide for the answer

So what causes pressure in a fluid? There are two major causes of pressure:1. Pressure due to the thermal motion of the molecules. Remember that fluids are made up of lots and lots and lots of molecules. Each of these molecules is vibrating around in a random fashion due to the fluids thermal energy. The hotter the fluid, the faster the vibrations of the molecules will be. These vibrating molecules collide with anything the fluid comes in contact with. The diagram shows the molecules colliding with the wall of a container. Each collision imparts a small force on the wall. Because of the large number of random collisions that occur in every direction, any sideward forces exerted by the collisions on the walls will cancel out! However, the perpendicular component of the collision forces will not cancel out. This means that the forces caused by fluid pressure will always be perpendicular to the surface the fluid is in contact with. 2. Pressure due to gravity. The diagram shows a stationary liquid in a glass. Since the liquid is stationary, it must be in equilibrium which means that F = 0. Now consider points A and B in the liquid. At each point the forces must cancel out so that they can remain stationary. Each point must support the weight of all the fluid above itself with a counteracting force upward in order to maintain equilibrium. Otherwise the liquid above would accelerate downward due to its weight. Point B is deeper in the liquid then point A. Therefore, at point B the counteracting force must be greater then point A. This implies that the pressure at point B must be greater then at point A simply because it has to support more fluid above itself in a gravitational field.The Thermal Effect and the Gravitational Effect combine to cause the overall pressure in a fluid.Gases: The thermal effect causes most of the pressure in a gas. Gases have a very small density thus the gravitational effect on a gas are very small. In fact you would have to go to the top of a 30 story building just to decrease the air pressure just 1%. This means that if you climb a flight of steps there really isnt any change in the air pressure. However, if you go the top of the Empire State Building, you might notice your ears popping. If you have ever flown in a plane, you certainly notice the change in pressure on your ears as you takeoff or land. The general rule of thumb is that we assume air pressure to be constant unless there is a change in vertical height of 100m or more.Liquids: Liquids have a much larger density then gases. Thus the gravitational effect causes most of the pressure in a liquid. Swim just 10ft to the bottom of a pool and the water pressure goes up a whopping 33%!

Static Fluids:

Now that we have talked about Volume, Density, and Pressure, lets talk about what goes on in stationary fluids.

The Gravitational Effect on Pressure in more detail:

In a gas: Normally this effect is very small in a gas. One place it does show up is in the atmosphere. Due to gravity, the pressure in the atmosphere is greatest at the surface of the planet at sea level. Atmospheric pressure is greater in Houston then in Katmandu. On average sea level pressure is: patm = 101,325 Pa. For simplicity we call 101,352 Pa = 1 atmosphere = 1 atm

Note: On the AP Exam they use 1 atm= 100,000 Pa to make the math simpler.

In a liquid: The diagram shows a glass filled with a liquid. The atmosphere pushes down on the liquid from above. A dashed line is drawn horizontally through the liquid. To maintain equilibrium, the liquid below the line must push upward with a force to counteract both the weight of the fluid above and the additional downward force due to the atmospheric pressure on top of the liquid.

Using our physics and math skills we can derive an expression for the pressure at any point in a static liquid: p = p0 + ghThere are several things to note about this equation:

1. The pressure in a fluid depends on p0, how much pressure is being exerted on top of the liquid itself. (This is usually caused by the atmosphere on top of the liquid but could be caused by a piston or even another liquid floating above.)

2. The surface area canceled out of the equation! Only the depth of the fluid contributes to the gravitational effect on the pressure.

3. We have assumed that the liquid is incompressible. That means that we assume the liquid to stay the same density no matter how deep we are in the liquid.

Question 2: Which water tower will produce the most pressure at the bottom?

Question 3: Why dont we see water towers built like C?

This diagram shows a bent tube with liquid inside. The level of the liquid is higher on the left side then the right side. Question 4: Is it possible for this to happen in a static fluid? Liquids that are connected will flow until the level of the fluid is the same everywhere.

This diagram shows a large reservoir of water on the left connected to a smaller reservoir of water on the right.

Question 5: Which location has greater pressure p1 or p2?

The pressure is the same along any horizontal line drawn through in a stationary connected fluid. Horizontal lines higher in the fluid represent lower pressure.

Horizontal lines deeper in the fluid represent higher pressure.

Problem: Water fills a tube as shown. What is the pressure at the top of the closed end at the right of the tube? Assume 1 atm at the top of the open left end of the tube.

Since the pressure is the same along a horizontal line, the pressure 0.9 m deep in the left side of the tube will be equal to the pressure at the top of the closed end on the right. Absolute Pressure -vs- Gauge Pressure:

In the problem above we got an answer of 108,820 Pa. That is the absolute pressure. Absolute pressure is the real pressure. There is another way to report pressure: gauge pressure. Gauge pressure is the pressure in excess of 1 atm. It is the delta pressure above 1 atm. When you measure the air pressure in your tires you are measuring gauge pressure. A tire gauge measures zero when held out in the atmosphere. It only measures pressures greater the 1 atm. In the problem above the gauge pressure would be 8,820 Pa. (The gh part only.)

Bottom line: absolute pressure = gauge pressure + 1atm

When you are asked to find pressure, calculate absolute pressure because that is the real pressure.

Only calculate gauge pressure if you want to know the delta pressure above atmospheric or, are asked to find gauge pressure.Alternative Units for Pressure:In the Physics World physicists love to have one standard unit for things.

V - Volume (m3)

- Density (kg/m3)

p - Pressure (Pa - which is actually N/m2)

m - Mass (kg)

h - Height (m)

g - Acceleration due to Gravity (m/s2)

All the Physics equations are set up for these standard units. This means that if you use different units in an equation you wont get the answer you expect.

Many times in the real world the physics units are not very convenient. This is the case for pressure. As you have already seen above, it is a lot easier to say 1 atm then 101,325 Pa. Here are some of the most common ways to measure pressure and their conversion factors to Pascal.

UnitAbbreviationApproximate conversion to Pascals

atmosphereAtm1atm = 101,325 Pa (about 100,000 Pa)

millimeters of mercurymm of Hg1 mm of Hg = 130 Pa

inches of mercuryin of Hg1 in of Hg = 3390 Pa

pounds per square inchpsi1 psi = 6890 Pa

Remember: You always have to use Pascals in the physics equations!

Applications of the hydrostatic pressure equation: p = p0 + gh:

Scuba Diver:A scuba diver floats 20 m below the surface of a lake as shown. What are the absolute pressure and the gauge pressure on the diver?

The Barometer:Weather reports frequently give the barometric pressure. This is the pressure in the atmosphere, which varies a bit from day to day. It is measured in units of inches of mercury. So what is a barometer and what are inches of mercury? The original barometer was a long test tube filled with mercury that was inverted into an open container also filled with mercury. See diagram. Some, but not all, of the mercury will flow out. This leaves a vacuum gap at the top of the test tube!

Question: Why doesnt all the mercury flow out?

Answer: The pressure at point A = 1 atm.

The pressure at point B must equal the pressure at point A.

The pressure at point B = p0 + gh. But, p0 = 0 because it is a vacuum!

Therefore: pB = gh and h = 0.75 m.

Thus, 1 atm is approximately 750 mm of Hg = 29.5 in of Hg.

So, inches of Hg is a way to measure pressure.

All of the mercury cant flow out of the tube because there isnt any pressure in the vacuum at the top of the tube. Or, put another way, the mercury stays in the tube because the atmospheric pressure at point A pushes, or holds, the mercury up in the tube.

The Monometer: Gas pressure can be measured with a U shaped tube filled with liquid, a monometer. One side of the liquid filled tube is attached to a chamber of gas. If the gas has a pressure greater then atmospheric it will push the liquid up the opposite side of the tube as shown in the diagram. (The atmospheric pressure will push the liquid toward the gas chamber is the gas pressure in the chamber is less than 1 atm.) Blood Pressure and IVs:A reasonably good blood pressure to have is 120 over 80. (Actually it is: 120 mm of Hg over 80 mm of Hg) Ok What does that mean?? When you heart beats and pumps blood through your circulatory system, the pressure in your blood reaches a maximum of 120 mm of Hg. When your heart is at rest, your blood pressure drops to a low of 80 mm of Hg. Note: these are gauge pressure readings. Question 5: When you are standing up, where is your blood pressure greatest?

Lets say you get sick and are in the hospital. The doctor prescribes an IV. An IV is a bag of fluid that contains medicine or blood that the doctor wants to get into your body. To do this the doctor or nurse inserts a tube that is attached to the IV bag into one of your veins. Then they hang the IV bag from a tall stand. Why? Once the tube is inserted into your vein, the bag and your circulatory system become one connected fluid system. The fluid in the IV bag pushes its way into your body because it is elevated.

Question 6: An accident victim needs blood. How high must the IV bag of blood be elevated for the fluid to enter the persons body? Assume blood pressure = 120 over 80.

Creating Pressure in a Piston Full of Gas:

A cylinder of gas is shown in the diagram at the right. The cylinder has a movable piston fitted to its top. Initially the piston is at the top of the cylinder and the pressure of the gas inside is 1 atm. Then a 0.4 kg mass is placed on top of the piston and the gas is compressed to a smaller volume.

Question 7: What is the new pressure in the gas?

Pascals Principle:

Speaking of pistons there is another great property of fluids. An external pressure applied to any point of a confined fluid increases the pressure everywhere in the fluid. When the mass is added to the piston in the figure above, the extra pressure it applies to the gas is added to all parts of the gas. The pressure goes up everywhere in the gas by the same amount! This is called Pascals Principle.

We can put this property to good use in devices called hydraulics (liquid devices) and pneumatics (gaseous devices). In the figure to the right you see two different sized cylinders of fluid attached by a connecting tube. When force F1 pushes down on the left cylinders piston fluid flows into the right cylinder moving the piston up. The extra pressure applied to the left cylinder is transmitted to the right cylinder. This creates a force F2 that pushes upward.Now look closer Since the area A2 is larger then area A1, the only way for the ratios F/A to remain equal is for the force F2 to be larger then F1! Thus, this device multiplies our force output by a ratio = A2/A1.

Question 8: This device seems to magically increase our force and thus violate conservation of energy. Explain why this device really does not break any physics rules. (Hint: What do we give up to increase our force?)Answer 1: Sure as long as the area is big enough! F = pAAnswer 2: The pressure will be the same at the bottom of each water tower because the height of the fluid is the same!

Answer 3: All three of the water towers will produce the same pressure at the bottom. However, the water tower on the right has a very small reservoir of water inside. When someone flushes the toilet it will begin to empty and its water level will fall quickly. This decrease in water height will quickly decrease the pressure at the bottom. The two towers on the left are better designs because flushing the toilet will not lower the level of the water very quickly.Answer 5: Remember that the area of the fluid does not matter. Only the depth matters Answer 4: Since the fluid is deeper on the left there will be a greater pressure at the bottom of the fluid on the left then at the bottom of the fluid on the right. Thus the pressures will not cancel out. The fluid is not in equilibrium and cant stay static! The fluid will flow from left to right until equilibrium is reached when the fluid level is the same on both sides.

Answer 5: At your feet because there is greater height of blood (gh) above your feet then anywhere else in your body. Try reversing the situation. Sit on a couch upside down with your feet up high and your head hanging down low. Wait for a minute or two You will feel the extra pressure in your ears and your head will start to hurt!

Answer 8: While hydraulics and pneumatics are great devices to increase force output the work output of the device is no greater then the work input. When the smaller left cylinder gets pushed downward only a small amount of fluid moves into the larger right cylinder. Therefore the right cylinder moves upward a less then the left cylinder is pushed downward. The work input (Work = Force x Distance) for the left cylinder is at least as big as the work output of the right cylinder.Answer 9: Fluids are made up of atoms & molecules that do not have a definite structure.

These atoms & molecules randomly move around and run into each other and the container that holds the fluid.

Each of these atomic collisions exerts a force.

The sum total of all these collisions causes Pressure on whatever the fluid is in contact with.

Pressure is always perpendicular to the surface!

Fluid Statics:

Static Pressure:

If you have ever swam to the bottom of a pool you know that as you descend into the water the pressure on you increases. This pressure is due to the weight of water (fluid) above you. This is called static pressure.

Note: that only the density of the fluid and height (depth) of the fluid matter! This means:

The pressure is the same at every point in the fluid that has the same height!

The volume of the fluid does not matter. The pressure is the same 1 foot below the surface of the water in a pool, ocean, or bathtub!

Question: Where is your blood pressure the greatest?

Air Pressure and the Barometer:

The atmosphere is stacked up on top of you and therefore you experience pressure from the air.

On average this pressure is 101,325 Pa or about 100,000 Pa

This is referred to as 1 atmosphere of pressure or 1 atm for short.

(Remember to convert you unit from atm to Pa before you do any calculations!)

If you listen to the weather report you will here them talk about this pressure.

High pressure usually means nice weather and low pressure usually means bad weather.

We routinely measure atmospheric pressure with a barometer.

A picture of a barometer is shown at the right

Absolute Pressure:

If you are at the bottom of a pool you have 2 fluids above you: water and air. The absolute pressure you experience is the addition of both.

Pascals Principle:

If you confine a fluid completely inside a closed container, an external pressure will be transmitted equally throughout the fluid. This means that P1 = P2 This is used is Hydraulic Machines:

Buoyancy Force:

Question: In the picture at the right, is the static pressure the same on all parts of the object? If not where is it the greatest?

Note that the pressure is greatest on the bottom of the object and less on the top. The pressure is the same on both sides but in opposite directions so it cancels out. This means that the bottom of the object receives more force up than the top receives in the downward direction. The object wants to float!

This is called Buoyancy Force:

Interesting facts about Buoyancy Force

Specific Gravity:Fluid Dynamics

Continuity Equation:

Bernoullis Equation:

Examples:Answer 6:

Work Space:

Answer 6: Look at the end of this study guide for the answer

0.4 kg mass

Initial State:

Final State

Movable piston

Gas molecules trapped in the cylinder

Area = 200cm3

Work Space:

Answer 7: Look at the end of this study guide for the answer

Answer 7:

Chris BruhnPage 49/12/2008cbruhn@dallasisd.org214) 932-5102