Casehardening The chemical activity of titanium and its rapid Pressure gage absorption of oxygen, nitrogen, and carbon at relatively low temperatures make casehardening Hydraulic advantageous for special applications. Nitriding, actuating carburizing, or carbonitriding can be used to unit produce a wear-resistant case of 0.0001 to 0.0002 inch in depth.
HARDNESS TESTING Hardness testing is a method of determining the results of heat treatment as well as the state of a Hand metal prior to heat treatment. Since hardness pump values can be tied in with tensile strength values and, in part, with wear resistance, hardness tests are a valuable check of heat-treat control and of material properties.
Practically all hardness-testing equipment now -Penetrator uses the resistance to penetration as a measure of hardness. Included among the better known hardness testers are the Brinell and Rockwell, both - Elevating screw of which are described and illustrated in this section. Also included is a popular portable-type hardness tester currently being used. Microscope Brinell Tester The Brinell tester (figure 6-68) uses a hardened spherical ball, which is forced into the surface of the metal. This ball is 10 millimeters (0.3937 inch) in diameter. A pressure of 3,000 kilograms is used for ferrous metals and 500 kilograms for nonferrous metals. The pressure must be maintained at least 10 seconds for ferrous metals and at least 30 seconds for nonferrous metals. The load is applied by hydraulic pressure. The hydraulic pressure is built up by a hand pump or an electric motor, depending on the model of tester. A pressure gage indicates the amount of pressure. There is a release mechanism for relieving the pressure after the test has been made, and a calibrated microscope is provided for measuring the diameter of the impression in millimeters. The machine has various shaped anvils for supporting the specimen and an elevating screw for bringing the specimen in contact with the ball penetrator. These are attachments for special tests.
In order to determine the Brinell hardness number for a metal, the diameter of the impression is first measured, using the calibrated microscope furnished with the tester. After measuring the diameter of the impression, the measurement is FIGURE 6-68. Brinell hardness tester.
converted into the Brinell hardness number on the conversion table furnished with the tester.
Rockwell Tester The Rockwell hardness tester (figure 6-69) measures the resistance to penetration, as does the Brinell tester. Instead of measuring the diameter of the impression, the Rockwell tester measures the depth, and the hardness is indicated directly on a dial attached to the machine. The dial numbers in the outer circle are black, and the inner numbers are red. Rockwell hardness numbers are based on the difference between the depth of penetration at major and minor loads. The greater 218
Weight pan Scale Penetrator Major load Dial symbol (kg.) number Weights Diamond 60 Black B 16-inch ball 100 Red Diamond 150 Black Penetrator D Diamond 100 Black Specimen E ⅛-inch ball 100 Red Anvil F 16-inch ball 60 Red G 6-inch ball 150 Red Elevating screw- H ⅛-inch ball 60 Red K g-inch ball 150 Red Hand wheel FIGURE 6-70. Standard Rockwell hardness scales.
Zero adjuster Trip lever FICURE 6-69. Rockwell hardness tester.
this difference, the less the hardness number and the softer the material.
Two types of penetrators are used with the Rockwell tester, a diamond cone and a hardened steel ball. The load which forces the penetrator into the metal is called the major load and is measured in kilograms. The results of each penetrator and load combination are reported on separate scales, designated by letters. The penetrator, the major load, and the scale vary with the kind of metal being tested For hardened steels, the diamond penetrator is used; the major load is 150 kilograms; and the hardness is read on the "C" scale. When this reading is recorded, the letter "C" must precede the number indicated by the pointer. The C-scale setup is used for testing metals ranging in hardness from C-20 to the hardest steel (usually about C-70). If the metal is softer than C-20, the B-scale setup is used. With this setup, the 6-inch ball is used as a penetrator; the major load is 100 kilograms; and the hardness is read on the B-scale.
In addition to the "C" and "B" scales, there are other setups for special testing. The scales, penetrators, major loads, and dial numbers to be read are listed in figure 6-70.
The Rockwell tester is equipped with a weight pan, and two weights are supplied with the machine. One weight is marked in red. The other weight is marked in black. With no weight in the weight pan, the machine applies a major load of 60 kilograms. If the scale setup calls for a 100- kilogram load, the red weight is placed in the pan.
For a 150-kilogram load, the black weight is added to the red weight. The black weight is always used with the red weight; it is never used alone.
Practically all testing is done with either the B-scale setup or the C-scale setup. For these scales, the colors may be used as a guide in selecting the weight (or weights) and in reading the dial. For the B-scale test, use the red weight and read the red numbers. For a C-scale test, add the black weight to the red weight and read the black numbers.
In setting up the Rockwell machine, use the diamond penetrator for testing materials known to be hard. If the hardness is unknown, try the diamond, since the steel ball may be deformed if used for testing hard materials. If the metal tests below C-22, then change to the steel ball.
Use the steel ball for all soft materials, those testing less than B-100. Should an overlap occur at the top of the B-scale and the bottom of the C-scale, use the G-scale setup.
Before the major load is applied, the test specimen must be securely locked in place to prevent slipping and to seat the anvil and penetrator properly. To do this, a load of 10 kilograms is applied before the lever is tripped. This preliminary load is called the minor load. The minor load is 10 kilograms regardless of the scale setup.
The metal to be tested in the Rockwell tester must be ground smooth on two opposite sides and be free of scratches and foreign matter. The surface should be perpendicular to the axis of penetration, and the two opposite ground surfaces should be parallel. If the specimen is tapered, the amount of error will depend on the taper. A curved surface will also cause a slight error in the hardness test.
The amount of error depends on the curvature;
i.e., the smaller the radius of curvature, the greater the error. To eliminate such error, a small flat should be ground on the curved surface if possible.
Clad aluminum-alloy sheets cannot be tested directly with any accuracy with a Rockwell hardness tester. If the hardness value of the base metal is desired, the pure aluminum coating must be removed from the area to be checked prior to testing.
Barcol Tester The Barcol tester (figure 6-71) is a portable unit designed for testing aluminum alloys, copper, brass, or other relatively soft materials. It should not be used on aircraft steels. Approximate range of the tester is 25 to 100 Brinell. The unit can be FIGURE 6-71. Barcol portable hardness tester.
Alloy Barcol and temper number 1100-0 35 3003-0 42 3003-H14 56 2024-0 60 5052-0 62 5052-H34 75 6061-T 78 2024-T 85 FIGURE 6-72. Typical Barcol readings for aluminum alloy.
used in any position and in any space that will allow for the operator's hand. It is of great value in the hardness testing of assembled or installed parts, especially to check for proper heat treatment. The hardness is indicated on a dial conveniently divided into 100 graduations.
The design of the Barcol tester is such that operating experience is not necessary. It is only necessary to exert a light pressuse against the instrument to drive the spring-loaded indenter into the material to be tested. The hardness reading is instantly indicated on the dial.
Several typical readings for aluminum alloys are listed in figure 6-72. Note that the harder the material is, the higher the Barcol number will be.
To prevent damage to the point, avoid sliding or scraping when it is in contact with the material being tested. If the point should become damaged, it must be replaced with a new one. No attempt should be made to grind the point.
Each tester is supplied with a test disk for checking the condition of the point. To check the point, press the instrument down on the test disk.
When the downward pressure brings the end of the lower plunger guide against the surface of the disk, the indicator reading should be within the range shown on the test disk.
CHAPTER 7
PHYSICS
GENERAL Physics is the term applied to that area of knowledge regarding the basic and fundamental nature of matter and energy. It does not attempt to determine why matter and energy behave as they do in their relation to physical phenomena, but rather how they behave.
The persons who maintain and repair aircraft should have a knowledge of basic physics, which is sometimes called the science of matter and MATTER Although matter is the most basic of all things related to the field of physics and the material world, it is the hardest to define, Since it cannot be rigidly defined, this chapter will point out those characteristics which are easily recognizable.
Matter itself cannot be destroyed, but it can be changed from one state into another state by chemical or physical means. It is usually considered in terms of the energy it contains, absorbs, or gives off. Under certain controlled conditions, it can be made to aid man in his everyday life.
Matter is any substance that occupies space and has weight. There are three states of matter:
(1) Solids, (2) liquids, and (3) gases. Solids have a definite volume and a definite shape; liquids have a definite volume, but they take the shape of the containing vessel; gases have neither a definite volume nor a definite shape. Gases not only take the shape of the containing vessel, but they expand and fill the vessel, no matter what its volume.
Water is a good example of matter changing from one state to another. At high temperature it is in the gaseous state known as steam. At moderate temperatures it is a liquid, aud at low temperatures it becomes ice, a solid state. In this example, the temperature is the dominant factor in determining the state that the substance assumes. Pressure is another important factor that will effect changes in the state of matter. At pressures lower than atmospheric, water will boil and thus change into steam at temperatures lower than 212° F. Pressure is a critical factor in changing some gases to liquids or solids. Normally, when pressure and chilling are both applied to a gas, it assumes a liquid state. Liquid air, which is a mixture of oxygen and nitrogen, is produced in this manner.
Characteristics of Matter All matter has certain characteristics or general properties. These properties are defined elementally and broadly at this point, and more specifically in applications throughout the text.
Among these properties and relationships are:
a. Volume-meaning to occupy space; having some measurements such as length, width, and height. It may be measured in cubic inches, cubic centimeters, or the like.
b. Mass-the measurement of quantity or the measure of the quantity of matter in a body.
Mass does not vary even though the state changes.
c. Attraction- a force acting mutually between particles of matter, tending to draw them together. Sir Issac Newton called this the "Law of Universal Gravitation." He showed how each particle of matter attracts every other particle, how people are bound to the earth, and how the planets are attracted in the solar system.
d. Weight-the measure of universal gravitation. The pull of gravity on a body is called the weight of the body and indicates how heavy the
e. Density-the mass (weight) of a substance per unit volume. Density can be used to distinguish various types of matter. If a substance is very dense, a large quantity of this matter would occupy a small volume.
f. Inertia-the opposition which a body offers to any change of motion. The property of inertia is common to all matter. It is best expressed in Newton's first law: "A body at rest remains at 221
rest, and a body in motion continues to move at constant speed along a straight line, unless the body is acted upon in either case by an external force."
g. Porosity-having pores or spaces where smaller particles may fit when a mixture takes place. This is sometimes referred to as granular;
consisting or appearing to consist of small grains
h. Impenetrability-simply stated means that no two objects can occupy the same place at the same time. Thus, two portions of matter cannot at the same time occupy the same space.
Matter may be classified as either an element or a compound, depending upon the complexity of its structure. An element is matter that cannot be reduced chemically into a simpler substance.
A compound is matter formed by some combination of elements.
Two basic particles, the atom and the molecule, make up all matter. The molecule is the smallest particle of a substance which still has all the properties of the original substance. In physics the molecule is the unit of matter. The atom is the smallest particle of an element that can combine with other atoms to form molecules. In chemistry, the atom is the unit of matter.
While the subject of matter may seem complex, it is difficult to think of anything simpler than matter. It can be referred to as "anything that occupies space."
Systems of Measurement The two most commonly used systems of measurement are the English sýstem, which is still in general use in the United States, and the metric system, used in most European countries and now adopted by the Armed Forces of the United States. The metric system is normally used in all scientific applications.
The three basic quantities which require units of measurement are mass (weight), length (distance), and time.
The metric system is sometimes called the CGS system because it uses as basic measuring units, the centimeter (C) to measure length, the gram (G) to measure mass, and the second (S) to measure time.
The English system uses different units for the measurement of mass and length. The pound is the unit of weight; the foot is used to measure length. The second is used to measure time as in the metric system.
The units of one system can be converted to units in the other system by using a conversion factor or by referring to a chart similar to that shown in figure 7-1. In this figure the English and the metric systems are compared; in addition, a column of equivalents is included which can be used to convert units from one system to the FLUIDS General Because both liquids and gases flow freely, they are called fluids, from the Latin word "fluidus," meaning to flow. A fluid is defined as a substance which changes its shape easily and takes the shape of its container. This applies to both liquids and gases. The characteristics of liquids and gases may be grouped under similarities and differences.
Similar characteristics are as follows:
1. Each has no definite shape but conforms to the shape of the container.
2. Both readily transmit pressures.
Differential characteristics are as follows:
1. Gases fill their containers completely, but liquids may not.
2. Gases are lighter than equal volumes of
3. Gases are highly compressible, but liquids are only slightly so.
These differences are described in the appropriate areas of the following discussion concerning the properties and characteristics of fluids at rest.
Also included are some of the factors which affect fluids in different situations.
Density and Specific Gravity The density of a substance is its weight per unit volume. The unit volume selected for use in the English system of measurement is 1 cubic foot.
In the metric system it is 1 cubic centimeter.
Therefore, density is expressed in Ibs./cu. ft.
(pounds per cubic foot) or in g./cu. cm. (grams per cubic centimeter).
To find the density of a substance, its weight and volume must be known. Its weight is then divided by its volume to find the weight per unit
Metric System English System Equivalents Length CENTIMETER FOOT (distance) 1 centimeter = 10 millimeters 1 foot = 12 inches 1 in. = 2.54 cm.
1 decimeter = 10 centimeters 1 yard = 3 feet 1 ft. = 30.5 cm.
1 meter = 100 centimeters 1 mile = 5,280 feet 1 meter = 39.37 in.
1 kilometer = 1000 meters 1 km. = 0.62 mile Weight GRAM POUND (mass) 1 gram = 1000 milligrams 1 pound = 16 ounces 1 lb. = 453.6 gr.
1 kilogram = 1000 grams 1 ton = 2,000 pounds 1 kg. = 2.2 lb.
Time SECOND SECOND Same as for English system 1 second = 86,400 systems Time same for both of average solar day.
FIGURE 7-1. Comparison of metric and English systems of measurement.
For example, the liquid which fills a certain container weighs 1,497.6 pounds. The container is 4 feet long, 3 feet wide, and 2 feet deep. Its volume is 24 cubic feet (4 ft. X 3 ft. X 2 ft.).
If 24 cubic feet of liquid weights 1,497.6 pounds, then 1 cubic foot weighs 1,497.6/24, or 62.4 pounds. Therefore, the density of the liquid is
62.4 Ibs./cu. ft.
This is the density of water at 4° C. (centigrade) and is usually used as the standard for comparing densities of other substances. (In the metric system the density of water is 1 g./cu. cm.). The standard temperature of 4° C. is used when measuring the density of liquids and solids. Changes in temperature will not change the weight of a substance, but will change the volume of the substance by expansion or contraction, thus changing its weight per unit volume.
The procedure for finding density applies to all substances; however, it is necessary to consider the pressure when finding the density of gases.
Temperature is more critical when measuring the density of gases than it is for other substances.
The density of a gas increases in direct proportion i de comportion to the pressure exerted on it. Standard conditions for the measurement of the densities of gases have been established at 0° C. for temperature and a pressure of 76 cm. of mercury. (This is the average pressure of the atmosphere at sea level.)
Density is computed based on these conditions for all gases.
It is often necessary to compare the density of one substance with that of another. For this purpose, a standard is needed. Water is the standard that physicists have chosen to use when comparing the densities of all liquids and solids.
For gases, air is most commonly used. However, hydrogen is sometimes used as a standard for gases. In physics, the word specific implies a ratio.
Thus, specific gravity is calculated by comparing the weight of a definite volume of the given substance with the weight of an equal volume of water. The terms "specific weight" or "specific density" are sometimes used to express this ratio.
The following formulas are used to find the sp. gr. (specific gravity) of liquids and solids:
Weight of the substance sp. gr. = Weight of an equal volume of water or, sp. gr. - Density of the substance Density of water The same formulas are used to find the density of gases by substituting air or hydrogen for water.
Specific gravity is not expressed in units, but as pure numbers. For example, if a certain hydraulic liquid has a sp. gr. of 0.8, 1 cu. ft. of the liquid weighs 0.8 times as much as 1 cu. ft. of water: 62.4 times 0.8 or 49.92 pounds. In the metric system, 1 cu. cm. of a substance with a 223
Gases (Air standard at 0°C, Sp. Liquids Sp. and 76.0 centimeters Sp.
Solids (Room temperatures) gr of mercury) gr.
Aluminum 2.7 Alcohol, ethyl 0.789 Air 1.000 Bronze 8.8 Gasoline 0.68 Hydrogen 0.0695
0.72 Copper 8.9 Oil (paraffin) 0.8 Nitrogen 0.967 Ice 0.917 Water 1.00 Oxygen 1.105 FIGURE 7-2. Typical values of specific gravity.
specific gravity of 0.8 weighs 1 times 0.8 or 0.8 gr.
(Note that in the metric system the specific gravity of a liquid or solid has the same numerical value as its density. Since air weighs 1.293 gr./l.
(grams per liter), the specific gravity of gases does not equal the metric densities.)
Specific gravity and density are independent of the size of the sample under consideration and depend only upon the substance of which it is made. See figure 7-2 for typical values of sp. gr.
A device called a hydrometer is used for measuring specific gravity of liquids. This device consists of a tubular-shaped glass float contained in a larger glass tube. (See figure 7-3.) The larger glass tube provides the container for the liquid. A rubber suction bulb draws the liquid up into the container. There must be enough liquid to raise the float and prevent it from touching the bottom.
The float is weighted and has a vertically graduated scale. To determine specific gravity, the scale is read at the surface of the liquid in which the float is immersed. An indication of 1000 is read when the float is immersed in pure water. When immersed in a liquid of greater density, the float rises, indicating a greater specific gravity. For liquids of lesser density the float sinks, indicating a lower specific gravity.
An example of the use of the hydrometer is its use in determining the specific gravity of the electrolyte (battery liquid) in an aircraft battery.
When a battery is discharged, the calibrated float immersed in the electrolyte will indicate approximately 1150. The indication of a charged battery is between 1275 and 1310.
Buoyancy A solid body submerged in a liquid or a gas weighs less than when weighed in free space. This is because of the upward force, called buoyant force, which any fluid exerts on a body submerged in it. An object will float if this upward force of the fluid is greater than the weight of the object.
Objects denser than the fluid, even though they sink readily, appear to lose a part of their weight when submerged. A person can lift a larger weight under water than he can possibly lift in the air.
The following experiment is illustrated in figure
7-4. The overflow can is filled up to the spout with water. The heavy metal cylinder is first weighed in still air and then is weighed while completely submerged in the water. The difference between the two weights is the buoyant force of the water. As the cylinder is lowered into the overflow can, the water is caught in the catch bucket. The volume of water which overflows equals the volume of the cylinder. (The volume of irregular-shaped objects can be measured by this method.) If this experiment is performed carefully, the weight of the water displaced by the metal cylinder exactly equals the buoyant force of the water.
Similar experiments were performed by Archimedes (287-212 B.C.). As a result of his experiments, he discovered that the buoyant force which a fluid exerts upon a submerged body is equal to the weight of the fluid the body displaces.
This statement is referred to as Archimedes' principle. This principle applies to all fluids, gases as well as liquids. Just as water exerts a buoyant 224
Overflow can HISO 1150 Discharged 1275 Charged Catch bucket Cylinder FIGURE 7-4. Measurement of buoyant force.
FIGURE 7-3. A hydrometer.
force on submerged objects, air exerts a buoyant force on objects submerged in it.
TEMPERATURE Temperature is a dominant factor affecting the physical properties of fluids. It is of particular concern when calculating changes in the state of gases.
The three temperature scales used extensively are the centigrade, the Fahrenheit, and the absolute or Kelvin scales. The centigrade scale is constructed by using the freezing and boiling points of water, under standard conditions, as fixed points of zero and 100, respectively, with 100 equal divisions between. The Fahrenheit scale uses 32° as the freezing point of water and 212° as the boiling point, and has 180 equal divisions between. The absolute or Kelvin scale is constructed with its zero point established as
- 273° C., or - 459.4° F. below the freezing point of water. The relationships of the other fixed points of the scales are shown in B of figure 7-5.
Absolute zero, one of the fundamental constants of physics, is commonly used in the study of gases. It is usually expressed in terms of the centigrade scale. If the heat energy of a given gas sample could be progressively reduced, some temperature would be reached at which the motion of the molecules would cease entirely. If accurately determined, this temperature could then be taken as a natural reference, or as a true "absolute zero" value.
Experiments with hydrogen indicated that if a gas were cooled to -273.16° C. (used as - 273° for most calculations), all molecular motion would cease, and no additional heat could be extracted from the substance.
Kelvin or TEMPERATURE Fahrenheit absolute Centigrade Fahrenheit CONVERSION absolute (Rankine) Fahrenheit 373° 100° Water 212° Kelvin to centigrade boils and fahrenheit 672° - - 212° °K = C + 273 640° - - 180° =(F-32) +273 9 = F + 255.23 9 Ice Centigrade to kelvin 540° - - 80° 273° 0° melts 32° and fahrenheit °C = K - 273
- (F - 32) 460° - 0° 9 Fahrenheit to kelvin 410° - - 50° and centigrade 9 °F = - (K-273) +32 5
- 273° • 459.4° 9 - K - 459.4 5 = 9 - C + 32 5 B FIGURE 7-5. (A) Rankine scale used to convert Farenheit to absolute. (B) Comparison of Fahrenheit, centigrade, and Kelvin temperature.
When temperatures are measured with respect to the absolute zero reference, they are expressed as zero in the absolute or Kelvin scale. Thus, absolute zero may be expressed as 0° K., as -273° C., or as - 459.4° F. (used as ~460° for most calculations).
When working with temperatures, always make sure which system of measurement is being used and know how to convert from one to another. The conversion formulas are shown in B of figure 7-5.
For purposes of calculations, the Rankine scale illustrated in A of figure 7-5 is commonly used to convert Fahrenheit to absolute. For Fahrenheit readings above zero, 460° is added. Thus, 72° F. equals 460° plus 72°, or 532° absolute.
If the Fahrenheit reading is below zero, it is subtracted from 460°. Thus - 40° F. equals 460° minus 40°, or 420° absolute. It should be stressed that the Rankine scale does not indicate absolute temperature readings in accordance with the Kelvin scale, but these conversions may be used for the calculations of changes in the state of gases.
The Kelvin and centigrade scales are used more extensively in scientific work; therefore, some technical manuals may use these scales in giving directions and operating instructions. The Fabrenheit scale is commonly used in the United States, and most people are familar with it. Therefore, the Fahrenheit scale is used in most areas of this text.
PRESSURE The term "pressure" as used throughout this chapter is defined as a force per unit area. Pressure is usually measured in p.s.i. (pounds per square inch). Sometimes pressure is measured in inches of mercury or, for very low pressure, inches of water.
Gas FIGURE 7-6. Exertion of pressure.
Pressure may be in one direction, several directions, or in all directions. (See figure 7-6.) Ice (a solid) exerts pressure downward only. Water (a fluid) exerts pressure on all surfaces with which it comes in contact. Gas (a fluid) exerts pressure in all directions because it completely fills the container.
Atmospheric Pressure The atmosphere is the whole mass of air surrounding the earth. Although it extends upward for about 500 miles, the section which is of primary interest is that portion of the air which rests on the earth's surface and extends upward for about 7½ miles. This layer is called the troposphere, and the higher above the earth, the lower its pressure.
This is because air has weight. If a column of air I-inch square extending all the way to the top of the atmosphere could be weighed, it would weigh approximately 14.7 pounds at sea level.
Thus, atmospheric pressure at sea level is approximately 14.7 p.s.i. As altitude increases, the atmospheric pressure decreases approximately 1.0
p.s.i. for every 2,343 feet. However, below sea level, atmospheric pressure increases. Pressures under water differ from those under air only because the weight of the water must be added to the weight of the air.
Atmospheric pressure, its temperature effects, and the means used to measure it are discussed in greater detail in another section of this chapter.
Absolute Pressure As stated previously, absolute temperature is used in the calculation of changes in the state of gas. It is also necessary to use absolute pressure for these calculations.
Absolute pressure is measured from absolute zero pressure rather than from normal or atmospheric pressure (approximately 14.7 p.s.i.). Gage pressure is used on all ordinary gages, and indicates pressure in excess of atmospheric. Therefore, absolute pressure is equal to atmospheric pressure plus gage pressure. For example, 100
p.s.i.g. (pounds per square inch gage) equals 100
p.s.i. plus 14.7 p.s.i. or 114.7 p.s.i.a. (pounds per square inch absolute).
Incompressibility and Expansion of Liquids Liquids can be compressed only slightly; that is, the reduction of the volume which they occupy, even under extreme pressure, is very small. If a pressure of 100 p.s.i. is applied to a body of water, the volume will decrease only 3/10,000 of its original volume. It would take a force of 64,000
p.s.i. to reduce its volume 10 percent. Since other liquids behave in about the same manner, liquids are usually considered incompressible.
In some applications of hydraulics where extremely close tolerances are required, the compressibility of liquids must be considered in the design of the system. In this study, however, liquids are considered to be incompressible.
Liquids usually expand when heated. This action is normally referred to as thermal expansion.
All liquids do not expand the same amount for a certain increase in temperature. If two flasks are placed in a heated vessel, and if one of these flasks is filled with water and the other with alcohol, it will be found that the alcohol expands much more than the water for the same rise in temperature. Most oils expand more than water.
Aircraft hydraulic systems contain provisions for compensating for this increase of volume in order to prevent breakage of equipment.
Compressibility and Expansion of Gases The two major differences between gases and liquids are their compressibility and expansion characteristics. Although liquids are practically incompressible, gases are highly compressible.
Gases completely fill any closed vessel in which they are contained, but liquids fill a container only to the extent of their normal volume.
KINETIC THEORY OF GASES The simple structure of gases makes them readily adaptable to mathematical analysis from which has evolved a detailed theory of the behavior of gases. This is called the kinetic theory 227
of gases. The theory assumes that a body of gas is composed of identical molecules which behave like minute elastic spheres, spaced relatively far apart and continuously in motion.
The degree of molecular motion is dependent upon the temperature of the gas. Since the molecules are continuously striking against each other and against the walls of the container, an increase in temperature with the resulting increase in molecular motion causes a corresponding increase in the number of collisions between the molecules.
The increased number of collisions results in an increase in pressure because a greater number of molecules strike against the walls of the container in a given unit of time.
If the container were an open vessel, the gas would expand and overflow from the container.
However, if the container is sealed and possesses elasticity (such as a rubber balloon), the increased pressure causes the container to expand.
For instance, when making a long drive on a hot day, the pressure in the tires of an automobile increases, and a tire which appeared to be somewhat "soft" in cool morning temperature may appear normal at a higher midday temperature.
Such phenomena as these have been explained and set forth in the form of laws pertaining to gases and tend to support the kinetic theory.
At any given instant, some molecules of a gas are moving in one direction, some in another direction; some are traveling fast while some are traveling slowly; some may even be in a state of rest. The combined effect of these varying velocities corresponds to the temperature of the gas.
In any considerable amount of gas, there are so many molecules present that in accordance with the "laws of probability? some average velocity can be found. If this average velocity were possessed by every molecule in the gas, it would produce the same effect at a given temperature as the total of the many varying velocities.
Gas FIGURE 7-7. Gas compressed to half its original volume by a double force.
as the applied pressure was decreased, the resulting volume increased. From these observations, he concluded that for a constant temperature the product of the volume and pressure of an enclosed gas remains constant. Boyle's law is normally stated: "The volume of an enclosed dry gas varies inversely with its pressure, provided the temperature remains constant."
This law can be demonstrated by confining a quantity of gas in a cylinder which has a tightly fitted piston. A force is then applied to the piston so as to compress the gas in the cylinder to some specific volume. When the force applied to the piston is doubled, the gas is compressed to onehalf its original volume, as indicated in figure 7-7.
In equation form, this relationship may be expressed either ViP: = V2P2 or V1 = P Boyle's Law As previously stated, compressibility is an outstanding characteristic of gases. The English scientist Robert Boyle was among the first to study this characteristic which he called the "springiness of air." By direct measurement he discovered that when the temperature of a combined sample of gas was kept constant and the pressure doubled, the volume was reduced to half the former value;
where V1 and P1 are the original volume and pressure, and ½ and P2 are the revised volume and pressure.
Example of Boyle's law: 4 cu. ft. of nitrogen are under a pressure of 100 p.s.i.g. The nitrogen is allowed to expand to a volume of 6 cu. ft.
What is the new gage pressure?
Formula or equation:
ViP1 = Velz 228
Substituting:
4 × (100) = 6 X P Pz = 1 × 100 Pz = 66.6 p.s.i.g.
A gas which conforms to Boyle's law is termed an ideal gas. When pressure is increased upon such a gas, its volume decreases proportionally and its density is increased. Thus, the density of a gas varies directly with the pressure, if the since gases expand when heated and contract when cooled.
The useful applications of Boyle's law are many and varied. Some applications more common to aviation are: (1) The carbon dioxide (CO2) bottle used to inflate life rafts and life vests;
(2) the compressed oxygen and the acetylene tanks used in welding; (3) the compressed air brakes and shock absorbers; and (4) the use of oxygen tanks for high-altitude flying and emergency use.
Charles' Law The French scientist Jacques Charles provided much of the foundation for the modern kinetic theory of gases. He found that all gases expand and contract in direct proportion to the change in the absolute temperature, provided the pressure is held constant. In equation form, this part of the law may be expressed.
ViTz = V211 or Vz = I= This equation means that with a constant volume, the absolute pressure of a gas varies directly with the absolute temperature, Examples of Charles' law: A cylinder of gas under a pressure of 1,800 p.s.i.g. at 70° F. is left out in the sun in the tropics and heats up to a temperature of 130° F. What is the new pressure within the cylinder? The pressure and temperature must be converted to absolute pressure and temperature.
Formula or equation:
P1 = T= Pz Using the Rankine system:
70° F. = 530° absolute 130° F. = 590° absolute Substituting:
1,800 + 14.7 530 Pz - 590 Then:
P2 = (590) (1,814.7) 530 Pz = 2,020 p.s.i.a.
Converting absolute pressure to gage pressure:
2,020.0
- 14.7 2,005.3 p.s.i.g.
Free balloon flights into the stratosphere, the expanding gases of jet-propelled aircraft, and the effects of clouds and weather on instrument recordings may be explained by the use of Charles' law. Here are practical applications of a law of physics that aid the pilot, air controller, and aerographer in their work. Flying is made safer when humans are able to apply this law in handling weather data so vital to aviation.
General Gas Law The facts concerning gases discussed in the preceding sections are summed up and illustrated in figure 7-8. Boyle's law is expressed in (A) of the figure, and the effects of temperature changes on pressure and volume (Charles' law) are illustrated in (B) and (C), respectively.
By combining Boyle's and Charles' laws, a single expression can be derived which states all the information contained in both. This expression is called the general gas law, a very useful form of which is given in the following equation.
(NOTE: The capital P and T signify absolute pressure and temperature, respectively.)