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.)
PAL - PE 229
Then:
Volume 179.4 540 = = 760 Temperature constant Pressure constant Pz = (179.4) (760) constant = ₽z 540 PęV½ Pr = 252.5 p.s.i.a.
Converting absolute pressure to gage pressure:
252.5
- 14.7
237.8 p.s.i.g.
(А) (B) (C) 2. Four cubic feet of a gas at 75 p.s.i.g. and 80° F. are compressed to 237.8 p.s.i.g. and heated FIGURE 7-8. The general gas law. to a temperature of 300° F. What is the volume of the gas resulting from these changes?
Formula or equation:
three equations are special cases of the general An examination of figure 7-8 reveals that the PIV: = I= Pavz equation. Thus, if the temperature remains constant, T1 equals T2, and both can be eliminated from the general formula, which then reduces to Using the Rankine system:
the form shown in (A). When the volume remains 80° F. = 540° absolute constant, V1 equals V½, reducing the general equa- 300° F. = 760° absolute tion to the form given in (B). Similarly P, is equated to P2 for constant pressure, and the Substituting:
equation then takes the form given in (C).
(75 + 14.7) (4) (237.8 + 14.7) V½ The general gas law applies with exactness only to "ideal" gases in which the molecules are as- 540 760 sumed to be perfectly elastic. However, it de- Then:
scribes the behavior of actual gases with sufficient accuracy for most practical purposes. (89.7) (4) = (252.5) V½ Two examples of the general equation follow: 540 760
1. Two cu. ft. of a gas at 75 p.s.i.g. and 80° F.
are compressed to a volume of 1 cu. ft. and then heated to a temperature of 300° F. What is the V2 = 540 × 252.5 358.8 × 760 new gage pressure? V½ = 2 cu. ft.
Formula or equation:
Avogadro's Law An Italian physicist, Avogadro, conceived the theory that "at the same temperature and pres- Using the Rankine system: sure, equal volumes of different gases contain equal numbers of molecules." This theory was 80° F. = 540° absolute proven by experiment and found to agree with 300° F. = 760° absolute as Avogadro's law. the kinetic theory, so it has come to be known Substituting:
Dalton's Law (75 + 14.7) (2) = Pг(1) If a mixture of two or more gases which do not 540 760 combine chemically is placed in a container, each 230
equally and undiminished in every direction throughout the column-forward, backward, and sideways-so that the containing vessel is literally filled with pressure.
If a gas is used instead of a liquid, the force is transmitted in the same manner. The one difference is that gas, being compressible, provides a much less rigid force than the liquid, which is incompressible. (This is the main difference in the action of liquids and gases in fluid power systems.)
(A) (B) FIGURE 7-9. Transmission of force:
(A) solid; (B) fluid.
gas expands throughout the total space and the absolute pressure of each gas is reduced to a lower value, called its partial pressure. This reduction is in accordance with Boyle's law. The pressure of the mixed gases is equal to the sum of the partial pressures. This fact was discovered by Dalton, an English physicist, and is set forth in Dalton's law: "A mixture of several gases which do not react chemically exerts a pressure equal to the sum of the pressures which the several gases would exert separately if each were allowed to occupy the entire space alone at the given temperature."
Pascal's Law The foundations of modern hydraulics and pneumatics were established in 1653 when Pascal discovered that pressure set up in a fluid acts equally in all directions. This pressure acts at right angles to containing surfaces. Thus, in figure 7-10, if the liquid standing on a square inch (A) at the bottom of the tank weighs 8 pounds, a pressure of 8 p.s.i. is exerted in every direction at (A). The liquid resting on (A) pushes equally downward and outward. The liquid on every square inch of the bottom surface is pushing downward and outward in the same way, so that the pressures on different areas are in balance.
At the edge of the tank bottom, the pressures act against the wall of the tank, which must be strong enough to resist them with a force exactly equal to the push. Every square inch of the bottom of the tank must also be strong enough to resist the downward pressure of the liquid resting on it. The same balance of pressures exists at every other level in the tank, though of lesser pressures as one approaches the surface. There- Transmission of Forces Through Fluids When the end of a bar is struck, the main force of the blow is carried straight through the bar to the other end (see A of figure 7-9). This happens because the bar is rigid. The direction of the blow almost entirely determines the direction of the transmitted force. The more rigid the bar, the less force is lost inside the bar or transmitted outward at right angles to the direction of the blow.
8 p.s.i.
When a force is applied to the end of a column of confined liquid (B of figure 7-9), it is transmitted straight through to the other end and also FIGURE 7-10. Pressure acting on a container.
Surface Head FICURE 7-11. Pressure relationship with shape.
fore, the liquid remains at rest; it does not leak out and the tank does not collapse.
One of the consequences of Pascal's law is that the shape of the container in no way alters pressure relations. Thus, in figure 7-11, if the pressure due to the weight of the liquid at one point on the horizontal line (H) is 8 p.s.i., the pressure is 8 p.s.ì. everywhere at level (H) in the system.
Pressure due to the weight of a fluid depends, at any level, on the height of the fluid from the level to the surface of the fluid. The vertical distance between two horizontal levels in a fluid is known as the head of the fluid. In figure 7-11, the liquid head of all points on level (H) with respect to the surface is indicated.
Pressure due to fluid head also depends on the density of the fluid. Water, for example, weighs
62.4 lb../eu. ft. or 0.036 lb./cu. in., but a certain oil might weigh 55 lbs./cu. ft., or 0.032 lb./cu. in.
To produce a pressure of 8 p.s.i., it would take 222 inches of head using water, and 252 inches of head using the oil (see figure 7-12).
on a unit area of the surface acted upon. In hydraulics and pneumatics, pressure is expressed in pounds per square inch. Thus, pressure is the amount of force acting upon 1 square inch of area.
Computing Force, Pressure, and Area A formula, similar to those used with the gas laws, is used in computing force, pressure, and area in fluid power systems. Although there appears to be three formulas, it is only one formula written in three variations, where P refers to pressure, F indicates force, and A represents area.
Force equals pressure times area. Thus, the Force and Pressure In order to understand how Pascal's law is applied to fluid power, a distinction must be made between the terms "force" and "pressure." Force may be defined as a push or pull. It is the push 8 Ibs. 8 Ibs.
or pull exerted against the total area of a par- Water Oil ticular surface and is expressed in pounds. As previously stated, pressure is the amount of force FIGURE 7-12. Pressure and density relationship 232
circular. Either the diameter or the radius (one half the diameter) may be given. The radius in inches must be known to find the area. Then, the formula for finding the area of a circle is used.
This is written A = Tr?, where A is the area, 7 is 3.1416 (3.14 or 37 for most calculations), and r' indicates radius squared.
FIGURE 7-13. Device for determining the arrangement of the force, pressure, and area formulas.
formula is written:
F = PXA.
Pressure equals force divided by the area. By rearranging the formula, this statement is condensed into:
P= Since area equals force divided by pressure, the formula is written:
A = P Figure 7-13 illustrates a device for recalling these formulas. Any letter in the triangle may be expressed as the product or quotient of the other two, depending upon its position within the triangle.
For example, to find area, consider the letter "A" as being set off by itself, followed by an equal sign. Now look at the other two letters.
The letter "F" is above the letter "P"; therefore, A = F/P.
In order to find pressure, consider the letter "p" as being set off by itself, and look at the other two letters. The letter "F" is above the letter "A"; therefore, P = F/4.
In a similar manner, to find force, consider the letter "F" as being set off by itself. The letters "p" and "A" are side by side; therefore, F= PXA.
Sometimes the area may not be expressed in square inches. If it is a rectangular surface, the area may be found by multiplying the length (in inches) by the width (in inches). The majority of areas to be considered in these calculations are Pressure and Force in Fluid Power Systems In accordance with Pascal's law, any force applied to a confined fluid is transmitted equally in all directions throughout the fluid regardless of the shape of the container. Consider the effect of this in the system shown in figure 7-14, which is a modification of B in figure 7-9. The column of fluid is curved upward to its original level, with a second piston at this point. It is clear that when the input piston (1) is pushed downward, a pressure is created through the fluid, which acts equally at right angles to surfaces in all parts of the container.
Referring to figure 7-14, if the force (1) is 100 Ibs. and the area of the piston is 10 sq. in., then the pressure in the fluid is 10 p.s.i. (110). This pressure acts on piston (2), so that for each square inch of its area it is pushed upward with a force of 10 pounds. In this case, a fluid column of uniform cross section is considered so that the area of the output piston (2) is the same as the input piston (1), or 10 square inches. Therefore, the upward force on the output piston (2) is 100 pounds, the same as applied to the input piston
(1). All that has been accomplished in this system was to transmit the 100-pound force around a Force 1 = 100 Ibs. Force 2 = 100 Ibs.
Input Output
• piston (1) piston (2).
10 sq. in. 10 sq. in.
Pressure 10 Ibs. per sq. inch FIGURE 7-14. Force transmitted through fluid.