If the volume of a container of gas remains the same, and we add heat energy to the gas, the molecules will collide with each other and with the walls of the container with more force. So the pressure will go up with the absolute temperature (see Figure 3-56).

T 1 = P1 T2 P2

If the second absolute temperature, T 2, is higher than first, T 1, the second pressure, P2, will be greater than the first, P 1

Figure 3-56. When the volume of a container of gas remains constant, an increase in the ahsolllle temperature of the gas causes its pressure to increase.

General Gas Law Since any change in the absolute pressure, absolute temperature, or volume of a gas affects the other two conditions, Boyle's law and Charles's law can be combined into the general gas law following the equation:

P1 . V1 P2 V2 = ---TI T2

P 1 and V1 are the f irst absolute pressure and volume of the gas, and T 1 is its first absolute temperature. P2 and V2 are the final absolute pressure and vol-ume of the gas, and T 2 is its final absolute temperature.

Let's try some examples of the way this general gas law works. Sup-pose we have a closed 50-cubic-inch container of gas under an absolute pressure of 100 psia and an absolute temperature of 250 Kelvin. If we heat the gas in this container to a temperature of 400 Kelvin, what will its final pressure be?

BASIC P HYSICS Chapter 3 113

P1 = 100 psia P2 = 160 psia v 2 =50 cubic in. T2 = 400K

V 1 = 50 cubic in. T1 = 250K

P1 x v1 = P2 x v2 T1 T2

p 2=P1xT2

T1

100 X 400

250

160 psia

Figure 3-57. Finding !he change in pressure with a change in temperature when !he volume remains constant

11 4

This is worked out in Figure 3-57. If the volume of the gas is held constant and the absolute temperature is increased from 250K to 400K, the pres-sure will go up from 100 psia to 160 psia.

Next, we have a container that will hold a constant pressure of 50 psia on a gas, but allows the gas to change its volume. If we start with a volume of I 00 cubic inches and a gas temperature of 400K, what will the volume of the gas be if we lower its temperature to 300K? See Figure 3-58.

When you lower the temperature of the gas, its molecular movement de-creases. Since the pressure is held constant at 50 psia, the volume will de-crease from 100 to 75 cubic inches.

This time, consider a cylinder with a piston in it that allows the vol ume of the gas to increase without increasing the pressure. We want to know how high the temperature of the gas will have to rise to increase the volume of the container from 50 to I 00 cubic inches, without the pressure ofthe gas chang-ing.ln Figure 3-59, we see that we will have to double the absolute tempera-ture if we double the volume without changing the absolute pressure.

P1 =50 psia P2 =50 psia V1 = 100 cubic in. T1 = 400K

v2 = 75 cubic in. T2 = 300K

P1 xV1 P2 xV2 --- = ---T1 T2

v2 = v1 x T2

T1

100 X 300 =----

400

P1 = 14.69 psia vl =50 cubic in. T1 = 300K

P2 = 14.69 psia v2 = 100 cubic in. T2 = 600 K

300 X 100 =--- -

50

= 75 cubic in. = 600K

Figure 3-58. Finding !he clwn~;e in l'olume Figure 3-59. Find in~; the change in with a change in rempemture when rhe temperature with a change in l'O!ume H'hen pressure remains COI!Stant the pressure remains consranr.

Dalton's Law Chemists have found that when equal volumes of every kind of gas are held at an equal temperature and pressure, there are an equal number of molecules in each volume. This fact is expressed as Dalton's law.

T n a mixture of gases in a container, the total pressure caused by these gases pushing against the walls of the container is the sum of the partial pres-sures caused by each of the gases in the mixture. The partial pressure, the amount of pressure caused by each type of gas, depends on how much of that particular gas is present.

The air we breathe is a mixture of gases that contains approximately 78% nitrogen and 21% oxygen. The other 1% is made up of traces of hydrogen, helium, neon, argon, krypton, and other gases. Under standard sea-level conditions, this air has a pressure of 29.92 or mercury. Now, according to Dalton's law, the nitrogen which makes up 78% or the volume of the gas also causes 78% of the pressure; the partial pressure of the nitrogen is 23.34 inches of mercury. The oxygen, which makes up 21% of the volume of the air, causes 21% of the pressure; its pressure is 6.28 inches of mercury.

STUDY QUESTIONS: GAS LAWS

Answers are on Page 136. Page numbers refer to chapter text.

Da lton's law. The gas law which states that there will always be the same number of molecules of gas in a container when the gas is held at a uniform pressure and temperature. Dalton's law explains the partial pressure of the gases which make up the ai r in our atmosphere.

partial pressure. The pressure caused by each of the gases in a mixture.

67. lf we hold the absolute temperature of a gas constant while we decrease its volume, the pressure will _ ________ ___ (increase or decrease). Page I J1

68. If we hold the absolute pressure of a gas constant while we increase its absolute temperature, its volume will (increase or decrease). Page 112

69. If we hold the volume of a gas constant while we increase its absolute temperature, its absolute pressure will (increase or decrease). Page 113

70. The temperature we must use when working problems using the gas laws is

- ----------------;-- temperature. Page 1/3

71. We have this mixture: 30% nitrogen, 20% oxygen, and 50% hydrogen. If the mixture has a pressure of 29.92 of mercury, what is the partial pressure or each gas? a. Nitrogen= _ ___ _

b. Oxygen = c. Hydrogen= ___ _

Page 115

inches of mercury inches of mercury inches of mercury

BASIC PHYSICS Chapter 3 115

Figure 3-60. The pressure at the bottom of a column of liquid is caused by the height of the liquid, and it is not affected by the quantity of the fluid or the shape of the container.

116

Fluid Mechanics Levers, inclined planes, pulleys, and gears all may be used to gain mechanical advantage. There is another way that is often used to achieve a mechan-ical advantage, and this is by fluid mechanics in the form of hydraulic or pneumatic systems.

Hydraulic systems transmit a force from one location to another by us-ing an incompressibie fluid, usually some form of oil. Hydraulic systems are used for operating the brakes in most airplanes, as well as for operating the retractable landing gear and many of the flight controls on large airplanes. Pneumatic systems use some form of compressible fluid such as air for trans-mitting force. Some airplanes use pneumatic systems to operate the brakes, flaps, and retractable landing gear.

Pressure Produced by a Fluid The pressure produced by a column of fluid is determined by the density of the fluid and the height of the column.

The shape or volume of the container does not have any effect on the pressure. In Figure 3-60 we see several containers of different shapes. lf we connect them all together at the bottom, the liquid in all of the containers will stay at the same height, h. The pressure shown on the gage is that caused by the height of the fluid.

The second thing that determines the pressure produced by a column of fluid is the density of the fluid. Pure water weighs 0.0361 pound per cubic inch, and since one gallon contains 231 cubic inches, a column of water 231 inches high will produce a pressure of 8.34 psi. Other liquids have different densi-ties and specific gravities, and a column of the same height will produce a different pressure. Mercury has a specific gravity of 13.6, and a column of mercury 231 inches high will produce a pressure of J 13.42 psi. The specific gravity of gasoline is only 0.72, so a column of gasoline 231 inches high will produce a pressure of 6 pounds per square inch. See Figure 3-61.

Matec.ial

Mercury Pure water Jet engine fuel Gasoline

Density (pounds cubic inches)

0.4913 0.0361 0.0289 0.0260

Specific Gravity

13.6 1.00 0.80 0.72

Figure 3-61. Density and specific gravity of various liquids

AVIATION MAINTENANCE T ECH :-I! ClAN SERIES G E.'\ERAL

We can find the pressure produced by a column of liquid by using the formula:

P=D h

Pis the pressure in pounds per square inch. D is the density of the liquid in pounds per cubic inch, and h is the height of the column of liquid in inches.

We can use this formula to find the amount of pressure pushing on the bottom of a gasoline tank if the level of the fuel in the tank is 30 inches above the bottom. Gasoline has a density of 0.026 pound per cubic inch.

P=D h = 0.026. 30 = 0.78 pounds per square inch

Pascal's Law

Pascal's law states that when there is an increase in pressure at any point in a confined fluid, there is an equal increase at every other point in the container.

If we have a container of liquid such as the one we see in Figure 3-62, the pressures shown on the gages Ph P2, and P3 are the pressures caused by the height of the liquid above the gage. P3 shows more pressure than either P2 or P1 because there is a greater height of liquid above it.

Put a piston in the container and put a load on it so that it pushes down on the liquid, the pressure will increase on each of the gages. All three gages will show the same amount of increase. See Figure 3-63.

Figure 3-62. The pressure produced by a liquid in a container is caused by the height of the liquid above the poin1 at which the pressure is measured. The higher the liquid above the gage, the greater the pressure.

BASIC PHYSICS

Pascal's law. The law that states that when pressure is applied to a fluid in an enclosed container, the pressure is transmitted equally throughout all of the flu id, and it acts at right angles to the walls that enclose the flu id.

Figure 3-63. When we apply pressure on the liquid in a closed container, the pressure rises the same amount in all parts of the container.

Chapter 3 117

118

In practical hydraulic systems, we do not consider the weight of the fluid in the system, but think only of the changes in pressure caused by the piston pushing on the fluid.

Figure 3-64 shows a practical hydraulic system that uses Pascal's law to give us a mechanical advantage. Here we have a cylinder with an area of 1 square inch connected to a cylinder having an area of 10 square inches. A piston in the smaller cylinder holding a weight of 1 pound balances the piston in the larger cylinder holding 10 pounds.

w1 = 1 pound

A1 = 1 square inch

r----!....:..:----1 / A2 " 1 0 square inches

~1 10inches ~ D2 = 1 inch~

Figure 3-64. Hydraulic cylinders produce a mechanical advantage. A 1 -pound force ( F 1) can lift a 10-pound weight (W2), but no work is gained. The work done by the small piston is the same as that done by the large piston.

The 1-pound load on the 1-square-inch piston causes a pressure increase in the cylinder of 1 psi. And, according to Pascal's law, this pressure increase is caqied to every part of the fluid and pushes up on the piston in the large cylinder.

The large piston has an area of 10 square inches, and the fluid pushes on every square inch with a force of 1 pound. So the fluid pushes up on the pis-ton with enough force for it to hold 10 pounds.

This arrangement of two cylinders having unequal area gives a mechani-cal advantage in the same way a lever does. The force on the small piston (F1), divided by the area of the small piston (A1), is equal to the force on the large piston (F2), divided by the area of the large piston (A2) .

F1 = F2 A 1 A2

AVIATION MAINTENANCE TECHNICIAN SERIES GENERAL

Another way in which this hydraulic system resembles the lever is that the work which is done by the small piston is the same as that done by the large piston. When the piston in the small cylinder moves down 10 inches, it forces 10 cubic inches of fluid out of the small cylinder into the large one. This fluid spreads out over alllO square inches of area and lifts the large piston only 1 inch. The work done by the small piston is the same as the work done by the large piston, 10 inch-pounds.

In our study of Mathematics, we introduced the formula for force: F ::: P A (force ::: pressure times area). A convenient way to remember this formula and all of its possible rearrangements is by the use of the circle we see in Fig-ure 3-65. The top half of the circle labeled F represents the force, and it is equal to the bottom half, labeled A and P, which represents area and pressure.

We can find the area needed to produce a specified force from the avail-able pressure by dividing the top quantity (F) by the known bottom quantity (P). A::: F 7 P. We can also find the pressure required to produce a given amount of force when the area of the piston is known. We can do this by di-viding the value represented by the top half of the circle (F) by the known value represented by one of the bottom parts of the circle (A). P::: F 7 A.

From the formula F = P A, we can see that the amount of force produced by a hydraulic system is equal to the amount of pressure in the system times the area of the piston that the pressure acts against. If we have a pressure of 100 psi acting on a piston whose area is 20 square inches, the force produced by the piston is 2,000 pounds. See Figure 3-65.

P 100 PSI A = 20 sq. in. F PxA 100 X 20 2,000 pounds

Figure 3-65. The amount of force produced by the piston in a hydraulic cylinder may be found by multiplying the area of the piston by the amount of pressure inside the cylinder.

BASIC PHYSICS Chapter 3 119

120

Look at Figure 3-66 to find the area needed to give us a certain amount of force when we know the pressure in the system. In this example, we want to know how large the piston will have to be for it to produce 100 pounds of force with a pressure of 20 psi.

To do this, we divide the force of J 00 pounds by the pressure of 20 psi, and find that we need a piston having an area of 5 square inches. See Figure 3-66.

We can also use our circle to find the amount of pressure that is built up in a cylinder when we know the area of the piston and the amount of force that is pushing on the piston. When a force of 40 pounds pushes on a piston whose area is 10 square inches, the pressure of the fluid in the cylinder increases by 4 psi, as shown in Figure 3-67.

This same kind of circle helps us visualize the relationship between the area of the piston, the distance the piston moves, and the amount of fluid that is forced out of the cyl inder.

100 pounds

A A=

p

F p

100 20

5 square inches

Figure 3-66. The area of a pisron needed 10 produce a given amount ufforce with a certain amount of pressure may be found by dividing the amount afforce by the pressure.

p

p

F A

40 10

= 4 PSI

6)1=====<

40 pounds

+--- A = 10 square inches

Figure 3-67. The amount of pressure produced in a hydraulic cylinder may be found by dividing the amount offorce on the piston by the area of the piston.

AVIATION MAINTE:\ANCE TECHNICIAN SERIES G ENERAL

In Figure 3-68, the shaded half of the circle shows that the volume of the fluid moved by a piston is equal to the area of the piston times the distance the piston moves. When a piston with an area of 2 square inches moves 4 inches into the cylinder, it pushes 8 cubic inches of fluid out of the cylinder.

This circle can also help us find the piston area needed to expel a given amount of fluid when it is moved a specified distance. In Figure 3-69, the piston moves 4 inches to force 8 cubic inches of fluid from the cylinder. By using the for-mula shown here, we see that the piston must have an area of2 squme inches.

r-- D = 4 in. ----1 _ : .,. A= 2 sq. in. F ~~ ~,~::tt===============:@Jl C ! -:

V= A D

= 2. 4 V = 8 cu. in.

= 8 cu. in.

Figure 3-68. The volume of fluid moved out of a cylinder by a piston may be found by multiplying the area of the piston by the distance rhe piston is moved.

r--D = 4 in. ----1

A= y_ D

8 4

= 2 sq. in.

V = 8 cu. in.

Figure 3-69. The area of a pis! on needed to move a given volume offluid when it moves a certain distance //lay be found by dividing the volume by rhe disrance rhe piston is moved.

And this circle also helps us find the distance a piston of a certain size will have to move in order to force a given amount of f luid out of the cylinder. The illustration in Figure 3-70 (page 122) shows a piston with an area of 2 square inches moving 8 cubic inches of fluid out of a cylinder. 1n order to do this, the piston must move for a distance of 4 inches.

BASIC PHYSICS Chapter 3 121

Bernoulli's principle. The principle that states that if energy is neither added to nor taken away from a fluid in motion, any increase in its velocity will cause a cotTesponding decrease in its pressure. The velocity of the moving fluid relates to its kinetic energy, and its pressure relates to its potential energy.

122

r-D=4in. --1

8 2

= 4 inches

V = 8 cu. in.

Figure 3-70. The dis lance a pis/on mus1 move to force a given amount rffluid ou/ of a cylinder may be found by dividing the volume of !he fluid hy the area of I he pis/on.

Bernoulli's Principle

Energy exists in two forms: potential and kinetic. In fluid mechanics, pres-sure is a form of potential energy in a fluid, and the velocity of the fluid is its kinetic energy.ln any flow of fluid, the total energy in the fluid is the sum of the kinetic and the potential energy.

Bernoulli's principle explains that if we neither add nor take away en-ergy from a flow of fluid, any increase in the velocity (kinetic energy) of the flow will cause a corresponding decrease in its pressure (potential energy). This principle is extremely important in helping us understand the way an airplane wing or a helicopter rotor produces lift as it passes through the air. It also helps us understand the way in which paint spray guns operate.

A venturi is a specially shaped tube through which a fluid, either a liquid or a gas, flows. There is a restriction in the tube where the area gets smaller, and then it returns to its original size. See Figure 3-71.

2 3

Figure 3-71. When energy is neither added ro nor rakenfrom.fluid in mol ion, anv restric-tion thai causes 1he fluid 10 speed up will cause the pressure ro decrease.

AVIATION MAINTEl\'ANCE T ECHNICIAN SERIES G ENERAL

Fluid flows through this tube, and, at position I, the pressure is the value PI. The speed, or velocity, is shown as VI. If we do not add or take away any energy from the fluid, it must speed up when it reaches the restriction to al-low the same volume of fluid to move the same distance through the tube in the same length of time.

When it speeds up, the kinetic energy (velocity) increases. But since no energy was added, the potential energy (pressure) had to decrease. We see this on the gages P2 and V2. As soon as the tube returns to its original size, at 3, the fluid slows down so the same volume will move the same distance in the same time. When it slows down, the velocity decreases, but the pres-sure increases to the value it had originally.

In a spray gun, air is forced through a venturi, and a tube carries the liquid to the restriction point. Here the velocity is the greatest and the pressure is the lowest. Atmospheric pressure forces the liquid out of the tube into the area of low pressure, where it is broken up into tiny droplets by the high-velocity air. See Figure 3-72.

Figure 3-72. An atomizer, such as is used in a spray gun, is a fonn of venturi. When the air flow is reslricted, the pressure drops, and atmospheric pressure forces the liquid up so that it mixes with the high-velocity air and is broken up into tiny droplets. it is atomized.

B ASIC PHYSICS Chapter 3 123

c:::::::> Relative wind

Figure 3-73. Aerodynamic lift is produced by an airfoil when the kinetic energy (velocity) in the airflowing over its upper surface increases and its potential energy (pressure) decreases. Below the swface, the velocity decreases and the pressure increases.

Figure 3-74. The pressure exerted by the liquid in a container increases with the depth of rhe liquid, and the pressure is greatest at the bottom.

When a block of material is submerged in the liquid, rhe pressure acts on all sides of the block, and since the pressure is greater on the bottom of rhe block than it is on the top, the liquid tries to force the block up. The block is said to be buoyed up by the liquid.

buoyancy. The uplifting force that acts on an object when it is placed in a tluid.

124

Bernoulli 's principle also helps us understand the way aerodynamic lift is produced by an airplane wing and by a helicopter rotor.

The cross-sectional shape of a wing o~ a rotor is much like the one we see in Figure 3-73: As the air strikes the wing and flows over the top, it finds the surface dropping away from it. For the air to continue to cling to the sur-face, it must speed up. Energy is needed to speed up the air, and this energy comes from changing some of the potential energy, or pressure, into veloc-ity, or kinetic energy. As the pressure over the top of the wing becomes less, it pulls air down to the surface, ~nd a force equal to the weight of the air being pulled down pulls upward on the wing.

The air flowing below the wing encounters the bottom surface rising into its flow path, and it slows down. This loss of velocity increases its potential energy, or pressure, and this pressure pushes the wing up. The low pressure on top of the wing and the high pressure below the wing produce aerody-namic lift.

Buoyancy There are two types of flying machines that allow us to overcome the force of gravity and rise into the air. Aerodynamic flying machines such as air-planes and helicopters depend upon movement through the air to produce lift. Aerostatic machines such as balloons rise in the air because of their buoyancy.

Balloons are filled with a gas, such as hot air, which is less dense than the colder air surrounding it. They rise because they displace a weight of air greater than their own weight.

If we put a block of aluminum in a container of water, the pressure of the liquid pushes against its top, bottom, and sides. Since the forces on the sides are exactly equal, they cancel each other, but there is more force on the bot-tom of the block than there is on its top, and the water will try to force the block up. The amount of this force is exactly equal to the weight of the water the block displaces. See Figure 3-7 4.

A 10-inch cube of aluminum has a volume of 1,000 cubic inches, and since its specific gravity is 2.8, the block is 2.8 times as heavy as an equal volume of water.

Archimedes' principle explains the way buoyancy acts on an object that is immersed in a fluid, either a liquid or a gas. We can understand this principle if we support the block of aluminum with a spring scale, as in Figure 3-75, and lower it into a container of water so that some of the water is forced out of the container into another container on the scales.

AVIATION MAINTENANCE T ECHNICIA:\ S ERIES G ENERAL

The aluminum block weighs 101 pounds when it is outside of the water. And when we lower it into the water, it displaces some of the water. As the block pushes the water out, the water pushes up on the block and the scale reads less. When the block is completely submerged in the water, the scale reads 64.9 pounds, because we have forced 36.1 pounds of water out of the con-tainer. The aluminum block is buoyed up by the water with a force equal to the weight of the water that was displaced.

The same size block of wood, with a specific gravity of 0.50, weighs 18.15 pounds outside of the water; and when lowered into the water, it forces out only 500 cubic inches of water. The scale will read zero because the block has displaced its own weight of water and the water holds up the entire weight of the block. The block floats.

Hot air balloons rise into the air because the heated air inside the balloon is less dense than the surrounding cooler air. The balloon displaces a weight of air equal to the weight of the balloon with its basket and occupants.

64.9 pounds

Figure 3-75. Aluminum weighs 0.101 pound per cubic inch, so a 10 10 10 inch hlock of aluminum weighs 101 pounds. When the block is lowered into a container of water, it rakes the place of 1,000 cubic inches of water, which ll'eighs 36.1 pounds. The block is buoyed up by a force equal to the weight of the water it displaced, and it now pulls down on the spring scale with a force of only 64.9 pounds.

BASIC P HYSICS

Archimedes ' principle. The principle that states that a body immersed in a nuid undergoes an apparent loss of weight equal to the weight of the f1uid it displaces.

Chapter 3 125

STUDY QUESTIONS: FLUID MECHANICS

Answers are on Page 136. Page numbers refer to chapter text.

72. The fluid used in a hydraulic system is ___________ (compressible or incompressible).

Page 116

73. The fluid used in a pneumatic system is ___ ________ (compressible or incompressible).

Page 116

74. Two things that determine the amount of pressure produced by a column of fluid are:

a. ------------b. ------------

Page 116

7 5. Refer to Figure SQ-7 5. If piston area A I is 3 square inches, and A2 is 30 square inches, weight WI must be ____ _______ pounds in order to balance a weight W 2 of 100 pounds. Page 118

Figure SQ-75

76. Refer to Figure SQ-75. The small piston moves down a distance DI of 6 inches, to force the large piston up a distance D2 of 0 .5 inch. If the area of the large piston A2 is 120 square inches, the area AI of the small piston must be __________ _ square inches. Page 118

77. Refer to Figure SQ-75. When a weight W 1 of 18 pounds pushes down on the small piston whose area A 1 is 9 square inches, the pressure inside the small cylinder is psi. Page 118

126 A VIATION M AINTENANCE T ECHNICIAN SERIES G ENERAL

78. Refer to Figure SQ-75. The small piston has an area A 1 of 8 square inches, and the large piston has an area A2 of 32 square inches. In order to force the large piston upward for a distance D2 of 0.5 inch, the small piston must move down a distance D 1 of inches. Page 118

79. A piston whose area is 30 square inches, when moved 20 inches, will force _ __________ _

cubic inches of fluid from a cylinder. Page 121

80. The velocity of a moving fluid is a form of ___________ _ (kinetic or potential) energy. Page 121

81. Pressure of a moving fluid is a form of ___________ _ (kinetic or potential) energy. Page 122

82. If energy is neither added to nor taken from fluid in motion, when the velocity of the fluid increases, the pressure will (increase or decrease). Page 122

83. When a 10-pound block of wood floats in a container of water, it displaces __________ _

pounds of water. Page 125

Vibration and Sound Vibration is one of the major problems in aircraft design. All physical ob-jects have a resonant frequency at which they will vibrate at the maximum intensity for a given amount of excitation. All moving parts of an aircraft and powerplant produce vibrations. It is important that no part of the aircraft structure is resonant at any frequency produced by the engine or any aerody-namic vibration.

frequency. The number of complete

cycles of a recurring event that takes place in one unit of time.

We are mindful of sound because of the unusual things that happen when any part of an aircraft moves through the air at the speed of sound.

Vibration Vibration is the up-and-down or back-and-forth movement of an object. Vibrations use up energy and cause wear. Vibration affects almost all me-chanical devices, and airplanes and helicopters are especially affected, be-cause they are built without the extra weight needed to absorb vibrations.

B ASIC PHYSICS Chapter 3 127

Figure 3-76. A playground swing is a form a,{ pendulum. Its period, or the time needed for one complete cycle, is determined by its length.

resonance. The condition of a vibrating object that causes it to have the greatest amplitude of vibration for the amount of energy put into it.

I DIRECTION OF WAVE TRAVEL>

Transverse wave

Longitudinal wave

t ~

Figure 3-77. In a transverse wave, the particles in motion rise above and drop below their original position, and the wave travels away from. the point of disturbance. In a longitudinal wave, the particles in motion move back and forth parallel to the direction the wave is moving.

128

Resonance Every natural body has a frequency at which it vibrates most easily, and this is called its resonant frequency. Any time the body is disturbed, it vibrates at this particular frequency. Resonance is extremely important in aircraft de-sign and maintenance because vibrations at the resonant frequency of an air-craft part can actually cause its destruction.

Think about a playground swing, which is a form of pendulum. A person weighing 100 pounds can be swung well above your head with only some very small pushes, but the pushes must be done at exactly the frequency at which the swing is resonant. See Figure 3-76.

If the swing is resonant at 30 cycles per minute, its period, or time re-quired for one complete cycle, is 2 seconds. We must push the swing every 2 seconds exactly, to keep it swinging. We can start it swinging and keep it swinging at this frequency with very little energy, but we cannot make it swing any faster nor can it swing any slower and remain resonant.

When an aircraft is designed and the prototype is built, it is subjected to an intense series of vibration tests. Electronic transducers are connected to the aircraft structure, the structure is vibrated through a w ide range of frequen-cies, and the amount of movement of the structure is measured. When the transducer produces the frequency at which the structure is resonant, the amplitude of vibration increases tremendously.

When the engineers identify the resonant frequencies of all the parts of the structure, and the frequencies of vibrations caused by the engines, the propellers, the exhaust systems, and disturbances of air flowing over the surface of the structure, revisions are made in the design that either change the resonant frequencies of the structure or eliminate the vibrations in these ranges. Helicopters are especially affected by vibration caused by the chang-ing aerodynamic forces produced by the spinning rotors.

Sound We normally think of sound as something we hear. But the human ear can-not hear all sound; that which we hear is only a small part of what is techni-cally known as sound, a form of mechanical energy that is transmitted by longitudinal pressure waves.

There are two different kinds of waves that occur in nature, transverse and longitudinal waves. When we drop a stone into a pool of calm water, transverse waves form ripples. These ripples begin where the stone enters the water, and they move out in concentric circles. The particles of water rise and fall above and below the normal level of the water, and the wave motion moves away from the point of the disturbance. The ripples are the highest at the center and become smaller as they spread out. As the distance doubles from the point the stone struck the water, the wave height decreases to one fourth of its original height. See Figure 3-77.

AVIATION M Al "T E!\ANCE T ECHNICIAN SER IES GENERAL

Sound waves are a form of longitudinal wave. Rather than the particles of air moving up and down, they move back and forth parallel to the direction the wave is traveling. When we strike a tuning fork so its tines vibrate, sound is produced. This sound is caused by the tines of the fork alternately pushing and pulling on the air. When the fork moves toward us, it pushes on the air and moves the molecules of air c loser together. Then, as it moves away from us, it pulls back on the molecules. This is called compressing and rarefying the air. When the air with this motion in it strikes our ears, our ear drums vibrate back and forth exact! y as the tines of the tuning fork vibrate, and we hear the sound. See Figure 3-78.

The number of complete cycles of sound energy that take place in one second is called the frequency of the sound; and the amount of change in sound pressure is called the intensity of the sound.

Vibrations above the range we can hear, called ultrasonic vibrations, have a very important place in the technical world. They are used for such things as nondestructive inspection and parts cleaning, as well as for forcing bubbles out or some liquids.

Sound Intensity The basic unit for measuring sound intens ity is the decibel, abbreviated dB. One dB is the smallest change in sound intensity the human ear can detect. The ticking of a small watch makes a sound of about one dB. Soft music used as a background in some homes and offi ces is around 60 dB , and very loud music can have as much as 100 decibels of sound energy. Any sound above about I 30 decibels can vibrate ear drums enough to cause pain.

Speed of Sound Sound travels at different speeds in different materials. Some materials are good conductors of sound and others act as effective sound insulators. Air, like all gases, is a poor conductor of sound, liquids such as water are better conductors, and solids are the best conductors. Generally, the more dense the solid material is, the better it is as a conductor of sound.

Sound waves travel in air at approximately 761 miles per hour, depend-ing on the temperature. In water, they travel much faster, and in iron or steel, they travel still faster.

The speed at which sound travels in the air has become of increasing importance in the fie ld of aviation. This is because we are now able to build airplanes that can Jly at the speed of sound and even much faster. When an airplane passes through the air. the air flowing over its surface is disturbed, and sound waves are set up that radiate out in all directions from the surface.

If the airplane itself moves as fast as the sound waves can travel in the air, these waves cannot go out ahead of it. Instead, they pile up in front of the aircraft, like the wave in front of a boat; and since the sound waves are waves of pressure, all of thi s pressure I ies a long a very thin line. We call this a shock wave, and it produces the familiar sonic boom (see Figure 3-79). When air llows through a shock wave, the velocity of the airflow decreases and its static pressure increases.

B ASIC PHYSICS

\ !\ !))))))))))))))))))))))))))))))))))))))))))))))))))))) 1 1 1 1 I b ompression

Rarefaction

Tuning fork

Figure 3-78. When the ti11es of a tuning fork vibrate, they cause the particles of air to be alternately compressed and rarefied. This longitudinal wave affects our ear drums so we hear sound.

tines. The prongs which eJdend from a fo rk-like object.

decibel (acous tic). The ba~ic unit for measuring sound intensity. One decibel (dB) is the smallest change in sound intensity the normal human car can detect.

Shock wave

I

Figure 3-79. When the source of sound moves at the speed of sound, the sound waves cannot move ow ahead of the source. They pile up and form a shock wave that causes the familiar sonic boom.

Chapter 3 129

Shock waves form on an aircraft when air flows over the surface at the speed of sound. And the speed of sound is not constant; it varies with the tempera-ture of the air.

At sea level, with a standard temperature of I5C, the speed of sound is 661.2 knots. At 10,000 feet, the standard temperature of the air drops to -4.8C, and the speed of sound is down to 638.0 knots.

At 20,000 feet the standard temperature is -24.6C and the speed of sound is 614.1 knots. The temperature continues to drop until we reach an altitude of approximately 36,000 feet. At this altitude, the temperature is -56.2C, and the speed of sound is 573.7 knots. It remains at this value even though the pressure of the ai r continues to drop, until an altitude of approximately 82.000 feet is reached. Above this altitude the temperature begins to rise and the speed of sound starts back up.

When an airplane is flying at the speed of sound. it is said to be flying at a speed of Mach one. When it is flying at a speed of 75% of the speed of sound, it is flying at a speed of Mach 0.75.

STUDY QUESTIONS: VIBRATION AND SOUND

Answers are on Page 136. Page numbers refer to chapter text.

84. The number of complete cycles of sound energy that take place in one second is called the ____________ of the sound. Page 127

85. Vibrations at a frequency higher than the human ear is capable of hearing are called ____________ vibrations. Page 129

86. The amount of change in the sound pressure is cal led the ___________ _

Page 129

87. The smallest change in sound intensity the human ear can detect is called one ____________ of sound energy. Page 129

of the sound.

88. When an airplane travels faster than the speed of sound, the pressure waves from air disturbances on its

surface cannot move out ahead of the airplane. These pressure waves pile up and form a ____________ wave. Page 129

89. The speed of sound varies with the __________ _ (pressure or temperature) of the air.

Page 129

130 A VIATIO\ M Al \ I U\ \NCI-. TH"H"CI \N SicRIES G E\ERAL

90. The freq uency at which any natural body vibrates most easily is called the ___________ _

frequency of the body. Page 128

9 1. The resonant freq uency of a pendulum is determined by its ___________ . Page 128

Light Visible light is a form of electromagnetic energy having a very limited f re-quency range. It is of extreme importance to us because it is light that en-ables us to see.

Natural Light Like most of the energy on the earth, most light comes from the sun. in waves of electromagnetic radiation; but only an extremely small portion of this energy produces light that is visible to the human eye. Only e lectromagnetic waves whose wavelengths are in the range between 0.000 038 to 0.000 078 centimeter arc visible, and rather than using such small terms when we speak of the wavelength of visible light, we use a system called angstroms. One angstrom, abbreviated A, is equal to Ill 0,000,000 o f a meter (1 10 10 or 0.000 000 000 1 meter). Using this system, the wavelength of visible light extends from about 3,800 A to about 7,800 A. See F igure 3-80.

,.,,

:-?t~ Wavelength Typeotwave 1,000

100 Miles

10

1

1,000 Radio waves

100 Feet .

10

1

1

0.1

0.01 Infrared Inches 0.001

VISIBLE LIGHT

1 X 106 Ultraviolet

angstrom . A convenient unit used to measure the wavelength of light. One angstrom, or A, i~ equal to I II 0.000,000 meter. The wavelength~ of visible light are between about 3,800 and 7,800 angstroms.

color . The characteristic of light that is caused by the different wavelengths of electromagnetic energy that make up lighL Violet light has the shortest wave lengths, and red has the longest.

1 X 109

1 X 10"12 X-rays and gamma rays

F igure 3-80. Visible light makes 11p only a 1ery small portion of the 1pectn1111 of electromagnetic radiation. We can see only the electromag-netic ll'mes ahose length is between 0.000 038 and 0.000 078 centimeters.

B ASIC' P HYSICS Chapter 3 131

90. The frequency at which any natural body vibrates most easily is called the ___________ _

frequency of the body. Page 128

91. The resonant frequency of a pendulum is determined by its _ __________ . Page 128

Light Visible light is a form of electromagnetic energy having a very limited fre-quency range. It is of extreme importance to us because it is light that en-ables us to see.

Natural Light Like most of the energy on the earth, most light comes fro m the sun. in waves of electromagnetic radiation; but only an extremely small portion of this energy produces light that is visible to the human eye. Only electromagnetic waves whose wavelengths are in the range between 0.000 038 to 0.000 078 centimeter are visible, and rather than using such small terms when we speak or the wavelength of visible light, we use a system called angstroms. One angstrom, abbreviated A, is equal to 1/10,000,000 of a meter ( I I0- 10 or 0.000 000 000 I meter). Using this system, the wavelength of visible light extends from about 3,800 A to about 7,800 A. See Figure 3-80.

.

.-~:.:s~ Wave.length TYpe of wave 1,000

100 Miles

10

1

1,000 Radio waves

100 Feet .

10

1

1

0.1

0 .01 Infrared Inches 0.001

VISIBLE LIGHT

1 X 10-6 Ultraviolet

a ngst rom . A convenient unit used to measure the wavelength of light. One angstrom. or A, is equal to 1/10,000,000 meter. The wavelengths of visible light are between about 3.800 and 7,800 angstroms.

color . The characterist ic of light that is caused by the different wavelengths of electromagnetic energy that make up light. Violet light has the shortest wave lengths, and red has the longest.

1 X 109 X-rays

1 X 1Q12 and gamma rays .

Figure 3-80. Visible light makes up mrly a l'ery small portion of tire spectrum of electromagnetic radiation. We can see only tire electromag-netic 11'1\'es 11-lwse length is between 0.000 038 and 0.000 078 centimeters.

B ASIC P HYSICS Chapter 3 131

Figure 3-81. Light travels from its so-urce in a straight Line. /fa beam of light is interrupted, a shadow is formed.

Figure 3-82. When light passes through a hole, it spreads ow. The closer the hole is to the source, the more the light spreads out.

Inverse Square Law. The inte nsity of a physical quantity varies inversely with the square of the distance between the source and the point at which it acts .

132

Characteristics of Light Light, like any other form of energy, obeys certain laws of physics, and while some of its characteristics can be changed, its basic energy can be neither created nor destroyed.

Light Travels in Straight Lines Because we see shadows, we know that the waves of light energy leaving a source of light travel in straight lines. If we shine a spotlight on a light-colored wall in a dark room, it fom1s a circle of light on the wall. But if we hold the corner of a card between the I ight and the wall, part of the circle of light is blocked, and a shadow the shape of the part of the card in the beam shows up in the circle. Since the light is traveling in straight lines, it does not fill in the part of the circle that is blocked by the card. See Figure 3-81.

Light Spreads Out as it Leaves its Source Light from a source such as the candle we see in Figure 3-82 travels out from the source in waves.lf we hold a piece of cardboard with a hole in it in front of the candle, we can see the way light spreads out as it comes through the hole. The closer the cardboard is to the light, the more the light spreads.

Since the light spreads out as it travels away from the source, the amount of illumination decreases as the square of the distance from the source increases. In Figure 3-83, we have a candle 4 inches away from a card that has a hole cut in it. The hole is I inch square. If we hold a piece of white paper 4 inches from the card, we have doubled the distance between the source and the card, and the same amount of light that came through the !-square-inch hole has now spread out to light up 4 square inches of area.

Each square inch of area that is lighted gets only \/4 of the light that passed through the hole in the card. Now. if we move the paper 12 inches away from the candle (3 times the original distance), the light passing through the hole in the card is spread out over 9 square inches of area. And each square inch gets only 1/ 9 of the light that came through the hole. When the paper is moved out 16 inches (4 times the original distance), each square inch will receive only \/16 of the light.

This experiment demonstrates an important law of physics, called the In-verse Square Law: "The amount of light from a point source that falls on a surface is inversely proportional to the square of the distance between the source and the surface." See Figure 3-83.

AVIATIO:\ MAINTENANCE TECH~ICIAN SERIES G EI\ERAL

-c: 4 inches--+

Figure 3-83. Light obeys the Inverse Square Law. The light that illuminates a suiface spreads olll as it gets farther from the source. If we double the distance between the source of light and the swface on which it falls, the same amount of light that fell on one square unil of smface spreads out Ol'er 4 square unils. Each square unil of suiface recei1es one-quar/er of !he light.

The Law of Reflection

If we have a po int source of light that shines on a mirror, the light will be reflected, or bounced, off the surface, and it will travel in a special direction. Tn Figure 3-84 there is a line that is normal, or perpendicular to, the surface of the mirror, and the beam of light which strikes the mirror forms an angle with this normal line . This angle is called the ang le of incidence. The reflec-tion of the point source of light can be seen only along a line that extends up from the mirror at an angle (called the ang le of reflectance) that is exactly the same as the angle of incidence. We can move the reflected spot of light wherever we want by changing the angle of incidence, which also changes the angle of reflectance.

Normal

Angle of incidence ~

Point

Mirror

Figure 3-84. The angle of rejleuance of a light beam is always exactly the same as the angle of incidence.

B ASIC P HYSICS Chapter 3 133

A

B

Figure 3-85 A. Light reflects from a smooth surface and causes sharp-edged shadows if it is blocked. B. When light strikes a rough surface, it is diffused, or scattered. it does not cause sharp-edged shadows.

Normal

Velocity in air

Figure 3-86. The speed at which light travels through glass is less than its speed through air, so a beam of light is refracted (bent) as it passes through glass.

134

Diffusion of Light When parallel rays of light strike a smooth surface, all of them have the same angle of incidence and the same angle of reflectance; they leave the surface as a beam just like the beam from the source. Any object that interrupts the reflected beam causes a shadow, since none of the light can get behind the object.

If the parallel rays strike a rough, or irregular, surface, the reflected rays no longer form a beam. Instead, they bounce out in all directions. Any object that interrupts these reflected rays of light does not form a sharp shadow because some of the light gets behind it.

Most incandescent light bulbs used for home lighting are frosted, or have a rough surface on the inside. This rough surface diffuses the light leaving the bulb, and it produces a more even lighting than would be produced if the filament were inside a clear bulb. See Figure 3-85.

Speed of Light Experiments have proven that light travels at an extremely fast speed, about 186,000 miles a second as it travels to Earth from the sun or from the stars through empty space. But the speed of light is different as it passes through different substances. For example, light in water travels 139,000 miles per second, and through glass, it is slowed down to 124,000 miles per second.

When a beam of light shines through a glass plate at an angle, such as we see in Figure 3-86, the light slows down. The beam changes its angle as it travels through the glass. The amount the angle changes is determined by the density of the glass. The denser the glass, the slower the light travels, and the more the beam is bent. When the beam leaves the glass, it speeds up and leaves at the same angle it entered.

Light is refracted, or bent, in camera lenses to make images appear larger or smaller, and in eyeglasses, light is refracted to correct any faulty refrac-tion of light by the natural lenses in our eyes. A common example of re-fraction occurs when an object like a spoon is placed in a glass of water. See Figure 3-87.

Figure 3-87. The spoon appears to bend when a part of it is seen through air and a part is seen through the water. The shape of the glass and the water forms a lens that magnifies the spoon.

AVIATION MAINTENANCE TECHNICIAN SERIES GENERAL

STUDY QUESTIONS: LIGHT

Answers are on Page 136. Page numbers refer to chapter text.

92. Our main source of natural light is the ___________ . Page I 31

93. When we double the distance between a source of light and the surface on which it falls, the amount of illumination on the surface decreases to (what fraction) of the original illumination. Page 133

94. When a beam of light strikes a smooth surface and is reflected, the angle of incidence is always the same as the angle of . Page 134

95. Light travels through empty space at the rate of second. Page 134

_ _ _ ______ (how many) miles per

96. Light travels ___________ (faster or slower) when it passes through glass than it does

when it is passing through air. Page 134

BASIC PHYSICS Chapter 3 - 135 --

Answers to Chapter 3 Study Questions

1. matter

2. molecule

3. elements

4. protons, neutrons, electrons

5. protons, neutrons

6. electrons

7. negative

8. solid, liquid, gaseous

9. no 10. ice, steam

11. solid

12. liquid

13. gas 14. heat

15. mass 16. weight

17. weight

18. density 19. specific gravity

20. float

21. 50.5

22. sun

23. potential

24. kinetic

25. nucleus 26. control

27. heat exchanger

28. 750

29. 120 30. 1.14

31. force

32. acceleration 33. 200

34. arm 35. moment

36. zero 37. 10

38. 120

136

39. 12

40. 400

4 1. velocity 42. gravity

43. centrifugal

44. centripetal

45. direction, magnitude 46. 11.1 8, 26.6

47. 12.75, 138.5

48. 13.86, 245 49. a. tension

b. compression c. torsion d. shear e. bending

50. a. tension b. compression

51. 45

52. compression 53. strained

54. expands 55. heat

56. calorie

57. British thermal unit

58. sensible 59. latent

60. less

61 . a. conduction b .. convection c. radiation

62. zero 63. a. 16.67

b. 143.6 c. 93.3 d. 392 e. 773 f. 227 g. 960 h.40

64. pressure

A VIATIO:\' M AINTENANCE T ECH:\ICIAN SERIES

65. absolute

66. a. 760 b. 14.69 c. 29.92 d. 1013.2 e. I

67. increase

68. increase 69. increase

70. absolute 71. a. 8.98

b. 5.98 c. 14.96

72. incompressible 73. compressible

74. a. height of the column b. density of the fluid

75. 10

76. 10 77. 2

78. 2

79. 600

80. kinetic 81. potential

82. decrease

83. 10

84. frequency

85. ultrasonic

86. intensity

87. decibel

88. shock

89. temperature 90. resonant

91. length

92. sun

93. 1/ 4

94. reflectance

95. 186,000

96. slower

G ENERAL