# AMT Handbook - General # Chapter 5: Physics for Aviation ## Heat Heat is a form of energy. It is produced only by the conversion of one of the other forms of energy. Heat may also be defined as the total kinetic energy of the molecules of any substance. Some forms of energy which can be converted into heat energy are as follows: - Mechanical Energy—this includes all methods of producing increased motion of molecules such as friction, impact of bodies, or compression of gases. - Electrical Energy—electrical energy is converted to heat energy when an electric current flows through any form of resistance such as an electric iron, electric light, or an electric blanket. - Chemical Energy—most forms of chemical reaction convert stored potential energy into heat. Some examples are the explosive effects of gunpowder, the burning of oil or wood, and the combining of oxygen and grease. - Radiant Energy—[[electromagnetism|electromagnetic]] waves of certain frequencies produce heat when they are absorbed by the bodies they strike such as x-rays, light rays, and infrared rays. - Nuclear Energy—energy stored in the nucleus of atoms is released during the process of nuclear fission in a nuclear reactor or atomic explosion. •Sun—all heat energy can be directly or indirectly traced to the nuclear reactions occurring in the sun. When a gas is compressed, work is done and the gas becomes warm or hot. Conversely, when a gas under high pressure is allowed to expand, the expanding gas becomes cool. In the first case, work was converted into energy in the form of heat; in the second case heat energy was expended. Since heat is given off or absorbed, there must be a relationship between heat energy and work. Also, when two surfaces are rubbed together, the friction develops heat. However, work was required to cause the heat, and by experimentation, it has been shown that the work required and the amount of heat produced by friction is proportional. Thus, heat can be regarded as a form of energy. According to this theory of heat as a form of energy, the molecules, atoms, and electrons in all bodies are in a continual state of motion. In a hot body, these small particles possess relatively large amounts of kinetic energy, but in cooler bodies they have less. Because the small particles are given motion, and hence kinetic energy, work must be done to slide one body over the other. Mechanical energy apparently is transformed, and what we know as heat is really kinetic energy of the small molecular subdivisions of matter. ### Heat Energy Units Two different units are used to express quantities of heat energy. They are the calorie and the BTU. One calorie is equal to the amount of heat required to change the temperature of 1 gram of water 1 degree Centigrade. This term “calorie” (spelled with a lower case c) is 1/1,000 of the Calorie (spelled with a capital C) used in the measurement of the heat energy in foods. One BTU is defined as the amount of heat required to change the temperature of 1 lb of water 1 degree Fahrenheit (1 °F). The calorie and the gram are seldom used in discussing aviation maintenance. The BTU, however, is commonly referred to in discussions of engine thermal efficiencies and the heat content of aviation fuel. A device known as the calorimeter is used to measure quantities of heat energy. In application, it may be used to determine the quantity of heat energy available in 1 pound of aviation gasoline. A given weight of the fuel is burned in the calorimeter, and the heat energy is absorbed by a large quantity of water. From the weight of the water and the increase in its temperature, it is possible to compute the heat yield of the fuel. A definite relationship exists between heat and mechanical energy. This relationship has been established and verified by many experiments which show that: $\text{On BTU of heat energy} = \text{778 ft-lb of work}$ As discussed earlier in this chapter under the topic “Potential Energy,” one pound of aviation gasoline contains 18,900 BTU of heat energy. Since each BTU is capable of 778 ft-lb of work, 1 lb of aviation gasoline is capable of 14,704,200 ft-lb of work. ### Heat Energy and Thermal Efficiency Thermal efficiency is the relationship between the potential for power contained in a specific heat source, and how much usable power is created when that heat source is used. The formula for calculating thermal efficiency is: $\text{Thermal Efficiency} = \text{Horsepower Produced} \div \text{Potential Horsepower in fuel}$ For example, consider the piston engine used in a small general aviation airplane, which typically consumes 0.5 lb of fuel per hour for each horsepower it creates. Imagine that the engine is creating 200 hp. If we multiply 0.5 by the horsepower of 200, we find the engine is consuming 100 lb of fuel per hour, or 1.67 lb per minute. Earlier in this chapter, one horsepower was found to be 33,000 ft-lb of work per minute. The potential horsepower in the fuel burned for this example engine would be: $\begin{align*} Hp &= \frac{1.67lb/minute \times 18,900BTU/lb \times 778ft-lb/BTU}{33,000ft-lb/min}\\ Hp &= 744\\ \end{align*}$ The example engine is burning enough fuel that it has the potential to create 744 horsepower, but it is only creating 200. The thermal efficiency of the engine would be: $\begin{align*} \text{Thermal Efficiency } &= \text{Hp Produced} \div \text{Hp in fuel}\\ &= 200 \div 744\\ &= 0.2688 \text{ or } 26.88%\\ \end{align*}$ ### Heat Transfer There are three methods by which heat is transferred from one location to another or from one substance to another. These three methods are conduction, convection, and radiation. #### Conduction Heat transfer always takes place by areas of high heat energy migrating to areas of low heat energy. Heat transfer by conduction requires that there be physical contact between an object that has a large amount of heat energy and one that has a smaller amount of heat energy. Everyone knows from experience that the metal handle of a heated pan can burn the hand. A plastic or wood handle, however, remains relatively cool even though it is in direct contact with the pan. The metal transmits the heat more easily than the wood because it is a better conductor of heat. Different materials conduct heat at different rates. Some metals are much better conductors of heat than others. Aluminum and copper are used in pots and pans because they conduct heat very rapidly. Woods and plastics are used for handles because they conduct heat very slowly. ![[5-27.png|350]] *[[5-27.png|Figure 5-27 ]]* illustrates the different rates of conduction of various metals. Of those listed, silver is the best conductor and lead is the poorest. As mentioned previously, copper and aluminum are used in pots and pans because they are good conductors. It is interesting to note that silver, copper, and aluminum are also excellent conductors of electricity. Liquids are poorer conductors of heat than metals. Notice that the ice in the test tube shown in *[[5-28.png|Figure 5-28 ]]* is notmelting rapidly even though the water at the top is boiling. The water conducts heat so poorly that not enough heat reaches the ice to melt it. ![[5-28.png|350]] Gases are even poorer conductors of heat than liquids. It is possible to stand quite close to a stove without being burned because air is such a poor conductor. Since conduction is a process whereby the increase in molecular energy is passed along by actual contact, gases are poor conductors. At the point of application of the heat source, the molecules become violently agitated. These molecules strike adjacent molecules causing them to become agitated. This process continues until the heat energy is distributed evenly throughout the substance. The gases are much poorer conductors of heat because molecules are farther apart in gases than in solids. Materials that are poor conductors are used to prevent the transfer of heat and are called heat insulators. A wooden handle on a pot or a soldering iron serves as a heat insulator. Certain materials, such as finely spun glass or asbestos, are particularly poor heat conductors. These materials are therefore used for many types of insulation. #### Convection Convection is the process by which heat is transferred by movement of a heated fluid (gas or liquid). For example, an incandescent light bulb will, when heated, become increasingly hotter until the air surrounding it begins to move. The motion of the air is upward. This upward motion of the heated air carries the heat away from the hot light bulb by convection. Transfer of heat by convection may be hastened by using a ventilating fan to move the air surrounding a hot object. The rate of cooling of a hot electronics component, such as the CPU in a computer, can be increased if it is provided with copper fins that conduct heat away from the hot surface. The fins provide large surfaces against which cool air can be blown. A convection process may take place in a liquid as well as in a gas. A good example of this is a pan of water sitting on the stove. The bottom of the pan becomes hot because it conducts heat from the surface it is in contact with. The water on the bottom of the pan also heats up because of conduction. As the heated water starts to rise and cooler water moves in to take its place, the convection process begins. When the circulation of gas or liquid is not rapid enough to remove sufficient heat, fans or pumps are used to accelerate the motion of the cooling material. In some installations, pumps are used to circulate water or oil to help cool large equipment. In airborne installations, electric fans and blowers are used to aid convection. ![[5-29.png|350]] An aircraft air-cooled piston engine is a good example of convection being used to transfer heat. The engine shown in *[[5-29.png|Figure 5-29 ]]* is a Continental IO-520, with six heavily finned air-cooled cylinders. This engine does not depend on natural convection for cooling, but rather forced air convection coming from the propeller on the engine. The heat generated inside the engine finds its way to the cylinder cooling fins by conduction, meaning transfer within the metal of the cylinder. Once the heat gets to the fins, forced air flowing around the cylinders carries the heat away. #### Radiation Conduction and convection cannot wholly account for some of the phenomena associated with heat transfer. For example, the heat one feels when sitting in front of an open fire cannot be transferred by convection because the air currents are moving toward the fire. It cannot be transferred through conduction because the conductivity of the air is very small, and the cooler currents of air moving toward the fire would more than overcome the transfer of heat outward. Therefore, there must be some way for heat to travel across space other than by conduction and convection. The existence of another process of heat transfer is still more evident when the heat from the sun is considered. Since conduction and convection take place only through some medium, such as a gas or a liquid, heat from the sun must reach the earth by another method, since space is an almost perfect vacuum. Radiation is the name given to this third method of heat transfer. The term “radiation” refers to the continual emission of energy from the surface of all bodies. This energy is known as “radiant energy.” It is in the form of [[electromagnetism|electromagnetic]] waves, radio waves, or x-rays, which are all alike except for a difference in wave length. These waves travel at the velocity of light and are transmitted through a vacuum more easily than through air because air absorbs some of them. Most forms of energy can be traced back to the energy of sunlight. Sunlight is a form of radiant heat energy that travels through space to reach the earth. These [[electromagnetism|electromagnetic]] heat waves are absorbed when they come in contact with nontransparent bodies. The result is that the motion of the molecules in the body is increased as indicated by an increase in the temperature of the body. The differences between conduction, convection, and radiation may now be considered. First, although conduction and convection are extremely slow, radiation takes place at the speed of light. This fact is evident at the time of an eclipse of the sun when the shutting off of the heat from the sun takes place at the same time as the shutting off of the light. Second, radiant heat may pass through a medium without heating it. In application, the air inside a greenhouse may be much warmer than the glass through which the sun’s rays pass. Third, although heat transfer by conduction or convection may travel in roundabout routes, radiant heat always travels in a straight line. For example, radiation can be cut off with a screen placed between the source of heat and the body to be protected. ### Specific Heat One important way in which substances differ is in the requirement of different quantities of heat to produce the same temperature change in a given mass of the substance. Each substance requires a quantity of heat, called its specific heat capacity, to increase the temperature of a unit of its mass 1 °C. The specific heat of a substance is the ratio of its specific heat capacity to the specific heat capacity of water. Specific heat is expressed as a number which, because it is a ratio, has no units and applies to both the English and the metric systems. ![[5-30.png|350]] It is fortunate that water has a high specific heat capacity. The larger bodies of water on the earth keep the air and solid matter on or near the surface of the earth at a constant temperature. A great quantity of heat is required to change the temperature of a large lake or river. Therefore, when the temperature falls below that of such bodies of water, they give off large quantities of heat. This process keeps the atmospheric temperature at the surface of the earth from changing rapidly. The specific heat values of some common materials are listed in *[[5-30.png|Figure 5-30. ]]* ### 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. ![[5-31.png|350]] 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 minus 273 °C, meaning 273° below the freezing point of water. The relationships of the other fixed points of the scales are shown in *[[5-31.png|Figure 5-31. ]]* 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 as follows: $\begin{align*} &\text{Degrees Fahrenheit} = (1.8 \times \text{Degrees Celcius})+ 32\\ &\text{Degrees Celcius} = (\text{Degrees Fahrenheit}-32) \times \frac{5}{9}\\ &\text{Degrees Kelvin} = \text{Degrees Celcius} + 273\\ &\text{Degrees Rankine} = \text{Degrees Celcius} + 460\\ \end{align*}$ For purposes of calculations, the Rankine scale 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. ^bay7ay 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 Fahrenheit scale is commonly used in the United States, and most people are familiar with it. Therefore, the Fahrenheit scale is used in most areas of this book. ### Thermal Expansion/Contraction Thermal expansion takes place in solids, liquids, and gases when they are heated. With few exceptions, solids will expand when heated and contract when cooled. The expansion of solids when heated is very slight in comparison to the expansion in liquids and gases because the molecules of solids are much closer together and are more strongly attracted to each other. The expansion of fluids is discussed in the study of Boyle’s law. Thermal expansion in solids must be explained in some detail because of its close relationship to aircraft metals and materials. ![[5-32.png|350]] It is necessary to measure experimentally the exact rate of expansion of each one because some substances expand more than others. The amount that a unit length of any substance expands for a one degree rise in temperature is known as the coefficient of linear expansion for that substance. The coefficient of linear expansion for various materials is shown in *[[5-32.png|Figure 5-32.]]* To estimate the expansion of any object, such as a steel rail, it is necessary to know three things about it: its length, the rise in temperature to which it is subjected, and its coefficient of expansion. This relationship is expressed by the equation: $\text{Expansion} = \text{(coefficient)} \times \text{(length)} \times \text{(rise in temperature)}$ If a steel rod measures exactly 9 ft at 21 °C, what is its length at 55 °C? The coefficient of expansion for steel is $11 \times 10^{-6}.$ $\begin{align*} \text{Expansion} &= (11 \times 10^{-6}) \times (9 \text{ feet}) \times 34^{\circ}\\ \text{Expansion} &= 0.003366 \text{ feet} \end{align*}$ This amount, when added to the original length of the rod, makes the rod 9.003366 ft long. Its length has only increased by 4⁄100 of an inch. The increase in the length of the rod is relatively small, but if the rod were placed where it could not expand freely, there would be a tremendous force exerted due to thermal expansion. Thus, thermal expansion must be taken into consideration when designing airframes, power plants, or related equipment. ## Pressure Pressure is the amount of force acting on a specific amount of surface area. The force is typically measured in pounds and the surface area in square inches, making the units of pressure pounds per square inch or psi. If a 100-lb weight was placed on top of a block with a surface area of 10 in2, the average weight distribution would be 10 lb for each of the square inches (100 ÷ 10), or 10 psi. When atmospheric pressure is being measured, in addition to psi, other means of pressure measurement can be used. These include inches or millimeters of mercury, and millibars. Standard day atmospheric pressure is equal to 14.7 psi, 29.92 inches of mercury ("Hg), 760 millimeters of mercury (mm hg), or 1013.2 millibars. The relationship between these units of measure is as follows: $\begin{align*} 1 \text{ psi} &= 2.04 \text{ "Hg}\\ 1 \text{ psi} &= 51.7 \text{ mmHg}\\ 1 \text{ psi} &= 68.9 \text{ millibars}\\ \end{align*}$ ![[5-33.png|350]] The concept behind measuring pressure in inches of mercury involves filling a test tube with the liquid mercury and then covering the top. The test tube is then turned upside down and placed in an open container of mercury, and the top is uncovered. Gravity acting on the mercury in the test tube will try to make the mercury run out. Atmospheric pressure pushing down on the mercury in the open container tries to make the mercury stay in the test tube. At some point these two forces, gravity and atmospheric pressure, will equal out and the mercury will stabilize at a certain height in the test tube. Under standard day atmospheric conditions, the air in a 1-in2 column extending all the way to the top of the [[atmosphere]] would weigh 14.7 lb. A 1 in2 column of mercury, 29.92 inches tall, would also weigh 14.7 lb. That is why 14.7 psi is equal to 29.92 "Hg. *[[5-33.png|Figure 5-33]]* demonstrates this point. #### Gauge Pressure ![[5-34.png|350]] A [[Gauge Pressure]] (psig) is a reading that refers to when an instrument, such as an oil pressure gauge, fuel pressure gauge, or hydraulic system pressure gauge, displays pressure which is over and above ambient. This can be seen on the fuel pressure gauge shown in *[[5-34.png|Figure 5-34]]*. When the oil, fuel, or hydraulic pump is not turning, and there is no pressure being created, the gauge will read zero. #### Absolute Pressure ![[5-35.png|350]] A gauge that includes atmospheric pressure in its reading is measuring what is known as [[absolute pressure]], or psia. [[Absolute pressure]] is equal to [[Gauge Pressure]] plus atmospheric pressure. If someone hooked up a psia indicating instrument to an engine’s oil system, the gauge would read atmospheric pressure when the engine was not running. Since this would not make good sense to the typical operator, psia gauges are not used in this type of application. For the manifold pressure on a piston engine, a psia gauge does make good sense. Manifold pressure on a piston engine can read anywhere from less than atmospheric pressure if the engine is not supercharged, to more than atmospheric if it is supercharged. The only gauge that has the flexibility to show this variety of readings is the [[absolute pressure]] gauge. *[[5-35.png|Figure 5-35]]* shows a manifold pressure gauge, with a readout that ranges from 10 "Hg to 35 "Hg. Remember that 29.92 "Hg is standard day atmospheric. #### Differential Pressure Differential pressure, or psid, is the difference between pressures being read at two different locations within a system. For example, in a turbine engine oil system the pressure is read as it enters the oil filter, and as it leaves the filter. These two readings are sent to a [[transmitter]] which powers a light located on the flight deck. Across anything that poses a resistance to flow, like an oil filter, there will be a drop in pressure. If the filter starts to clog, the pressure drop will become greater, eventually causing the advisory light on the flight deck to come on. ![[5-36.png|350]] *[[5-36.png|Figure 5-36]]* shows a differential pressure gauge for the pressurization system on a Boeing 737. In this case, the difference in pressure is between the inside and the outside of the airplane. If the pressure difference becomes too great, the structure of the airplane could become overstressed. ## Gas Laws 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 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. ### 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 that 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 [[absolute pressure]] doubled, the volume was reduced to half the former value. As the applied absolute pressure was decreased, the resulting volume increased. From these observations, he concluded that for a constant temperature the product of the volume and [[absolute pressure]] of an enclosed gas remains constant. Boyle’s law is normally stated: “The volume of an enclosed dry gas varies inversely with its [[absolute pressure]], provided the temperature remains constant.” The following formula is used for Boyle’s law calculations. Remember, pressure needs to be in the absolute. $\begin{align*} \text {Volume 1} \times \text {Pressure 1} &= \text{Volume 2} \times \text {Pressure 2}\\ &\text{or}\\ \text{V}_1 \text{P}_1 &= \text{V}_2 \text{P}_2\\ \end{align*}$ ![[5-37.png|350]] Example: $10 ft^3$ of nitrogen is under a pressure of 500 psia. If the volume is reduced to $7 ft^3$, what will the new pressure be? *[[5-37.png|[Figure 5-37] ]]* $\begin{align*} \text{V}_1 \text{P}_1 &= \text{V}_2 \text{P}_2\\ 10(500) &= 7 (P_2)\\ 10(500) \div 7 &= P_2\\ P_2 &= 714.29 \text{ psia}\\ \end{align*}$ The useful applications of Boyle’s law are many and varied. Some applications more common to aviation are: (1) the carbon dioxide $(CO_2)$ 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. As a formula, this law is shown as follows: $\begin{align*} \text {Volume 1} \times \text {Absolute Temperature 2} &= \text{Volume 2} \times \text {Absolute Temprature 1}\\ &\text{or}\\ \text{V}_1 \text{T}_2 &= \text{V}_2 \text{T}_1\\ \end{align*}$ Charles’ law also works if the volume is held constant, and pressure and temperature are the variables. In this case, the formula would be as follows: $\text{P}_1 \text{T}_2 = \text{P}_2 \text{T}_1$ For this second formula, pressure and temperature must be in the absolute. Example: A 15-ft3 cylinder of oxygen is at a temperature of 70 °F and a pressure of 750 psig. The cylinder is placed in the sun and the temperature of the oxygen increases to 140 °F. What would be the new pressure in psig? $\begin{align*} \text {70 degrees Fahrenheit} &= \text{530 degrees Rankine}\\ \text {140 degrees Fahrenheit} &= \text{600 degrees Rankine}\\ \text {750 psig} + 14.7 &= \text{764.7 psia.}\\ \text{P}_1 \text{T}_2 &= \text{P}_2 \text{T}_1\\ 764.7(600) &= \text{P}_2 (530)\\ \text{P}_2 &= 764.7(600) \div 530\\ \text{P}_2 &= 865.7 \text{ psia}\\ \text{P}_2 &= 851 \text{ psig} \end{align*}$ ### General Gas Law By combining Boyle’s and Charles’ laws, a single expression can be derived which states all the information contained in both. The formula which is used to express the general gas law is as follows: $\begin{align*} \frac {\text {Pressure 1 (Volume 1)}}{\text{Temperature 1}} &= \frac {\text {Pressure 2 (Volume 2)}}{\text{Temperature 2}}\\ &\text{or}\\ P_1 (V_1) (T_2) &= P_2 (V_2) (T_1)\\ \end{align*}$ When using the general gas law formula, temperature and pressure must be in the absolute. Example: 20 ft3 of the gas argon is compressed to 15 ft3. The gas starts out at a temperature of 60 °F and a pressure of 1,000 psig. After being compressed, its temperature is 90 °F. What would its new pressure be in psig? $\begin{align*} \text {60 degrees Fahrenheit} &= \text{520 degrees Rankine}\\ \text {90 degrees Fahrenheit} &= \text{550 degrees Rankine}\\ \text {1,000 psig} + 14.7 &= \text{1,014.7 psia.}\\ P_1 (V_1) (T_2) &= P_2 (V_2) (T_1)\\ 1,014.7 (20) (550) &= P_2 (15) (520)\\ \text{P}_2 &= 1,431 \text{ psia}\\ \text{P}_2 &= 1,416.3 \text{ psig} \end{align*}$ ### Dalton’s Law If a mixture of two or more gases that do not combine chemically is placed in a container, each 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.” ## Fluid Mechanics By definition, a fluid is any substance that is able to flow if it is not in some way confined or restricted. Liquids and gases are both classified as fluids, and often act in a very similar way. One significant difference comes into play when a force is applied to these fluids. In this case, liquids tend to be incompressible and gases are highly compressible. Many of the principles that aviation is based on, such as the theory of lift on a wing and the force generated by a hydraulic system, can be explained and quantified by using the laws of fluid mechanics. ### 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 or she can possibly lift in the air. ![[5-38.png|350]] The following experiment is illustrated in *[[5-38.png|Figure 5-38]]*. The overflow can is filled to the spout with water. The heavy metal cube is first weighed in still air and weighs 10 lb. It is then weighed while completely submerged in the water and it weighs 3 lb. The difference between the two weights is the buoyant force of the water. As the cube 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 cube. The volume of irregular shaped objects can also be measured by using this method. If this experiment is performed carefully, the weight of the water displaced by the metal cube exactly equals the buoyant force of the water, which the scale shows to be 7 lb. Archimedes (287–212 B.C.) performed similar experiments. As a result, 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 force on submerged objects, air exerts a buoyant force on objects submerged in it. The amount of buoyant force available to an object can be calculated by using the following formula: $\text{Buoyant Force} = \text{Volume of Object} \times \text{Density of Fluid Displaced}$ If the buoyant force is more than the object weighs, the object will float. If the buoyant force is less than the object weighs, the object will sink. For the object that sinks, its measurable weight will be less by the weight of the displaced fluid. Example: A 10-ft3 object weighing 700 lb is placed in pure water. Will the object float? If the object sinks, what is its measurable weight in the submerged condition? If the object floats, how many cubic feet of its volume is below the water line? $\begin{align*} \text{Buoyant Force} &= \text{Volume of Object} \times \text{Density of Fluid Displaced}\\ &= 10(62.4)\\ &= 624lb.\\ \end{align*}$ The object will sink because the buoyant force is less than the object weighs. The difference between the buoyant force and the object’s weight will be its measurable weight, or 76 lb. ![[5-39.png|350]] Two good examples of buoyancy are a helium filled airship and a seaplane on floats. An airship is able to float in the [[atmosphere]] and a seaplane is able to float on water. That means both have more buoyant force than weight. *[[5-39.png|Figure 5-39]]* is a DeHavilland Twin Otter seaplane, with a gross takeoff weight of 12,500 lb. At a minimum, the floats on this airplane must be large enough to displace a weight in water equal to the airplane’s weight. According to Title 14 of the Code of Federal Regulations (14 CFR) part 23, the floats must be 80 percent larger than the minimum needed to support the airplane. For this airplane, the necessary size of the floats would be calculated as follows: Divide the airplane weight by the density of water. $ 12,500 \div 62.4 = 200.3 ft^3$ Multiply this volume by 80%. $200.3 × 80\% = 160.2 ft^3$ Add the two volumes together to get the total volume of the floats. $200.3 + 160.2 = 360.5 ft^3$ By looking at the Twin Otter in *[[5-39.png|Figure 5-39]]*, it is obvious that much of the volume of the floats is out of the water. This is accomplished by making sure the floats have at least 80 percent more volume than the minimum necessary. ![[5-40.png|350]] Some of the large Goodyear airships have a volume of 230,000 ft3. Since the fluid they are submerged in is air, to find the buoyant force of the airship, the volume of the airship is multiplied by the density of air $(.07651 lb/ft^3)$. For this Goodyear airship, the buoyant force is 17,597 lb. *[[5-40.png|Figure 5-40]]* shows an inside view of the Goodyear airship. The forward and aft ballonets are air chambers within the airship. Through the air scoop, air can be pumped into the ballonets or evacuated from the ballonets in order to control the weight of the airship. Controlling the weight of the airship controls how much positive or negative lift it has. Although the airship is classified as a lighter-than-air aircraft, it is in fact flown in a condition slightly heavier than air. ### Fluid Pressure ![[5-41.png|350]] The pressure exerted on the bottom of a container by a liquid is determined by the height of the liquid and not by the shape of the container. This can be seen in *[[5-41.png|Figure 5-41]]*, where three different shapes and sizes of containers are full of colored water. Even though they are different shapes and have different volumes of liquid, each one has a height of 231 inches. Each one would exert a pressure on the bottom of 8.34 psi because of this height. The container on the left, with a surface area of 1 in$^2$, contains a volume of 231 in$^3$ (one gallon). One gallon of water weighs 8.34 lb, which is why the pressure on the bottom is 8.34 psi. Still thinking about *[[5-41.png|Figure 5-41]]*, if the pressure was measured half way down, it would be half of 8.34, or 4.17 psi. In other words, the pressure is adjustable by varying the height of the column. Pressure based on the column height of a fluid is known as static pressure. With liquids, such as gasoline, it is sometimes referred to as a head of pressure. For example, if a carburetor needs to have 2 psi supplied to its inlet, or head of pressure, this could be accomplished by having the fuel tank positioned the appropriate number of inches higher than the carburetor. As identified in the previous paragraph, pressure due to the height of a fluid column is known as static pressure. When a fluid is in motion, and its velocity is converted to pressure, that pressure is known as ram. When ram pressure and static pressure are added together, the result is known as total pressure. In the inlet of a gas turbine engine, for example, total pressure is often measured to provide a signal to the fuel metering device or to provide a signal to a gauge on the flight deck. ### 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. When the pressure in the fluid is caused solely by the fluid’s height, the pressure against the walls of the container is equal at any given level, but it is not equal if the pressure at the bottom is compared to the pressure half way down. The concept of the pressure set up in a fluid, and how it relates to the force acting on the fluid and the surface area through which it acts, is Pascal’s law. In *[[5-41.png|Figure 5-41]]*, if a piston is placed at the top of the cylinder and an external force pushes down on the piston, additional pressure will be created in the liquid. If the additional pressure is 100 psi, this 100 psi will act equally and undiminished from the top of the cylinder all the way to the bottom. The gauge at the bottom will now read 108.34 psi, and if a gauge were positioned half way down the cylinder, it would read 104.17 psi, which is found by adding 100 plus half of 8.34. Pascal’s law, when dealing with the variables of force, pressure, and area, is dealt with by way of the following formula. $\text{Force} = \text{Pressure} \times \text{Area}$ In this formula, the force is in units of pounds, the pressure is in pounds per square inch (psi), and the area is in square inches. By transposing the original formula, we have two additional formulas, as follows: ![[5-42.png|350]] $\begin{align*} \text{Pressure} &= \text{Force} \div \text{Area}\\ &\text{and}\\ \text{Area} &= \text{Force} \div \text{Pressure}\\ \end{align*}$ An easy and convenient way to remember the formulas for Pascal’s law, and the relationship between the variables, is with the triangle shown in *[[5-42.png|Figure 5-42]]*. If the variable we want to solve for is covered up, the position of the remaining two variables shows the proper math relationship. For example, if the “A,” or area, is covered up, what remains is the “F” on the top and the “P” on the bottom, meaning force divided by pressure. ![[5-43.png|350]] The simple hydraulic system in *[[5-43.png|Figure 5-43]]* has 5 lb force acting on a piston with a 1/2 in$^2$ surface area. Based on Pascal’s law, the pressure in the system would be equal to the force applied divided by the area of the piston, or 10 psi. As shown in *[[5-43.png|Figure 5-43]]*, the pressure of 10 psi is present everywhere in the fluid. The hydraulic system in *[[5-44.png|Figure 5-44]]* is a little more complex than the one in *[[5-43.png|Figure 5-43]]* . In *[[5-44.png|Figure 5-44]]*, the input force of 5 lb is acting on a 1/2 in$^2$ piston, creating a pressure of 10 psi. The input cylinder and piston is connected to a second cylinder, which contains a 5 in$^2$ piston. The pressure of 10 psi created by the input piston pushes on the piston in the second cylinder, creating an output force of 50 pounds. ![[5-44.png|350]] Often, the purpose of a hydraulic system is to generate a large output force, with the input force being much less. In *[[5-44.png|Figure 5-44]]*, the input force is 5 lb and the output force is 50 lb, or 10 times greater. The relationship between the output force and the input force, as discussed earlier in this chapter, is known as mechanical advantage. The mechanical advantage in *[[5-44.png|Figure 5-44]]* would be 50 divided by 5, or 10. The following formulas can be used to calculate mechanical advantage. $\begin{align*} \text{Mechanical Advantage} &= \text{Force Out} \div \text{Force In}\\ &\text{or}\\ \text{Mechanical Advantage} &= \text{Distance Out} \div \text{Distance In}\\ \end{align*}$ Earlier in this chapter when simple machines, such as levers and gears were discussed, it was identified that no machine allows us to gain work. The same statement holds true for a hydraulic system, that we get no more work out of a hydraulic system than we put in. Since work is equal to force times distance, if we gain force with a hydraulic system, we must lose distance. We only get the same work out, if the system is 100 percent efficient. In order to think about the distance that the output piston will move in response to the movement of the input piston, the volume of fluid displaced must be considered. In the study of geometry, one learns that the volume of a cylinder is equal to the cylinder’s surface area multiplied by its height. So, when a piston of 2 in$^2$ moves down in a cylinder a distance of 10 in, it displaces a volume of fluid equal to 20$^3$ (2 in$^2$ × 10 in). The 20 in3 displaced by the first piston is what moves over to the second cylinder and causes its piston to move. In a simple two-piston hydraulic system, the relationship between the piston area and the distance moved is shown by the following formula. $\text{Input Piston Area (Distance Moved)} = \text{Output Piston Area (Distance Moved)} $ This formula shows that the volume in is equal to the volume out. This concept is shown in *[[5-45.png|Figure 5-45]]*, where a small input piston moves a distance of 20 inches, and the larger output piston only moves a distance of 1 inch. ![[5-45.png|350]] Example: A two-piston hydraulic system, like that shown in *[[5-45.png|Figure 5-45]]*, has an input piston with an area of 1/4 in$^2$ and an output piston with an area of 15 in$^2$. An input force of 50 lb is applied, and the input piston moves 30 inches. What is the pressure in the system, how much force is generated by the output piston, how far would the output piston move, and what is the mechanical advantage? $\begin{align*} \text{Pressure} &= \text{Force} \div \text{Area}\\ &= 50 \div \frac{1}{4}\\ &= 200\text{ psi}\\ \text{Force} &= \text{Pressure} \times \text{Area}\\ &= 200 \times 15\\ &= 300lb\\ \text{Mechanical Advantage} &= \text{Force Out} \div \text{Force In}\\ &= 3000 \div 50\\ &= 60\\ \text{Input Piston Area (Disntance Moved)}& = \text{Output Piston Area (Distance Moved)}\\ \frac{1}{4} (30) &= 15\text{ (Distance Moved)}\\ \frac{1}{4} (30) \div 15 &=\text{Distance Moved}\\ \text{Distance Moved}&= \frac{1}{2} in\\ \end{align*}$ Part of understanding Pascal’s law and hydraulics involves utilizing formulas, and recognizing the relationship between the individual variables. Before the numbers are plugged into the formulas, it is often possible to analyze the variables in the system and come to a realization about what is happening. For example, look at the variables in *[[5-45.png|Figure 5-45]]* and notice that the output piston is 20 times larger than the input piston, 5 $in^2$ compared to 1/4 in$^2$. That comparison tells us that the output force will be 20 times greater than the input force, and also that the output piston will only move 1/20 as far. Without doing any formula based calculations, we can conclude that the hydraulic system in question has a mechanical advantage of 20. ### Bernoulli’s Principle Bernoulli’s principle was originally stated to explain the action of a liquid flowing through the varying cross-sectional areas of tubes. In *[[5-46.png|Figure 5-46]]* a tube is shown in which the cross-sectional area gradually decreases to a minimum diameter in its center section. A tube constructed in this manner is called a “venturi,” or “venturi tube.” Where the cross-sectional area is decreasing, the passageway is referred to as a converging duct. As the passageway starts to spread out, it is referred to as a diverging duct. ![[5-46.png|350]] As a liquid, or fluid, flows through the venturi tube, the gauges at points “A,” “B,” and “C” are positioned to register the velocity and the static pressure of the liquid. The venturi in *[[5-46.png|Figure 5-46]]* can be used to illustrate Bernoulli’s principle, which states that: The static pressure of a fluid, liquid or gas, decreases at points where the velocity of the fluid increases, provided no energy is added to nor taken away from the fluid. The velocity of the air is kinetic energy and the static pressure of the air is potential energy. In the wide section of the venturi (points A and C of *[[5-46.png|Figure 5-46]]*), the liquid moves at low velocity, producing a high static pressure, as indicated by the pressure gauge. As the tube narrows in the center, it must contain the same volume of fluid as the two end areas. As indicated by the velocity gauge reading high and the pressure gauge reading low, in this narrow section, the liquid moves at a higher velocity, producing a lower pressure than that at points A and C. A good application for the use of the venturi principle is in a float-type carburetor. As the air flows through the carburetor on its way to the engine, it goes through a venturi, where the static pressure is reduced. The fuel in the carburetor, which is under a higher pressure, flows into the lower pressure venturi area and mixes with the air. Bernoulli’s principle is extremely important in understanding how some of the systems used in aviation work, including how the wing of an airplane generates lift or why the inlet duct of a turbine engine on a subsonic airplane is diverging in shape. The wing on a slow-moving airplane has a curved top surface and a relatively flat bottom surface. The curved top surface acts like half of the converging shaped middle of a venturi. As the air flow over the top of the wing, the air speeds up, and its static pressure decreases. The static pressure on the bottom of the wing is now greater than the pressure on the top, and this pressure difference creates the lift on the wing. Bernoulli’s principle and the concept of lift on a wing are covered in greater depth in “Aircraft Theory of Flight” located in this chapter. [[AMT General Handbook Ch5_3|➡️]]