Chapter 5
Physics for Aviation
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 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:
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.
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.
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 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:
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
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:
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. Figure 5-33 demonstrates this point.