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Properties | |
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Properties In order to determine if the aerodynamic forces on an object are sufficient to allow flight, the forces must be measured. The different contributions of the fluid moving around the object must be categorized and defined, and they must be quantified. There are specific qualities that are used to categorize and define these contributions. In the Measurements section, units were introduced to help quantify these qualities. In this section, these qualities, or properties, of a fluid are defined. These definitions will use the units defined in the previous section. Before the aerodynamic forces on an object can be computed, the properties of the fluid must be defined. These properties include the temperature, pressure, density and viscosity of the fluid. The values of the aerodynamic forces are dependent on defining the conditions of the problem. In addition, several other quantities are defined to help further understanding of aerodynamics. These include weight and gravity, velocity, and acceleration. Temperature The temperature of the fluid is an important part of how the fluid behaves. Hot oil, for example, flows faster than cold oil. Warm air rises and cold air drops in a room; house designers often place heat vents at the floor level because of this. Very cold water is lighter than cool water, so it rises to the top of a lake. That's why lakes freeze from the surface down. Sound travels farther on cold days than hot days. It is crucial then, to know the temperature of the fluid when computing aerodynamic quantities. As mentioned in the Measurements section, temperature has units of degrees Fahrenheit or degrees Celsius. Pressure The pressure of a fluid is another important consideration for computing aerodynamic forces. When a fluid moves over or through an object, it exerts small pushes on the surface of the object. These pushes are defined as the pressure exerted on the object. Pressure is measured as force per unit area, because the pushes occur over the entire surface of the object. The units for pressure include mass times a length divided by time squared (the units for a force) divided by the area of the surface (length squared). In metric units, pressure is measured in Newtons per square meter (N/m2) or Pascals (Pa). A Newton, a force unit, is 1 kilogram times 1 meter divided by seconds squared. A Pascal is 1 Newton per meter squared. In the English system, pressure is most commonly measured in pounds per square inch (psi). In either system, pressure is sometimes measured in atmospheres, a measure of how the pressure differs from the atmospheric pressure in a typical room on the earth's surface. Atmospheric pressure has been defined experimentally as 14.7 psi or 101 kPa. A kiloPascal (kPa) is 1000 Pascals. Sometimes pressure is given in inches of mercury (inHg) or millimeters of mercury (mmHg) because old-style manometers and barometers (instruments to measure pressure) used to measure the length of a thin column of mercury to compute the pressures. Pressure can be a powerful quantity. It can also be deceiving. A small pressure spread over a very large area can add up to be a very large force. Air pressures decrease as the altitude increases; pressures also decrease when the speed of the fluid increases. When the temperature of a fluid increases, so does the pressure. The rules that govern these changes are part of the study of aerodynamics, and the pressures on an airplane contribute directly to its flight capabilities! Density Density is a measure of how much mass (the amount of molecules) is included in a given volume. Another way to think about it is that it can be considered the measure of how tightly the molecules are packed in a volume or object. The units for density are mass per volume, or kg/m3, for example. When we talk about the density of a fluid, we often compute the density using a unit volume, say 1 m by 1m by 1m (1m3). We do this for two reasons: first, we don't have to know exactly how large our volume is (could be tough in the earth's atmosphere, or in a large ocean!), and second, it allows us to compare densities at different conditions - a hot day versus a cold day, or high altitudes versus lower altitudes. The units for density are mass per volume, and the most common measurements are kg/m3, slugs per gallon, or slugs per cubic foot (slugs/ft3). What is a slug? The US uses terms for mass and weight interchangeably, but science requires precise definitions of properties and their units. A slug is equal to 32.174 pounds mass. Scientists and engineers have defined the terms pounds force (lbf) and pounds mass (lbm) to help differentiate between a mass and a force like weight. A fluid with a lot of molecules tightly packed together has a high density; one that has fewer molecules would have a lower density. Water, for example, has a much higher density than air. A 10 gallon fish tank with water in it has much more mass in it than a 10 gallon tank with air in it. Since it has more mass, it will weigh more (more on that in a later section). In addition, the density is used to define whether a fluid is incompressible or compressible. If the density of the fluid is fixed (constant), the fluid is incompressible; neither the mass or the volume can change. Water (an incompressible liquid) poured from an 8 ounce cylindrical glass will still have 8 ounces in a large round bowl. The amount of mass and the volume stay the same. If the density can change, the fluid is compressible. Gases are compressible fluids; they will expand to fill a new volume. The mass doesn't change, but the volume increases, so the density of the gas decreases in the new volume. All of the properties are linked together. If the pressure or the temperature of a fluid changes, its density will usually change, too. The density of air on a hot day is lower than the density of air on a cold day. At high altitudes, where the pressure is lower, the density is also lower. This is why an aerodynamicist must pay attention to all of the properties of the fluid when trying to define flow conditions. Viscosity This is one of the most difficult properties on this list to define. It is a measure of how much a fluid will resist flowing. If you spill water on an inclined board, it will run quickly down the board. However, if you spill honey on the same board, it will travel down the board much more slowly. Honey has a much higher viscosity than water. It is said that honey is a more viscous fluid than water. The units for viscosity come from the mathematical definition of the property. When a fluid flows over a surface, it exerts a force (measured in Newtons, for example) on it. The viscosity is measured by dividing this force by the speed of the fluid flowing (meters per second, m/s) and the thickness of the fluid layer (meters). So the units for the viscosity are Newton-seconds per square meter (N s/m2). However, the convention used by scientists and engineers is to define the property using units of mass. Since a Newton is equal to a kilogram meter per second squared (kg m/s2), the more commonly used units are kilogram per meter second (kg/m s) for the metric system, and pounds mass per foot second (lbm/ft s) in the English system. Scientists and engineers will use the above definition for viscosity and call it the dynamic viscosity. Sometimes they will divide the dynamic viscosity by the density of the fluid to make another term that is called the kinematic viscosity. The units for the kinematic viscosity, then, are meters squared per second (m2/s) or feet squared per second (ft2/s). Force Forces have been defined as pushes or pulls on an object. To determine the units of a force, scientists and engineers use Newton's second law of motion (Sir Isaac Newton, 1643-1727). The second law states that a force on a moving object is equal to the mass of the object times the acceleration (a measure of its motion) of the object. This is most commonly written as F=ma. Since the units of mass are kilograms or slugs, and the units of acceleration are meters per second squared (m/s2) or feet per second squared (ft/s2), then the units of force are kilogram meters per second squared (kg m/s2) or slug feet per second squared (slug ft/s2). However, scientists and engineers have defined the Newton (N) as equal to the kg m/s2 and the pound force (lbf) as equal to the slug ft/s2. Since the slug is equal to 32.174 pounds mass (lbm), then 1 lbf is equal to 32.174 lbm ft/s2. **** figure to be added **** An interesting point about the force is that in addition to a value and units, it also has a direction associated with it. In the figure above, the force is applied to the box to the right, and the corresponding motion is to the right. If the force were applied down on the top of the box, no motion would occur; since the box is already on the ground, it can't move any further. No matter how large the force was, there would be no motion. So, defining a direction for a force is very important. Weight and Gravity In other countries, objects are measured in terms of their mass, in grams or kilograms. In the United States, however, people use the terms for weight interchangeably with mass. Here, things are measured in terms of their weight, using Newton's law, or F=ma. The mass of the object is multiplied by its acceleration and is defined as the weight. Weight is a force, not a mass. The acceleration used in this calculation is the acceleration due to gravity, or gravitational acceleration (sometimes called the gravitational constant and designated g). Now, most people think of gravity as a force, like the weight of an object, and this has become common usage. In fact, many people talk about the gravitational force, or the force due to gravity. Gravity is often defined as the attraction force between 2 objects. What is usually thought of as the gravitational force, however, is the weight of the object. Technically, scientists and engineers must be more precise. They define the weight of an object as its mass times the acceleration due to gravity based on the object's position. The acceleration due to gravity can change, depending on where the object is. For example, at the earth's surface through the lower atmosphere, the acceleration due to gravity is equal to 32.174 feet per second squared (ft/s2) or 9.81 meters per second squared (m/s2). However, if you go out to the outer limits of the earth's atmosphere, the acceleration due to gravity decreases. The attraction between the object and the earth is weakened. An object weighs slightly less out there, because the weight (a force) is still equal to the mass of the object (which is unchanged) times the acceleration due to gravity, which has decreased. This is why an object on the moon weighs less than the same object on the earth. The gravitational attraction on the moon is less than that of earth, so the acceleration due to gravity is less (about 1/6th that of the earth). When an object is weighed on the moon, it will weigh about 1/6th as much as the same object on earth, because the calculation is still F=ma. Since the acceleration due to gravity is 1/6th smaller, the weight (force) is 1/6th smaller, too. Velocity How fast an object moves is measured by its velocity. Velocity is calculated by dividing the distance traveled (a length) by the time it takes to traverse the distance. The units of velocity are length per time: for example, meters per second (m/s) or feet per minute (ft/min). If a person runs 10 kilometers in 1 hour, his or her velocity is 10 kilometers per hour (km/hr). If a car travels from Los Angeles, CA, to San Diego, CA, a distance of 120 miles, in 2 hours, its velocity is 60 miles per hour (mph). One exception to these units is a term held over from sailing days, the knot. In aeronautics, the velocity of the air is often measured in knots. One knot is equal to about 1.7 feet per second (ft/s). Rate and speed are two of the many terms used interchangeably with velocity. When engineers work with velocities, they must know the direction of the motion as well as the numerical value. They will sometimes call the numerical value the rate or speed, and then define a direction: the box was moved at a rate of 3 ft/s to the right, or the rocket traveled upwards at a speed of 120 m/s. Acceleration The acceleration is a measure of how the velocity of an object is changing over time. It can be found by computing the difference in velocities at first one time, then some time later, and dividing that by the difference in time. The units, then, are length per time divided by time, or length divided by time squared (m/s2 or ft/s2). If a car goes from 0 mph to 60 mph in 2 minutes (1/30 of an hour), then the acceleration of the vehicle is 1800 miles per hour squared (60 mph - 0 mph divided by 1/30 hr = 1800 miles/hr2)! If the car continued to accelerate at this value for an hour, its velocity at the end of the hour would be 1800 mph! However, if the same car is traveling at 60 mph when it passes a mileage marker, and it maintains its speed to pass the next mileage marker one minute later (speed equals 1 mile divided by 1/60 hr = 60 mph), then the acceleration is equal to zero (60 mph - 60 mph divided by 1/60 hr = 0 mph)! In other words, when the velocity doesn't change over time, the acceleration for that time period is zero. Engineers compute accelerations that are both increasing (positive) and decreasing (negative). In conversation, this rate of slowing down is often called deceleration.
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