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Aerodynamic

Aerodynamic

Aerodynamics is a branch of fluid dynamics concerned with the study of gas flows, first analysed by George Cayley in the 1800s. The solution of an aerodynamic problem normally involves calculating for various properties of the flow, such as velocity, pressure, density, and temperature, as a function of space and time. Understanding the flow pattern makes it possible to calculate or approximate the forces and moments acting on bodies in the flow. This mathematical analysis and empirical approximation form the scientific basis for heavier-than-air flight. Aerodynamic problems can be classified in a number of ways. The flow environment defines the first classification criterion. External aerodynamics is the study of flow around solid objects of various shapes. Evaluating the lift and drag on an airplane, the shock waves that form in front of the nose of a rocket or the flow of air over a hard drive head are examples of external aerodynamics. Internal aerodynamics is the study of flow through passages in solid objects. For instance, internal aerodynamics encompasses the study of the airflow through a jet engine or through an air conditioning pipe. The ratio of the problem's characteristic flow speed to the speed of sound comprises a second classification of aerodynamic problems. A problem is called subsonic if all the speeds in the problem are less than the speed of sound, transonic if speeds both below and above the speed of sound are present (normally when the characteristic speed is approximately the speed of sound), supersonic when the characteristic flow speed is greater than the speed of sound, and hypersonic when the flow speed is much greater than the speed of sound. Aerodynamicists disagree over the precise definition of hypersonic flow; minimum Mach numbers for hypersonic flow range from 3 to 12. Most aerodynamicists use numbers between 5 and 8. The influence of viscosity in the flow dictates a third classification. Some problems involve only negligible viscous effects on the solution, in which case viscosity can be considered to be nonexistent. The approximations to these problems are called inviscid flows. Flows for which viscosity cannot be neglected are called viscous flows.

Aerodynamic forces on aircraft

viscous flow One of the major goals of aerodynamics is to predict the aerodynamic forces on aircraft. The four basic forces that act on a powered aircraft are lift, weight (or gravity), thrust, and drag. Weight is the force due to gravity and thrust is the force generated by the engine. Lift and drag are forces due to the motion of the vehicle through the air. Lift is defined as the aerodynamic force acting perpendicular to the relative airflow and drag is defined as the aerodynamic force acting parallel to the relative airflow. Lift is positive upwards and drag is positive rearwards.

Aerodynamics in other fields

Aerodynamics is important in a number of applications other than aerospace engineering. It is a significant factor in any type of vehicle design, including automobiles. It is important in the prediction of forces and moments in sailing. It is used in the design of small components such as hard drive heads. Civil engineers also use aerodynamics, and particularly aeroelasticity, to calculate wind loads in the design of large buildings and bridges.

Continuity assumption

Gases are composed of molecules which collide with one another and solid objects. In aerodynamics, however, gases are considered to have continuous quantities. That is, properties such as density, pressure, temperature, and velocity are taken to be well-defined at infinitely small points, and are assumed to vary continuously from one point to another. The discrete, molecular nature of a gas is ignored. The continuity assumption becomes less valid as a gas becomes more rarefied. In these cases, statistical mechanics is a more valid method of solving the problem than aerodynamics.

Conservation laws

Aerodynamic problems are solved using the conservation laws, or equations derived from the conservation laws. In aerodynamics, three conservation laws are used:
- Conservation of mass: Matter is not created or destroyed. If a certain mass of fluid enters a volume, it must either exit the volume or increase the mass inside the volume.
- Conservation of momentum: Also called Newton's second law of motion
- Conservation of energy: Although it can be converted from one form to another, the total energy in a given system remains constant. All aerodynamic problems are therefore solved by the same set of equations. However, they differ by the assumptions made in each problem. The equations become simpler as assumptions are made. Note that these laws are based on Newtonian Mechanics. They are not applicable in relativistic mechanics, which takes into account Einstein's theory of relativity. all the problem related to energy conservation must be well known

Subsonic aerodynamics

In a subsonic aerodynamic problem, all of the flow speeds are less than the speed of sound. This class of problems encompasses nearly all internal aerodynamic problems, as well as external aerodynamics for most aircraft, model aircraft, and automobiles. In solving a subsonic problem, one decision to be made by the aerodynamicist is whether or not to incorporate the effects of compressibility. Compressibility is a description of the amount of change of density in the problem. When the effects of compressibility on the solution are small, the aerodynamicist may choose to assume that density is constant. The problem is then an incompressible problem. When the density is allowed to vary, the problem is called a compressible problem. In air, compressibility effects can be ignored when the Mach number in the flow does not exceed 0.3. Above 0.3, the problem should be solved using compressible aerodynamics.

Transonic aerodynamics

Transonic aerodynamic problems are defined as problems in which both supersonic and subsonic flow exist. Normally the term is reserved for problems in which the characteristic Mach number is very close to one. Transonic flows are characterized by shock waves and expansion waves. A shock wave or expansion wave is a region of very large changes in the flow properties. In fact, the properties change so quickly they are nearly discontinuous across the waves. Transonic problems are arguably the most difficult to solve. Flows behave very differently at subsonic and supersonic speeds, therefore a problem involving both types is more complex than one in which the flow is either purely subsonic or purely supersonic. Š

Supersonic aerodynamics

Supersonic aerodynamic problems are those involving flow speeds greater than the speed of sound. Calculating the lift on the Concorde during cruise can be an example of a supersonic aerodynamic problem. Supersonic flow behaves very differently from subsonic flow. The speed of sound can be considered the fastest speed that "information" can travel in the flow. Gas travelling at subsonic speed diverts around a body before striking it, so it can be said to "know" that the body is there. Air cannot divert around a body when it is travelling at supersonic speeds. It subsonic flow and a diffuser in supersonic flow). Subsonic flow additional shock waves. In this case the fuselage reuses some displacement of the wings.

Velocity

This article is about velocity in physics. For other meanings, see velocity (disambiguation). The velocity of an object is simply its speed in a particular direction. Note that both speed and direction are required to define a velocity.

Explanation

The velocity (v) is an physical quantity of the motion. A change in an object's velocity can therefore arise from either a change in its speed or in its direction. For example an aeroplane that is circling at a constant speed of 200km/h is changing its velocity because it is continously changing its direction. A aeroplane that is taking-off may go from zero to 200km/h in a straight line and so would also be changing its velocity. A change in velocity is called an acceleration. Objects are only accelerated if a force is applied to them. (The amount of acceleration depends the size of the force and the mass of the object being shifted, see Newton's Second Law of Motion.) In the case of the circling aeroplane, the pilot banks to use the force of lift from the wings to change direction. In another example the Space Shuttle orbits the earth at a constant speed but is constantly changing its velocity because of the circular orbit. In this case the force causing the acceleration is provided by the earth's gravity acting on the shuttle. The average speed v of an object moving a distance d during a time interval t is described by the formula: :

v = \frac

Acceleration is the rate of change of an object's velocity over time. The average acceleration of a of an object whose speed changes from v_i to v_f during a time interval t is given by: :

a = \frac

Where

v_i

= an object's initial velocity and

v_f

= the object's final velocity over a period of time t

Formal description

Velocity (symbol: v) is a vector measurement of the rate and direction of motion. The scalar absolute value (magnitude) of velocity is speed. Velocity can also be defined as rate of change of displacement or just as the rate of displacement, depending on how the term displacement is used. It is thus a vector quantity with dimension length/time. In the SI (metric) system it is measured in metre per second The instantaneous velocity vector v of an object that has position at time t is given by x(t) can be computed as the derivative :

v= = \lim_

The instantaneous acceleration vector a of an object that has position at time t is given by x(t) is :

\mathbf = \frac   = \frac

The equation for an object's velocity can be obtained mathematically by taking the integral of the equation for its acceleration beginning from some initial period time $t_0$ to some point in time later $t_n$ . The final velocity v_f of an object which starts with velocity v_i and then accelerates at constant acceleration a for a period of time t is: :

v_f = v_i + a t

The average velocity of an object undergoing constant acceleration is (v_i + v_f)/2. To find the displacement d of such an accelerating object during a time interval t, substitute this expression into the first formula to get: :

d = t \times \frac

When only the object's initial velocity is known, the expression :

d = v_i t + \frac

can be used. These basic equations for final velocity and displacement can be combined to form an equation that is independent of time, also known as Torricelli's Equation: :

v_f^2 = v_i^2 + 2 a d

The above equations are valid for both classical mechanics and special relativity. Where classical mechanics and special relativity differ is in how different observers would describe the same situation. In particular, in classical mechanics, all observers agree on the value of t and the transformation rules for position create a situation in which all non-accelerating observers would describe the acceleration of an object with the same values. Neither is true for special relativity. The kinetic energy (energy of motion) of a moving object is linear with both its mass and the square of its velocity: :

E_ = \begin \frac \end mv^2

The kinetic energy is a scalar quantity.

Polar coordinates

In polar coordinates, a two-dimensional velocity can be decomposed into a radial velocity, defined as the component of velocity away from or toward the origin, and transverse velocity, the component of velocity along a circle centred at the origin, and equal to the distance to the origin times the angular velocity. Angular momentum in scalar form is the distance to the origin times the transverse speed, or equivalently, the distance squared times the angular speed, with a plus or minus to distinguish clockwise and anti-clockwise direction. If forces are in the radial direction only, as in the case of a gravitational orbit, angular momentum is constant, and transverse speed is inversely proportional to the distance, angular speed is inversely proportional to the distance squared, and the rate at which area is swept out is constant. These relations are known as Kepler's laws of planetary motion.

Density

: For other senses of "density", see density (disambiguation). Density (symbol: ρ - Greek: rho) is a measure of mass per unit of volume. The higher an object's density, the higher its mass per volume. The average density of an object equals its total mass divided by its total volume. A denser object (such as iron) will have less volume than an equal mass of some less dense substance (such as water). The SI unit of density is the kilogram per cubic metre (kg/m³) :

\rho = \frac

where :ρ is the object's density (measured in kilograms per cubic metre) :m is the object's total mass (measured in kilograms) :V is the object's total volume (measured in cubic metres) Under specified conditions of temperature and pressure, density of a fluid is defined as described above. However, the density of a solid material can be different, depending on exactly how it is defined. Take sand for example. If you gently fill a container with sand, and divide the mass of sand by the container volume you get a value termed loose bulk density. If you took this same container and tapped on it repeatedly, allowing the sand to settle and pack together, and then calculate the results, you get a value termed tapped or packed bulk density. Tapped bulk density is always greater than or equal to loose bulk density. In both types of bulk density, some of the volume is taken up by the spaces between the grains of sand. Also, in terms of candy making, density is affected by the melting and cooling processes. Loose granular sugar, like sand, contains a lot of air and is not tightly packed, but when it has melted and starts to boil, the sugar loses its granularity and entrained air and becomes a fluid. When you mold it to make a smaller, compacted shape, the syrup tightens up and loses more air. As it cools, it contracts and gains moisture, making the already heavy candy even more dense.

Other units

Density in terms of the SI base units is expressed in terms of kilograms per cubic metre (kg/m³). Other units fully within the SI include grams per cubic centimetre (g/cm³) and megagrams per cubic metre (Mg/m³). Since both the litre and the tonne or metric ton are also acceptable for use with the SI, a wide variety of units such as kilograms per litre (kg/L) are also used. Imperial units or U.S. customary units, the units of density include pounds per cubic foot (lb/ft³), pounds per cubic yard (lb/yd³), pounds per cubic inch (lb/in³), ounces per cubic inch (oz/in³), pounds per gallon (for U.S. or imperial gallons) (lb/gal), pounds per U.S. bushel (lb/bu), in some engineering calculations slugs per cubic foot, and other less common units. The maximum density of pure water at a pressure of one standard atmosphere is 999.972 kg/m³; this occurs at a temperature of about 3.98 °C (277.13 K). From 1901 to 1964, a litre was defined as exactly the volume of 1 kg of water at maximum density, and the maximum density of pure water was 1.000 000 kg/L (now 0.999 972 kg/L). However, while that definition of the litre was in effect, just as it is now, the maximum density of pure water was 0.999 972 kg/dm³. During that period students had to learn the esoteric fact that a cubic centimetre and a millilitre were slightly different volumes, with 1 mL = 1.000 028 cm³. (often stated as 1.000 027 cm³ in earlier literature).

Measurement of density

A common device for measuring fluid density is a pycnometer. A device for measuring absolute density of a solid is a gas pycnometer.

Density of substances

Perhaps the highest density known is reached in neutron star matter (see neutronium). The singularity at the centre of a black hole, according to general relativity, does not have any volume, so its density is undefined. The most dense naturally occurring substance on Earth is iridium, at about 22650 kg/m³. A table of densities of various substances:

Substance	Density in kg/m³
Iridium	22650
Osmium	22610
Platinum	21450
Gold	19300
Tungsten	19250
Uranium	19050
Mercury	13580
Palladium	12023
Lead	11340
Silver	10490
Copper	8960
Iron	7870
Tin	7310
Titanium	4507
Diamond	3500
Basalt	3000
Granite	2700
Aluminium	2700
Graphite	2200
Magnesium	1740
PVC	1300
Seawater	1025
Water	1000
Ice	917
Polyethylene	910
Ethyl alcohol	790
Gasoline	730
Aerogel	.003
any gas	0.0446 times the average molecular mass, hence between 0.09 and ca. 10.0 (at standard temperature and pressure)
For example air	1.2

Note the low density of aluminium compared to most other metals. For this reason, aircraft are made of aluminium. Also note that air has a nonzero, albeit small, density. Aerogel is the world's lightest solid.

Temperature

Temperature is the physical property of a system which underlies the common notions of "hot" and "cold"; the material with the higher temperature is said to be hotter. Physically, temperature is a measure of the random agitation of matter and ambiant photons, under the effect of thermal fluctuations. It is a fundamental parameter in thermodynamics and it is conjugate to entropy. More quantitatively, the order of magnitude of the fluctuations of the energy associated with an atom, molecule or another elementary constituant of a physical system is

k_B T

, where

k_B

is Boltzmann's constant, and T is temperature, expressed in Kelvins.

Overview

The formal properties of temperature are studied in thermodynamics and statistical mechanics. The temperature of a system at thermodynamic equilibrium is defined by a relation between the amount of heat

\delta Q

incident on the system during an infinitesimal quasistatic transformation, and the variation

\delta S

of its entropy during this transformation. :

\delta S = \frac

Contrarly to entropy and heat, whose microscopic definitions are valid even far away from thermodynamic equilibrium temperature can only be defined at thermodynamic equilibrium, or local thermodynamic equilibrium (see below). As a system receives heat its temperature rises, similarly a loss of heat from the system tends to decrease its temperature (at the - uncommon - exception of negative temperature, see below). When two systems are at the same temperature, no heat transfer occurs between them. When a temperature difference does exist, heat will tend to move from the higher-temperature system to the lower-temperature system, until they are at thermal equilibrium. This heat transfer may occur via conduction, convection or radiation (see heat for additional discussion of the various mechanisms of heat transfer). Temperature is also related to the amount of internal energy and enthalpy of a system. The higher the temperature of a system, the higher its internal energy and enthalpy are. Temperature is an intensive property of a system, meaning that it does not depend on the system size or the amount of material in the system. Other intensive properties include pressure and density. By contrast, mass and volume are extensive properties, and depend on the amount of material in the system.

Role of temperature in nature

Temperature plays an important role in almost all fields of science, including physics, chemistry, and biology. Many physical properties of materials including the phase (solid, liquid, gaseous or plasma), density, solubility, vapor pressure, and electrical conductivity depend on the temperature. Temperature also plays an important role in determining the rate and extent to which chemical reactions occur. This is one reason why the human body has several elaborate mechanisms for maintaining the temperature at 37 °C, since temperatures only a few degrees higher can result in harmful reactions with serious consequences. Temperature also controls the type and quantity of thermal radiation emitted from a surface. One application of this effect is the incandescent light bulb, in which a tungsten filament is electrically heated to a temperature at which significant quantities of visible light are emitted. Temperature-dependence of the speed of sound in air c, density of air ρ and acoustic impedance Z vs. temperature °C

Temperature measurement

Main article: Temperature measurement Temperature measurement using modern scientific thermometers and temperature scales goes back at least as far as the early 18th century, when Gabriel Fahrenheit adapted a thermometer (switching to mercury) and a scale both developed by Ole Christensen Rømer. Fahrenheit's scale is still in use, alongside the Celsius scale and the Kelvin scale.

Units of temperature

The basic unit of temperature (symbol: T) in the International System of Units (SI) is the kelvin (K). One kelvin is formally defined as 1/273.16 of the temperature of the triple point of water (the point at which water, ice and water vapor exist in equilibrium). The temperature 0 K is called absolute zero and corresponds to the point at which the molecules and atoms have the least possible thermal energy. An important unit of temperature in theoretical physics is the Planck temperature (1.4 × 10³² K). In the field of plasma physics, because of the high temperatures encountered and the electromagnetic nature of the phenomena involved, it is customary to express temperature in electronvolts (eV) or kiloelectronvolts (keV), where 1 eV = 11,605 K. In the study of QCD matter one routinely meets temperatures of the order of a few hundred MeV, equivalent to about 10¹² K. For everyday applications, it is often convenient to use the Celsius scale, in which 0 °C corresponds to the temperature at which water freezes and 100 °C corresponds to the boiling point of water at sea level. In this scale a temperature difference of 1 degree is the same as a 1 K temperature difference, so the scale is essentially the same as the kelvin scale, but offset by the temperature at which water freezes (273.15 K). Thus the following equation can be used to convert from degrees Celsius to kelvins. :

\mathrm

In the United States, the Fahrenheit scale is widely used. On this scale the freezing point of water corresponds to 32 °F and the boiling point to 212 °F. The following formula can be used to convert from Fahrenheit to Celsius: :

\mathrm

See temperature conversion formulas for conversions between most temperature scales. ¹ Only the kelvin, Celsius, Fahrenheit, and Rankine scales are in use today.
² Some numbers in this table have been rounded off.
³ Normal human body temperature is 36.8 °C ±0.7 °C, or 98.2 °F ±1.3 °F.

Negative temperatures

:See main article: Negative temperature. For some systems and specific definitions of temperature, it is possible to obtain a negative temperature. A system with a negative temperature is not colder than absolute zero, but rather it is, in a sense, hotter than infinite temperature (sic).

Articles about temperature ranges:

- 10⁻¹² K = 1 picokelvin (pK)
- 10⁻⁹ K = 1 nanokelvin (nK)
- 10⁻⁶ K = 1 microkelvin (µK)
- 10⁻³ K = 1 millikelvin (mK)
- 10⁰ K = 1 kelvin
- 10¹ K = 10 kelvins
- 10² K = 100 kelvins
- 10³ K = 1,000 kelvin = 1 kilokelvin (kK)
- 10⁴ K = 10,000 kelvins = 10 kK
- 10⁵ K = 100,000 kelvins = 100 kK
- 10⁶ K = 1 megakelvin (MK)
- 10⁹ K = 1 gigakelvin (GK)
- 10¹² K = 1 terakelvin (TK) See Orders of magnitude (temperature).

Theoretical foundation of temperature

Zeroth-law definition of temperature

While most people have a basic understanding of the concept of temperature, its formal definition is rather complicated. Before jumping to a formal definition, let us consider the concept of thermal equilibrium. If two closed systems with fixed volumes are brought together, so that they are in thermal contact, changes may take place in the properties of both systems. These changes are due to the transfer of heat between the systems. When a state is reached in which no further changes occur, the systems are in thermal equilibrium. Now a basis for the definition of temperature can be obtained from the so-called zeroth law of thermodynamics which states that if two systems, A and B, are in thermal equilibrium and a third system C is in thermal equilibrium with system A then systems B and C will also be in thermal equilibrium (being in thermal equilibrium is a transitive relation; moreover, it is an equivalence relation). This is an empirical fact, based on observation rather than theory. Since A, B, and C are all in thermal equilibrium, it is reasonable to say each of these systems shares a common value of some property. We call this property temperature. Generally, it is not convenient to place any two arbitrary systems in thermal contact to see if they are in thermal equilibrium and thus have the same temperature. Also, it would only provide an ordinal scale. Therefore, it is useful to establish a temperature scale based on the properties of some reference system. Then, a measuring device can be calibrated based on the properties of the reference system and used to measure the temperature of other systems. One such reference system is a fixed quantity of gas. The ideal gas law indicates that the product of the pressure and volume (P · V) of a gas is directly proportional to the temperature: :

P \cdot V = n \cdot R \cdot T

(1) where 'T is temperature, n is the number of moles of gas and R is the gas constant. Thus, one can define a scale for temperature based on the corresponding pressure and volume of the gas: the temperature in kelvins is the pressure in pascals of one mole of gas in a container of one cubic metre, divided by 8.31... In practice, such a gas thermometer is not very convenient, but other measuring instruments can be calibrated to this scale. Equation 1 indicates that for a fixed volume of gas, the pressure increases with increasing temperature. Pressure is just a measure of the force applied by the gas on the walls of the container and is related to the energy of the system. Thus, we can see that an increase in temperature corresponds to an increase in the thermal energy of the system. When two systems of differing temperature are placed in thermal contact, the temperature of the hotter system decreases, indicating that heat is leaving that system, while the cooler system is gaining heat and increasing in temperature. Thus heat always moves from a region of high temperature to a region of lower temperature and it is the temperature difference that drives the heat transfer between the two systems.

Temperature in gases

As mentioned previously for a monatomic ideal gas the temperature is related to the translational motion or average speed of the atoms. The kinetic theory of gases uses statistical mechanics to relate this motion to the average kinetic energy of atoms and molecules in the system. For this case 7736 K = 7463 degrees Celsius corresponds to an average kinetic energy of one electronvolt; to take room temperature (300 K) as an example, the average energy of air molecules is 300/7736 eV, or 0.0388 electronvolt. This average energy is independent of particle mass, which seems counterintuitive to many people. Although the temperature is related to the average kinetic energy of the particles in a gas, each particle has its own energy which may or may not correspond to the average. However, after an examination of some basic physics equations it makes perfect sense. The second law of thermodynamics states that any two given systems when interacting with each other will later reach the same average energy. Temperature is a measure of the average kinetic energy of a system. The formula for the kinetic energy of an atom is:
:

K_t = \begin \frac \end mv^2

(Note that a calculation of the kinetic energy of a more complicated object, such as a molecule, is slightly more involved. Additional degrees of freedom are available, so molecular rotation or vibration must be included.)

Thus, particles of greater mass (say a neon atom relative to a hydrogen molecule) will move slower than lighter counterparts, but will have the same average energy. This average energy is independent of the mass because of the nature of a gas, all particles are in random motion with collisions with other gas molecules, solid objects that may be in the area and the container itself (if there is one). A visual illustration of this [http://intro.chem.okstate.edu/1314F00/Laboratory/GLP.htm from Oklahoma State University] makes the point more clear. Not all the particles in the container have different velocities, regardless of whether there are particles of more than one mass in the container, but the average kinetic energy is the same because of the ideal gas law. In a gas the distribution of energy (and thus speeds) of the particles corresponds to the Boltzmann distribution. An electronvolt is a very small unit of energy, approximately 1.602×10^-19 joule.

Temperature of the vacuum

When a satellite in empty space is heated by sunshine and cooled by radiating energy away it is not in thermodynamic equilibrium and has no well-defined temperature. A system in a vacuum will radiate its thermal energy, i.e. convert heat into electromagnetic waves. If vacuum is filled with electromagnetic waves (say, radiation from walls of vacuum chamber, or relic microwave radiation in space) then the system will exchange by energy with these waves and thermally equilibrates at some finite (non zero) temperature. Cosmic microwave background radiation being remnant of radiation of hot early universe when radiation was in thermal equilibrium with matter has Planck spectrum (black body spectrum) with the temperature (at present) of about 2.7 K.

Second-law definition of temperature

In the previous section temperature was defined in terms of the Zeroth Law of thermodynamics. It is also possible to define temperature in terms of the second law of thermodynamics, which deals with entropy. Entropy is a measure of the disorder in a system. The second law states that any process will result in either no change or a net increase in the entropy of the universe. This can be understood in terms of probability. Consider a series of coin tosses. A perfectly ordered system would be one in which every coin toss would come up either heads or tails. For any number of coin tosses, there is only one combination of outcomes corresponding to this situation. On the other hand, there are multiple combinations that can result in disordered or mixed systems, where some fraction are heads and the rest tails. As the number of coin tosses increases, the number of combinations corresponding to imperfectly ordered systems increases. For a very large number of coin tosses, the number of combinations corresponding to ~50% heads and ~50% tails dominates and obtaining an outcome significantly different from 50/50 becomes extremely unlikely. Thus the system naturally progresses to a state of maximum disorder or entropy. Now, we have stated previously that temperature controls the flow of heat between two systems and we have just shown that the universe, and we would expect any natural system, tends to progress so as to maximize entropy. Thus, we would expect there to be some relationship between temperature and entropy. In order to find this relationship let's first consider the relationship between heat, work and temperature. A heat engine is a device for converting heat into mechanical work and analysis of the Carnot heat engine provides the necessary relationships we seek. The work from a heat engine corresponds to the difference between the heat put into the system at the high temperature, q_H and the heat ejected at the low temperature, q_C. The efficiency is the work divided by the heat put into the system or: :

\textrm = \frac  = \frac = 1 - \frac

(2) where w_cy is the work done per cycle. We see that the efficiency depends only on q_C/q_H. Because q_C and q_H correspond to heat transfer at the temperatures T_C and T_H, respectively, q_C/q_H should be some function of these temperatures: :

\frac = f(T_H,T_C)

(3) Carnot's theorem states that all reversible engines operating between the same heat reservoirs are equally efficient. Thus, a heat engine operating between T₁ and T₃ must have the same efficiency as one consisting of two cycles, one between T₁ and T₂, and the second between T₂ and T₃. This can only be the case if: :

q_ = \frac

which implies: :

q_13 = f(T_1,T_3) = f(T_1,T_2)f(T_2,T_3)

Since the first function is independent of T₂, this temperature must cancel on the right side, meaning f(T₁,T₃) is of the form g(T₁)/g(T₃) (i.e. f(T₁,T₃) = f(T₁,T₂)f(T₂,T₃) = g(T₁)/g(T₂)· g(T₂)/g(T₃) = g(T₁)/g(T₃)), where g is a function of a single temperature. We can now choose a temperature scale with the property that: :

\frac = \frac

(4) Substituting Equation 4 back into Equation 2 gives a relationship for the efficiency in terms of temperature: :

\textrm = 1 - \frac = 1 - \frac

(5) Notice that for T_C = 0 K the efficiency is 100% and that efficiency becomes greater than 100% below 0 K. Since an efficiency greater than 100% violates the first law of thermodynamics, this implies that 0 K is the minimum possible temperature. In fact the lowest temperature ever obtained in a macroscopic system was 20 nK, which was achieved in 1995 at NIST. Subtracting the right hand side of Equation 5 from the middle portion and rearranging gives: :

\frac  - \frac = 0

where the negative sign indicates heat ejected from the system. This relationship suggests the existence of a state function, S, defined by: :

dS = \frac

(6) where the subscript indicates a reversible process. The change of this state function around any cycle is zero, as is necessary for any state function. This function corresponds to the entropy of the system, which we described previously. We can rearranging Equation 6 to get a new definition for temperature in terms of entropy and heat: :

T = \frac

(7) For a system, where entropy S may be a function S(E) of its energy E, the temperature T is given by: :

\frac = \frac

(8) The reciprocal of the temperature is the rate of increase of entropy with energy.

References

External links

- [http://www.unitconversion.org/unit_converter/temperature.html Online Temperature Converter] - convert between various units of temperature, such as kelvin, Celsius, Fahrenheit, Rankine, Reaumur, and even Triple point of water
- [http://www.unitconversion.org/unit_converter/temperature-v.html Interactive Temperature Conversion Table] - convert selected unit to all other units of temperature
- [http://www.indiana.edu/~animal/fun/conversions/temperature.html Temperature Conversions: Celsius, Fahrenheit, Kelvin, Réaumur and Rankine]
- [http://www.unidata.ucar.edu/staff/blynds/tmp.html An elementary introduction to temperature aimed at a middle school audience]
- [http://www.straightdope.com/mailbag/mtempscales.html Why do we have so many temperature scales?]
- [http://thermodynamics-information.net A Brief History of Temperature Measurement] Category:Meteorology Category:Physical quantity Category:Thermodynamics Category:Heat ko:온도 ja:温度 th:อุณหภูมิ

Moment (physics)

: See also moment (mathematics) for a more abstract concept of moments that evolved from this concept of physics. right In physics, the moment of force (often just moment, though there are other quantities of that name such as moment of inertia) is a quantity that represents the magnitude of force applied to a rotational system at a distance from the axis of rotation. The concept of the moment arm, this characteristic distance, is key to the operation of the lever, pulley, gear, and most other simple machines capable of generating mechanical advantage.

Overview

In general, the moment M of a vector B is :

\mathbf = \mathbf \times \mathbf \,

; where :r is the position where quantity B is applied. If r is a vector relative to point A, then the moment is the "moment M with respect to the axis that goes through the point A", or simply "moment M around A". If A is the origin, one often omits A and says simply moment.

Parallel axis theorem

Since the moment is dependent on the given axis, the moment expression possess a common property when the observation axis is changed. If M_A is the moment around A, then the moment around the axis that goes through a point B is :

\mathbf = \mathbf + \mathbf \times \mathbf \,

where :R is the vector from point A to point B. This expression is usually referred to as the parallel axis theorem. For cases when the moment is the sum of individual "submoments", such as in rigid body dynamics where each particle of the body contribute to a moment, the axis change is the sum of a macroscopic and microscopic quantity, :

\mathbf = \mathbf \times \mathbf + \sum_ \,

where :

\mathbf = \sum_ \,

or alternatively, :

\mathbf = \mathbf \times \mathbf + \mathbf \,

Related quantities

Some notable physical quantities arise from the application of moments:
- Angular momentum (L = Iω), which is typically the cause of rotational motion of a body.
- Moment of inertia (I = mω×r), which is analogous to mass in discussions of rotational motion.
- Torque (τ = rF), which is a force applied on a position of a body. When no net torque is applied, angular momentum is conserved.

History

The principle of moments is derived from Archimedes' discovery of the operating principle of the lever. In the lever one applies a force, in his day most often human muscle, to an arm, a beam of some sort. Archimedes noted that the amount of force applied to the object, the moment of force, is defined as M = rF, where F is the applied force, and r is the distance from the applied force to object. Category:Physical quantity ja:モーメント

Lift (force)

Lift consists of the sum of all the fluid dynamic forces on a body perpendicular to the direction of the external flow around that body. There are a number of ways of explaining the production of lift, all of which are equivalent. That is, they are different expressions of the same underlying physical principles. perpendicular

Reaction due to accelerated air

In air (or comparably in any fluid), lift is created as an airstream passes by an airfoil and is deflected downward. The force created by this deflection of the air creates an equal and opposite force upward on an airfoil according to Newton's third law of motion. The deflection of airflow downward during the creation of lift is known as downwash. It is important to note that the acceleration of the air does not just involve the air molecules "bouncing off" the bottom of the airfoil. Rather, air molecules closely follow both the top and bottom surfaces of the airfoil, and so the airflow is deflected downward. In fact, the acceleration of the air during the creation of lift can also be described as a "turning" of the airflow. Nearly any shape will produce lift if curved or tilted with respect to the air flow direction. However, most shapes will be very inefficient and create a great deal of drag. One of the primary goals of airfoil design is to devise a shape that produces the most lift while producing the least lift-induced drag. It is possible to measure lift using the reaction model. The force acting on the airfoil is the negative of the time-rate-of-change of the momentum of the air. In a wind tunnel, the speed and direction of the air can be measured (using, for example, a Pitot tube or Laser Doppler velocimetry) and thence the lift derived.

Bernoulli's principle

Bernoulli's principle states that in fluid flow, an increase in velocity occurs simultaneously with decrease in pressure. It is named for the Dutch/Swiss mathematician/scientist Daniel Bernoulli, though it was previously understood by Leonhard Euler and others. For a mathematical formulation, see Bernoulli's equation. In a fluid flow with no viscosity, and therefore one in which a pressure difference is the only accelerating force, it is equivalent to Newton's laws of motion. One way of understanding how an airfoil develops lift relies upon the pressure differential above and below a wing. The pressure can be calculated by finding the velocities around the wing and using Bernoulli's equation. However, this explanation often uses false information, such as the incorrect assumption that the two parcels of air which separate at the leading edge of a wing must meet again at the trailing edge. Bernoulli's principle is responsible for the venturi effect that is used in carburetors and elsewhere. In a carburetor, air is passed through a Venturi tube to increase its speed and therefore decrease its pressure. The force on the wing can also be examined in terms of the pressure differences above and below the wing. (This method of explanation is mathematically equivalent to the Newton's 3rd law explanation as developed above.) The relationship between the velocities and pressures above and below the wing are nearly predicted by Bernoulli's equation. More generally, the resulting force (Lift + Drag) is, according to Bernoulli's equation, the integral of pressure on the contour of the wing.

\mathbf+\mathbf = \oint_p\mathbf \; d\partial\Omega

where:
- L is the Lift,
- D is the Drag,
-

\partial\Omega

is the frontier of the domain,
- p is the value of the pressure,
- n is the normal to the profile. This equation suffices to predict both lift and drag. However it is derived by making drastic assumptions on the flow. The flow is deemed a potential flow: this means more specifically:
- the field v of particle velocities must be so that :

\mathbf = \nabla \Psi

\Delta\Psi = 0

, with

\Delta

the Laplacian. Therefore it completely neglects all effects of:
- Vorticity,
- Viscosity,
- Compressibility. Depending on the conditions of flight those are in no way negligible. Notably vorticity is the dominating phenomenon explaining the lift of Concorde and other delta-winged aircraft at the high-angle-of-attack, low-airspeed conditions of takeoff and landing.

Circulation

A third way of calculating lift is a mathematical construction called circulation. Again, it is mathematically equivalent to the two explanations above. It is often used by practicing aerodynamicists as a convenient quantity, but is not often useful for a layperson's understanding. The circulation is the line integral of the velocity of the air, in a closed loop around the boundary of an airfoil. It can be understood as the total amount of "spinning" (or vorticity) of air around the airfoil. When the circulation is known, the section lift can be calculated using: :

l =  \rho \times V \times \Gamma

where

\rho

is the air density,

V

is the free-stream airspeed, and

\Gamma

is the circulation. The Helmholtz theorem states that circulation is conserved. When an aircraft is at rest, there is no circulation. As the flow speed increases (that is, the aircraft accelerates in the air-body-fixed frame), a vortex, called the starting vortex, forms at the trailing edge of the airfoil, due to viscous effects in the boundary layer. Eventually the vortex detaches from the airfoil and gets swept away from it rearward. The circulation in the starting vortex is equal in magnitude and opposite in direction to the circulation around the airfoil. Theoretically, the starting vortex remains connected to the vortex bound in the airfoil, through the wing-tip vortices, forming a closed circuit. In reality the starting vortex gets dissipated by a number of effects, as do the wing-tip vortices far behind the aircraft.

Coefficient of lift

Aerodynamicists are one of the most frequent users of dimensionless numbers. The coefficient of lift is one such term. When the coefficient of lift is known, for instance from tables of airfoil data, lift can be calculated using the Lift Equation: :

L = C_L \times \rho \times  \times A

where:
-

C_L

is the coefficient of lift,
-

\rho

is the density of air (1.225 kg/m³ at sea level)
-
- V is the freestream velocity, that is the airspeed far from the lifting surface
- A is the surface area of the lifting surface
- L is the lift force produced. This equation can be used in any consistent system. For instance, if the density is measured in kilograms per cubic metre, the velocity is measured in metres per second, and the area is measured in square metres, the lift will be calculated in newtons. Or, if the density is in slugs per cubic foot, the velocity is in feet per second, and the area is in square feet, the resulting lift will be in pounds force.
- Note that at altitudes other than sea level, the density can be found using the Barometric formula Compare with: Drag equation.

Coanda effect

Jef Raskin and a few others have claimed that the Coandă effect is needed to explain lift from an airfoil. They state that the "turning of the airflow" is caused at the microscopic level by the Coandă Effect. However the conventional explanation of lift makes verifiable predictions of lift using the lift equation without invoking the Coand Effect. Proponents of the Coandă Effect correctly claim that the effect is not fully understood, but currently their predictions are at variance with experiment. The practical applications of Coandă effect, such as blown flaps and other lift augmentation devices, create conditions different from the normal airflow over a wing.

Common explanation of lift is false

Many readers new to this topic may be looking for the explanation that is commonly put forward in many mainstream books, and even scientific exhibitions, that touch on flight and aerodynamic principles; namely, that due to the greater curvature (and hence longer path) of the upper surface of an aerofoil, the air going over the top must go faster in order to "catch up" with the air flowing around the bottom (and hence due to its faster speed its pressure is lower, etc). Despite the fact that this "explanation" is probably the most common of all, it must be made clear that it is utterly false. There is no requirement that the air over the top must catch up to the air below, and in fact it does not do so. In addition, such an explanation would mean that an aircraft could not fly inverted, which is demonstrably not the case. It also fails to account for aerofoils which are fully symmetrical yet still develop significant lift. It is unclear why this explanation has gained such currency, except by repetition and perhaps the fact that it is easiest to grasp intuitively without mathematics. However, since it is wrong, the assumed intuition which serves it is also wrong, and the wise reader would do well to discount this approach. Note that any text book claiming to be a serious work on the topic will never promote this theory. It is interesting to note that Albert Einstein, in attempting to design a practical aircraft based on this principle, came up with an aerofoil section that featured a large hump on its upper surface, on the basis that an even longer path must aid lift if the principle is true. Its performance was terrible, and we can suppose that in fact this was the point that Einstein was trying to prove. There is a book on this topic: "Understanding Flight", published by McGraw-Hill, ISBN 0071363777, by David Anderson and Scott Eberhardt. The authors are a physicist and an aeronautical engineer. They explain flight in non-technical terms and specifically address the Bernoulli myth.

External links

- [http://www.aa.washington.edu/faculty/eberhardt/lift.htm How Airplanes Fly: A Physical Description of Lift]
- [http://www.grc.nasa.gov/WWW/K-12/airplane/lift1.html NASA tutorial, with animation, describing lift]
- [http://jef.raskincenter.org/published/coanda_effect.html Beginners intro to why and how model planes fly]
- [http://www.av8n.com/irro/lecture_e.html Explanation of Lift with animation of fluid flow around an airfoil]
- [http://www.av8n.com/how/ An Excellent treatment of why and how wings generate lift] Category:Fluid dynamics Category:Aerodynamics Category:Force zh-min-nan:Seng-le̍k ko:양력 ja:揚力 Category:Fluid dynamics

Airplane!

covers.]] Airplane! is an American comedy film, first released on July 2, 1980, produced and directed by Jim Abrahams, David Zucker and Jerry Zucker, and starring Robert Hays, Julie Hagerty, Leslie Nielsen, Robert Stack, Lloyd Bridges, Peter Graves and Kareem Abdul-Jabbar. It is the second of a number of movies produced and directed by the trio (the first being The Kentucky Fried Movie). In some foreign releases (including Australia), Airplane! was entitled Flying High as in those countries airplanes are called aeroplanes. The film is regularly shown on television, with many devotees repeatedly rewatching the film, in the process catching other gags that they did not notice earlier due to the sheer number of often overlapping sight, sound, and dialogue gags. Airplane II: The Sequel, first released on December 10, 1982, attempted to tackle the science fiction film genre. Although most of the cast reunited for the sequel, the two films have no writers in common. Several actors were cast in order to spoof their established images: Leslie Nielsen, Robert Stack and Lloyd Bridges had played many adventurous, no-nonsense tough-guys, including Stack as the captain in one of the earliest airline "disaster" films, The High and the Mighty. Nielsen had played "more cops, doctors, and attorneys than you could shake a nightstick/stethoscope/law book at." [http://www.imdb.com/name/nm0000558/bio]

Plot synopsis

The plot of Airplane! is a well-travelled one. The story of an in-flight medical emergency, caused by food poisoning, started as the CBC TV movie Flight into Danger, then became the 1957 Paramount Pictures movie Zero Hour! Thus Airplane! is the fourth remake of the Arthur Hailey novel Runway Zero-Eight. Airplane! is very close to Zero Hour!, following it virtually scene for scene, and lifting its major characters and most of its story line. Indeed, many of the best known lines are repeated verbatim, for example, "Can you face some unpleasant facts?" and "Looks like I picked the wrong week to quit smoking," which becomes a running gag. As the plot escalates, so does the potency of the drug ("I guess I picked the wrong week to quit sniffing glue.") Even the odd sports cameo remains intact. In Zero Hour!, the cameo is by Elroy "Crazy Legs" Hirsch. In Airplane!, it is basketball star Kareem Abdul-Jabbar. Airplane! also has elements based on films in the Airport series, specifically Airport '75, which was also based on novels written by Arthur Hailey. The elements that the film lifted from Airport '75 included the guitar song (a flight attendant played by Lorna Patterson in Airplane! and a nun played by Helen Reddy in Airport '75) and the sick little girl that the guitar song is played for (played by Linda Blair in Airport '75 and Jill Whelan in Airplane!). When the pilots of a commercial airliner get sick, an ex-fighter pilot, Ted Striker (Robert Hays) must conquer his fear of flying and fly the plane to its destination. Striker's ex-girlfriend (Julie Hagerty) is a flight attendant. Nielsen portrays a doctor on board. His catchphrase in the film became famous worldwide. In response to the question from a passenger "Surely you can't be serious?" Nielsen's character would respond: "I am serious, and don't call me Shirley". ...and don't call me Shirley has entered the language as an all-purpose, nonplussed response. He gives a similar response to Ted later in the movie. Ted says, "Surely there must be something you can do." Nielsen's character responds, "I'm doing everything I can. And stop calling me Shirley." Nielsen's career would forever be changed due to this film; his deadpan, serious brand of comedy not only altered the subtext of his earlier, serious roles, but he'd become almost exclusively typecast in gag comedies, including the Naked Gun films by the Airplane! directors Zucker-Abrahams-Zucker. Stephen Stucker became known for the scene-stealing flamboyantly gay character Johnny Hinshaw, inspiring many catch-phrases like "And Leon's getting laaaaaarger!", "The tower, the tower, Rapunzel!" and describing the airplane as "Oh, it's a big pretty white plane with red stripes, curtains in the windows, wheels, and it looks like a big Tylenol!" Lloyd Bridges portrays the chief air traffic controller, and Robert Stack plays Hays' former commander, who is brought in to aid him in landing the airplane. Bridges' role was a direct spoof on his San Francisco International Airport television role of Jim Conrad. Howard Jarvis, the author of California's property tax initiative Proposition 13, plays a man who patiently waits in the back of Striker's cab throughout the movie. Some critics have claimed that the movie's most important achievement was in bringing to an end the Airport series of movies, which could no longer be taken seriously.

Gag-based comedies

Airplane! is one of the most famous and acclaimed examples of a genre of similar gag-based comedies that defy logic, reason, and the "fourth wall" to produce laughter in any way possible, with comic references to other famous 'straight' disaster films such as Airport. When this type of comedy works, it is exceptional (the animated cartoons of Tex Avery were a great influence), though it can be difficult for filmmakers to achieve success when working on a movie that often denies characterization and even plot development. Other successful movies of this type include Mel Brooks' Blazing Saddles and the "Road movies" of Bing Crosby and Bob Hope. More recent movies of this sort include Hot Shots!, The Naked Gun trilogy, the Austin Powers series, and the Scary Movie series. (A number of other films in this genre were less successful, including Loaded Weapon, The Big Bus, Kung Pow: Enter the Fist, and Spy Hard.)

Gags in this motion picture

- When Robert Stack is driving to the airport to talk Stryker down, the movie spoofs rear-projection behind an automobile mockup, with a road scene that speeds up even as it curves repeatedly, then switches to Indians chasing the car along a forest trail. Stack's character also runs down -- or more accurately upends over his car -- a bicyclist in a sweatsuit, who immediately arises from the pavement and angirly pumps his fist, yelling "asshole!".
- When Rex Kramer (Robert Stack) arrives at the airport, he takes off his clip-on sunglasses and he's wearing regular sunglasses underneath.
- At the front entrance to the airport, a pair of voices - one male, one female - announce not to stop in the red zone, and not to park in the white zone. They are assumed to be recordings, until the man gets mixed up as to which zone is which and they begin arguing. In a later scene at the entrance, they are discussing her pregnancy and his advice of the best place to get an abortion. Yet, not one person on the ground pays any mind to this personal conversation.
- When Ted gets his ticket for the flight, he's asked, "Smoking or non-smoking?"; he answers intently, "smoking, please," and is handed a ticket that is smoldering, and it is still giving off smoke when he is outside ready to climb aboard the aircraft.
- The last person to board is warned by a train conductor that it's time to get aboard, and as the plane "chugs" out of the terminal apron, the door of the plane is still open as his girlfriend runs along beside the plane. Oveur started the plane moving by moving a control similar to a train being put into motion. However, the airplane's engines resemble jets, while starting up like old prop-jobs and the plane sounding in flight like a bomber.
- When the plane is losing altitude, Elaine yells, "The mountains, Ted, the mountains!" He says, "What mountains? We're over Iowa." So, in the same scared voice, she yells, "The cornfields, Ted, the cornfields!"
- As Leslie Nielsen rattles off a list of the food poisoning's gradual effects, one of the poison's victims, Captain Oveur, begins experiencing the effects as they are verbally listed.
- The "automatic pilot" is nothing more than an inflatable doll, named "Otto", that inflates in the co-pilot's seat when activated. If it loses inflation during use, its control of the airplane slackens, but unfortunately, the manual inflation nozzle is in a... compromising location.
- A mechanic lifts the plane's hood to check the dipstick, but falls off the ladder while trying to leap onto the hood to get it shut.
- Two pieces of luggage being pulled with leashes start growling and snapping at each other, resisting the efforts to keep pulling them along.
- In a wartime flashback, Ted gives all kinds of classified information to Elaine, where and when they're going to be bombing, but when Elaine asks Ted when he'll be back, he says, "I can't tell you that. It's classified."
- Barbara Billingsley, the archetypal suburban mother on Leave It to Beaver, has an especially funny appearance when she offers to translate for a pair of hip African American passengers whose jive talking is incomprehensible to stewardesses: "Stewardess? I speak jive."
- A female passenger is putting on red lipstick when the plane hits turbulence and she gets a long lipstick streak across her cheek. Later the plane hits more turbulence and the same passenger is seen still applying makeup. Now she has green eyeshadow smudged on her face as well.
- McCroskey tells a group of reporters, "Okay boys, let's get some pictures." The reporters respond by grabbing framed pictures off the wall.
- Ethel Merman has a memorable cameo as a shell-shocked fighter pilot who thinks he's Ethel Merman.
- bilingual notices in normal English and phonetically-spelt "jive."
- Elaine, while serving with Ted in the Peace Corps in an isolated village in Africa or the East Indies, attempts to sell the natives "Supperware", a movie version of Tupperware.
- Ted develops a "drinking problem." (He brings the glass to his forehead instead of his mouth.)
- In a flashback sequence that shows how Ted and Elaine first met, a fist fight erupts between two girl scouts over a disputed poker hand.
- Ted is flying the plane. Elaine is operating the radio and relaying the messages between him and Kramer. Ted says, "It's a damn good thing he doesn't know how much I hate his guts." Elaine says to Kramer, "It's a good thing you don't know how much he hates your guts."
- At the beginning of the movie, Ted tells the passenger in his taxi that he'll be right back and goes to find Elaine. The passenger waits for him. At the end of the closing credits, the passenger is still in the taxi waiting for Ted and he says, "Well, I'll give him another twenty minutes, but that's it!"
- Whenever someone asks "What is it?" meaning "What's wrong?", another character interprets this as "Describe the object". For example "We must get this man to a hospital!" "A hospital? What is it?" "It's a big building with patients, but that's not important right now".
- Passengers pay no attention to Elaine while she tells them everything that's wrong with the plane but panic when she announces they just run out of coffee.

Response

- Airplane! was a major hit: The budget was about US$3.5 Million, and the film earned over US$80 Million at the box office, and another US$40 Million in rentals.
- Leslie Nielsen saw a major boost to his career, and since Airplane! has specialized in playing clueless deadpan bumblers. Lloyd Bridges and Robert Stack saw similar shifts in their public image, though to lesser degrees.
- In 2000, the American Film Institute listed Airplane! as #10 on its list of the 100 funniest American films. In the same year, readers of Total Film magazine voted it the 2nd greatest comedy film of all time.
- It is interesting to note that, according to the directors, the only airline to ever buy the rights to, and show the movie on its aircraft is Aeromexico.

External link

- Category:1980 films Category:Comedy films

Shock wave

:For the multimedia player platform, see Macromedia Shockwave. For the Transformers character, see Shockwave (Transformers). For the rollercoaster, see Shockwave Rollercoaster In a supersonic flow the compression of a nonreacting gas can be most simply modelled as an isentropic or Prandtl-Meyer compression, or as a shock wave. When an object (or disturbance) moves faster than the information about it can be propogated into the surrounding fluid, fluid near the disturbance cannot react or "get out of the way" before the disturbance arrives. In a shock wave the properties of the fluid(density, pressure, temperature, velocity, Mach number) change almost instantaneously. Measurements of the thickness of shock waves have resulted in values approximately one order of magnitude greater than the mean free path of the gas investigated. Shock waves are not sound waves; a shock wave takes the form of a very sharp change in the gas properties on the order of micro-meters in thickness. Shock waves in air are heard as a loud "crack" or "snap" noise. Over time a shock wave can change from a nonlinear wave into a linear wave, degenerating into a conventional sound wave as it heats the air and loses energy. The sound wave is heard as the familiar "thud" or "thump" of a sonic boom, commonly created by the supersonic flight of aircraft. Analogous phenomena are known outside fluid mechanics. For example, particles accelerated beyond the speed of light in a refractive medium (where the speed of light is less than that in a vacuum, such as water) create shock effects, a phenomenon known as Cerenkov radiation. There are several types of shock wave: # Shock propogating into a stationary flow #
- This shock appears is generally generated by the interaction of two bodies of gas at different pressure, with a shock wave propogating into the lower pressure gas, and an expansion wave propogating into the higher pressure gas. #
- Examples: Balloon bursting, Shock tube, shock wave from explosion #
- In this case, the gas ahead of the shock is stationary (in the laboratory frame), and the gas behind the shock is supersonic in the laboratory frame. The shock propogates normal to the oncoming flow. The speed of the shock is a function of the original pressure ratio between the two bodies of gas. # Shock in a pipe flow #
- This shock appears when supersonic flow in a pipe is decellerated. #
- Examples: Supersonic Ramjet, Scramjet, needle valve #
- In this case the gas ahead of the shock is supersonic (in the laboratory frame), and the gas behind the shock system is either supersonic (oblique shock) or subsonic (normal shock). The shock is the result of the deceleration of the gas by a converging duct, or by the growth of the boundary layer on the wall of a parallel duct. #Recompression shock on a transonic body #
- These shocks appear when the flow over a transsonic body is decelerated to subsonic speeds. #
- Examples: Transonic wings, Turbines,[http://www.airliners.net/open.file?id=955437&WxsIERv=ZpQbaaryy%20Qbhtynf%20S%2FN-18P%20Ubearg&Wm=0&WdsYXMg=Fjvgmreynaq%20-%20Nve%20Sbepr&QtODMg=Bss-Nvecbeg%20-%20Nknyc&ERDLTkt=Fjvgmreynaq&ktODMp=Bpgbore%2013%2C%202005&BP=0&WNEb25u=Fpbgg%20Enguobar&xsIERvdWdsY=W-5022&MgTUQtODMgKE=Ybbx%20ng%20gur%20fubpxjnirf%20ba%20gung%21%20V%20pna%27g%20fnl%20gung%20V%20unir%20frra%20fubpxjnirf%20nf%20ivfvoyr%20nf%20guvf%20orsber%2C%20whfg%20bar%20bs%20gubfr%20yhpxl%20fubgf%20V%20thrff.&YXMgTUQtODMgKERD=2602&NEb25uZWxs=2005-11-08&ODJ9dvCE=&O89Dcjdg=1371%2FFSP022&static=yes&width=1024&height=695&sok=%20BEQRE%20OL%20cubgb_vq%20QRFP&photo_nr=1&prev_id=&next_id=892143&tbl=COOL shockwave at mach1] #
- Where the flow over the suction side of a transonic wing is accelerated to a supersonic speed, the resulting recompression can be by either Prandtl-meyer compression or by the formation of a normal shock. This shock is of particular interest to makers of transonic devices because it can cause separation of the boundary layer at the point where it touches the transonic profile. This can then lead to full separation and stall on the profile, higher drag, or shock-buffet, a condition whereby the separtion and the shock inteact in a resonance condition, causing resonating loads on the underlying structure. # Attached shock on a supersonic body #
- These shocks appear as "attached" to the tip of a sharp body moving at supersonic speeds. #
- Examples: Supersonic wedges and cones at low angles. #
- The attached shock wave is a classic structure in aerodynamics because, for a perfect gas and inviscid flowfield, an analytic solution is available, whereby the pressure ratio, temperature ratio, angle of the wedge and the downstream Mach number can all be calculated knowing the upstream Mach number and the shock angle. Lower shock angles are associated with higher downstream Mach numbers, and the special case where the shock wave is at 90 degrees to the oncoming flow (Normal shock), is associated with a downstream Mach number of one. # Detached shock on a supersonic body #
- These shocks occur where the supersonic body is too blunt to allow the shock to attach to the tip. #
- Examples: Space return vehicles (Apollo, Space shuttle), bullets. The boundary of a magnetosphere. At the shock wave, particles from the solar wind will abruptly slow to subsonic speeds. #
- These shocks are curved, and form a small way in front of a supersonic body. Directly in front of the body, they are at 90 degrees to the oncoming flow, and then they curve around the body. Detached shocks allow the same type of analytic calculations as for the attached shock, for the flow near the shock. They are a topic of continuing interest, because the rules governing the distance between the blunt body and the shock are complicated, and are a function of the shape of the blunt body. Additionally, the distance of the shock standoff varies drastically with the temperature for a non-ideal gas, causing large differences in the heat transfer to the thermal protection system of the vehicle. # Detonation wave #
- This is not a shock wave, but is of a similar form. A detonation wave follows different rules to a shock wave since it is driven by chemical reactions occuring inside the wave itself. Detonation waves proceed at the Chapman-Jouguet velocity. It is also possible for a shock wave in a reactive mixture to induce combustion, but in this case the shock proceeds at the velocity indicated by the noncombusting mixture. This is shock-induced combustion.

External links

- Photo Gallery http://www.galleryoffluidmechanics.com/shocks/shock.htm
- eFluids gallery http://www.efluids.com/efluids/pages/gallery.htm
- Bomb Shock Wave Estimation http://www.makeitlouder.com/document_bombshockwaveestimation.html
- NASA Glenn Research Center information on:
- Oblique Shocks http://www.grc.nasa.gov/WWW/K-12/airplane/oblique.html

- Multiple Crossed Shocks http://www.grc.nasa.gov/WWW/K-12/airplane/crosshock.html

- Expansion Fans http://www.grc.nasa.gov/WWW/K-12/airplane/expans.html

Jet engine

is tested at Robins Air Force Base, Georgia, USA. The tunnel behind the engine muffles noise and allows exhaust to escape. The mesh cover at the front of the engine (left of photo) prevents debris—or people—from being pulled into the engine by the huge volume of air rushing into the inlet.]] A jet engine is any engine that accelerates and discharges a fast moving jet of fluid to generate thrust in accordance with Newton's third law of motion. This broad definition of jet engines includes turbojets, turbofans, turboprops, rockets and ramjets, but in common usage, the term generally refers to a gas turbine used to produce a jet of high speed exhaust gases for propulsive purposes.

Turbojet engines

A turbojet engine is a type of internal combustion engine often used to propel aircraft. Air is drawn into the rotating compressor via the intake and is compressed to a higher pressure before entering the combustion chamber. Fuel is mixed with the compressed air and ignited by flame in the eddy of a flame holder. This combustion process significantly raises the temperature of the gas. Hot combustion products leaving the combustor expand through the turbine, where power is extracted to drive the compressor. Although this expansion process reduces both the gas temperature and pressure at exit from the turbine, both parameters are usually still well above ambient conditions. The gas stream exiting the turbine expands to ambient pressure via the propelling nozzle, producing a high velocity jet in the exhaust plume. If the jet velocity exceeds the aircraft flight velocity, there is a net forward thrust upon the airframe. Under normal circumstances, the pumping action of the compressor prevents any backflow, thus facilitating the continuous flow process of the engine. Indeed, the entire process is similar to a four-stroke cycle, but with induction, compression, ignition, expansion and exhaust taking place simultaneously. The efficiency of a jet engine is strongly dependent upon the Overall Pressure Ratio (Combustor Entry Pressure/Intake Delivery Pressure) and the Turbine Inlet Temperature of the cycle. It is also perhaps instructive to compare turbojet engines with propeller engines. Turbojet engines take a relatively small mass of air and accelerate it by a large amount, whereas a propeller takes a large mass of air and accelerates it by a small amount. The high-speed exhaust of a jet engine makes it efficient at high speeds (especially supersonic speeds) and high altitudes. On slower aircraft and those required to fly short stages, a gas turbine-powered propeller engine, commonly known as a turboprop, is more common and much more efficient. Very small aircraft generally use conventional piston engines to drive a propeller but small turboprops are getting smaller as engineering technology improves. The turbojet described above is a single spool design, where a single shaft connects the turbine to the compressor. Higher Overall Pressure Ratio designs often have two concentric shafts, to improve compressor stability during engine throttle movements. The outer (HP) shaft connects the High Pressure (HP) Compressor to the HP turbine. This HP Spool, with the combustor, forms the core or gas generator of the engine. The inner shaft connects the Low Pressure (LP) Compressor to the LP Turbine to create the LP Spool. Both spools are free to operate at their optimum shaft speed.

Turbofan engines

Most modern jet engines are actually turbofans, where the LP Compressor acts as a fan, supplying supercharged air to not only the engine core, but to a bypass duct. The bypass airflow either passes to a separate Cold Nozzle or mixes with LP Turbine exhaust gases, before expanding through a Mixed Flow Nozzle. Forty years ago there was little difference between civil and military jet engines, apart from the use of afterburning in some (supersonic) applications. Turbofans, today, have a low specific thrust (net thrust/airflow) to keep jet noise to a minimum and to improve fuel efficiency. Consequently the bypass ratio (bypass flow/core flow) is relatively high (usually much greater than 3.0). Only a single fan stage is required, because a low specific thrust implies a low fan pressure ratio. Today's military turbofans, however, have a relatively high specific thrust, to maximize the thrust for a given frontal area, jet noise being of little consequence. Multi-stage fans are normally required to achieve the relatively high fan pressure ratio needed for a high specific thrust. Although high Turbine Inlet Temperatures are frequently employed, the bypass ratio tends to be low (usually significantly less than 2.0). An approximate equation for calculating the net thrust of a jet engine is: :F_net = m(v_jfe - v_a ) where: :m = intake mass flow :v_jfe = fully expanded jet velocity (in the exhaust plume) :v_a = aircraft flight velocity While the m·v_jfe term represents the gross thrust of the nozzle, the m·v_a term represents the ram drag of the intake. Most types of jet engine have an air intake, which provides the bulk of the gas exiting the exhaust. There is, however, a penalty for picking this air up and this is known as the ram drag. Conventional rocket motors, however, do not have an air intake, the oxidizer being carried within the airframe. Consequently, rocket motors do not have ram drag; the gross thrust of the nozzle is the net thrust of the engine. Consequently, the thrust characteristics of a rocket motor are completely different from that of an air breathing jet engine; at full throttle, the thrust of a rocket motor improves slightly with increasing altitude (because the back pressure from the atmosphere falls), whereas with a turbojet (or turbofan) the falling density of the air entering the intake causes the net thrust to decrease with increasing altitude.

History

Before the advent of the jet engine, the reciprocating piston engine in its different forms (rotary and static radial, aircooled and liquid-cooled inline) had been the only type of powerplant available to aircraft designers. This was understandable so long as low aircraft performance parameters were considered acceptable, and indeed inevitable. However, by approximately the late 1930s, engineers were beginning to realize that conceptually the piston engine was self-limiting in terms of the maximum performance which could be obtained from it; the limit was essentially one of propeller efficiency, which seemed to peak as blade tips approached supersonic tangential velocity. If engine, and thus aircraft, performance were ever to increase beyond such a barrier, a way would have to be found to radically improve the design of the piston engine, or a wholly new type of powerplant would have to be conceived. The latter would prove to be the case. The gas turbine (turbojet, or simply jet) engine, as subsequently developed, would become almost as revolutionary to aviation as the Wright brothers' first flight. The gas turbine was not an idea developed in the 1930s: the patent for a stationary turbine was granted to John Barber in England in 1791, although Colin Sullivan of Cowplain, England was said to have drawn up identical blueprints 2 years beforehand. The earliest attempts at jet engines were hybrid designs in which an external power source supplied the compression. In this system (called a thermojet by Secondo Campini) the air is first compressed by a fan driven by a conventional piston engine, then it is mixed with fuel and burned for jet thrust. The examples of this type of design were the Henri Coanda's Coanda-1910 aircraft, and the much later Campini Caproni CC.2, and the Japanese Tsu-11 engine intended to power Ohka kamikaze planes towards the end of World War II. None were entirely successful and the CC.2 ended up being slower than the same design with a traditional engine and propeller combination. World War II The key to the useful jet engine was the gas turbine, used to extract energy to drive the compressor from the engine itself. The first gas turbine to successfully run self-sustaining was built in 1903 by Norwegian engineer Aegidius Elling. The first patents for jet propulsion were issued in 1917. Limitations in design and practical engineering and metallurgy prevented such engines reaching manufacture. The main problems were safety, reliability, weight and, especially, sustained operation. On January 16, 1930, in England Frank Whittle submitted patents for his own design for a full-scale aircraft engine (granted in 1932). In 1935 Hans von Ohain started work on a similar design in Germany, seemingly unaware of Whittle's work. Ohain approached Ernst Heinkel, one of the larger aircraft industrialists of the day, who immediately saw the promise of the design. Heinkel had recently purchased the Hirth engine company, and Ohain and his master machinist Max Hahn were set up there as a new division of the Hirth company. They had their first HeS 1 engine running by September 1937. Unlike Whittle's design, Ohain used hydrogen as fuel, which he credits for the early success. Their subsequent designs culminated in the gasoline-fuelled HeS 3 of 1,100 lbf (5 kN), which was fitted to Heinkel's simple and compact He 178 airframe and flown by Erich Warsitz in the early morning of August 27, 1939, from Marienehe aerodrome, an impressively short time for development. The He 178 was the world's first jetplane. The engine was starting to look useful, and Whittle's Power Jets Ltd. started receiving Air Ministry money. In 1941 a flyable version of the engine called the W.1, capable of 1000 lbf (4 kN) of thrust, was fitted to the Gloster E28/39 airframe, and first flew on May 15, 1941 at RAF Cranwell. RAF Cranwell One problem with both of these early designs, which are called centrifugal-flow engines, was that the compressor works by "throwing" (accelerating) air outward from the central intake to the outer periphery of the engine where the air is then compressed by a divergent duct setup—converting velocity into pressure. The advantage was that such compressor designs were well understood in centrifugal superchargers but this leads to a very large cross section for the engine at rotational speeds that were usable at the time. A disadvantage was that the air flow had to be "bent" to flow rearwards through the combustion section and to the turbine and tailpipe. With improvements to bearings, the shaft speed of the engine would increase and the diameter of the centrifugal compressor would reduce greatly. The shortness of this engine is an advantage. The strength of this type of compressor is an advantage over the later axial-flow compressors that are still liable to foreign object damage (FOD in aviation parlance). Austrian Anselm Franz of Junkers' engine division (Junkers Motoren or Jumo) addressed this problem with the introduction of the axial-flow compressor. Essentially, this is a turbine in reverse. Air coming in the front of the engine is blown to the rear of the engine by a fan stage (convergent ducts), where it is crushed against a set of non-rotating blades called stators (divergent ducts). The process is nowhere near as powerful as the centrifugal compressor, so a number of these pairs of fans and stators are placed in series to get the needed compression. Even with all the added complexity, the resulting engine is much smaller in diameter. Jumo was assigned the next engine number, 4, and the result was the Jumo 004 engine. After many lesser technical difficulties were solved, mass production of this engine started in 1944 as a powerplant for the world's first jet-fighter aircraft, the Messerschmitt Me 262. Because Hitler wanted a new bomber the Me 262 came too late to decisively impact Germany's position in World War II, but it will be remembered as the first use of jet engines in service. After the end of the war the German Me 262 aircraft were extensively studied by the victorious allies and contributed to work on early Soviet and US jet fighters. British engines also were licensed widely in the US (see Tizard Mission). Their most famous design, the Nene would also power the USSR's jet aircraft also after a technology exchange. American designs would not come fully into their own until the 1960s.

Types

There are a large number of types of jet engines, which get propulsion from a high speed exhaust jet. Some examples are as follows:

Type	Description	Advantages	Disadvantages
Water jet	Squirts water out the back of a boat	Can run in shallow water, powerful, less harmful to wildlife	Can be less efficient than a propeller, more vulnerable to debris
Thermojet	Most primitive airbreathing jet engine		Very inefficient and underpowered
Turbojet	Generic term for simple turbine engine	Simplicity of design	Basic design, misses many improvements in efficiency and power
Turbofan	Power tapped off exhaust used to drive bypass fan	Quieter due to greater mass flow and lower total exhaust speed, more efficient for a useful range of subsonic airspeeds for same reason	Greater complexity (additional ducting, usually multiple shafts), large diameter engine, need to contain heavy blades. More subject to FOD and ice damage. Different degrees of bypass are possible - this is the design most commonly used on commercial airliners
Rocket	Carries own propellant onboard, emits jet for propulsion	Very few moving parts, Mach 0 to Mach 25+, efficient at very high speed (> Mach 10.0 or so), thrust/weight ratio over 100, relatively simple, no air inlet, doesn't require atmosphere, high compression ratio, very high speed exhaust	very low specific impulse- typically 100-450 seconds. Typically requires carrying oxidiser onboard which increases risks.
Ramjet	Intake air is compressed entirely by speed of oncoming air and duct shape (divergent)	Very few moving parts, Mach 0.8 to Mach 5+, efficient at high speed (> Mach 2.0 or so), lightest of all airbreathing jets (thrust/weight ratio up to 30 at optimum speed)	Must have a high initial speed to function, inherently inefficient at slow speeds due to poor compression ratio, difficult to arrange shaft power for accessories, difficult to engineer to be efficient over a wide range of airspeeds.
Turboprop (Turboshaft similar)	Strictly not a jet at all- a gas turbine engine is used as powerplant to drive (propeller) shaft	High efficiency at lower subsonic airspeeds(300 knots plus), high shaft power to weight	Limited top speed (aeroplanes), somewhat noisy, complexity of propeller drive, very large yaw (aeroplane) if engine fails
Propfan	Turboprop engine drives one or more propellers. much like a turbofan but without ductwork	Higher fuel efficiency, some designs are less noisy than turbofans, could lead to higher-speed commercial aircraft, popular in the 1980s during fuel shortages,	Development of propfan engines has been very limited, typically more noisy than turbofans, complexity
Pulsejet	Air enters a divergent-duct inlet, the front of the combustion area is shut, fuel injected into the air ignites, exhaust vents from other end of engine	Very simple design, commonly used on model aircraft	Noisy, inefficient (low compression ratio), works best at small scale, valves need to be replaced very often
Pulse detonation engine	Similar to a pulsejet, but combustion occurs as a detonation instead of a deflagration, may or may not need valves	Maximum theoretical engine efficiency	Extremely noisy, parts subject to extreme mechanical fatigue, hard to start detonation, not practical for current use
Integral rocket ramjet	Essentially a ramjet where intake air is compressed and burnt with the exhaust from a rocket	Mach 0 to Mach 4.5+ (can also run exoatmospheric), good efficiency at Mach 2 to 4	Similar efficiency to rockets at low speed or exoatmospheric, inlet difficulties, a relatively undeveloped and unexplored type, cooling difficulties
Scramjet	Intake air is compressed but not slowed to below supersonic, intake, combustion and exhaust occur in a single constricted tube	can operate at very high Mach numbers (Mach 8 to 15)[http://www.dod.mil/ddre/downloads/ddre_briefings/Merging_Air_and_Space071603.pdf]	still in development stages, must have a very high initial sp