Impact Pressure
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Impact Pressure
In compressible fluid dynamics, impact pressure (dynamic pressure) is the difference between total pressure (also known as pitot pressure or stagnation pressure) and static pressure. In aerodynamics notation, this quantity is denoted as q_c or Q_c. When input to an airspeed indicator, impact pressure is used to provide a calibrated airspeed reading. An air data computer with inputs of pitot and static pressures is able to provide a Mach number and, if static temperature is known, true airspeed. Some authors in the field of compressible flows use the term ''dynamic pressure'' or ''compressible dynamic pressure'' instead of ''impact pressure''.L. J. Clancy (1975) ''Aerodynamics'', Section 3.12 and 3.13"the dynamic pressure is equal to ''half rho vee squared'' only in incompressible flow."Houghton, E.L. and Carpenter, P.W. (1993), ''Aerodynamics for Engineering Students'', Section 2.3.1 Isentropic flow In isentropic flow the ratio of total pressure to static pressure is given by: ...
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Dynamic Pressure
In fluid dynamics, dynamic pressure (denoted by or and sometimes called velocity pressure) is the quantity defined by:Clancy, L.J., ''Aerodynamics'', Section 3.5 :q = \frac\rho\, u^2 where (in SI units): * is the dynamic pressure in pascals (i.e., kg/ m⋅ s2), * is the fluid mass density (e.g. in kg/m3), and * is the flow speed in m/s. It can be thought of as the fluid's kinetic energy per unit volume. For incompressible flow, the dynamic pressure of a fluid is the difference between its total pressure and static pressure. From Bernoulli's law, dynamic pressure is given by : p_0 - p_\text = \frac\rho\, u^2 where and are the total and static pressures, respectively. Physical meaning Dynamic pressure is the kinetic energy per unit volume of a fluid. Dynamic pressure is one of the terms of Bernoulli's equation, which can be derived from the conservation of energy for a fluid in motion. It can also appear as a term in the incompressible Navier-Stokes equation whic ...
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Pitot Pressure
Pitot pressure is the pressure that is measured by a Pitot tube, an open-ended tube connected to a pressure-measuring device. For subsonic flow, pitot pressure is equal to the stagnation pressure (or total pressure) of the flow, and hence the term pitot pressure is often used interchangeably with these other terms. For supersonic flow, however, pitot pressure is the stagnation pressure of the flow behind the normal shock ahead of the pitot tube. Pitot pressure is named for Henri Pitot Henri Pitot (; May 3, 1695 – December 27, 1771) was a French hydraulic engineer and the inventor of the pitot tube. In a pitot tube, the height of the fluid column is proportional to the square of the velocity of the fluid at the depth of the ..., French scientist. References Pressure {{Measurement-stub ...
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Stagnation Pressure
In fluid dynamics, stagnation pressure is the static pressure at a stagnation point in a fluid flow.Clancy, L.J., ''Aerodynamics'', Section 3.5 At a stagnation point the fluid velocity is zero. In an incompressible flow, stagnation pressure is equal to the sum of the free-stream static pressure and the free-stream dynamic pressure. Stagnation pressure is sometimes referred to as pitot pressure because the two pressures are numerically equal. Magnitude The magnitude of stagnation pressure can be derived from Bernoulli equation for incompressible flow and no height changes. For any two points 1 and 2: :P_1 + \tfrac \rho v_1^2 = P_2 + \tfrac \rho v_2^2 The two points of interest are 1) in the freestream flow at relative speed v where the pressure is called the "static" pressure, (for example well away from an airplane moving at speed v); and 2) at a "stagnation" point where the fluid is at rest with respect to the measuring apparatus (for example at the end of a pitot tube in an ai ...
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Static Pressure
In fluid mechanics the term static pressure has several uses: * In the design and operation of aircraft, ''static pressure'' is the air pressure in the aircraft's static pressure system. * In fluid dynamics, many authors use the term ''static pressure'' in preference to just ''pressure'' to avoid ambiguity. Often however, the word ‘static’ may be dropped and in that usage pressure is the same as static pressure at a nominated point in a fluid. * The term ''static pressure'' is also used by some authors in fluid statics. Static pressure in design and operation of aircraft An aircraft's static pressure system is the key input to its altimeter and, along with the pitot pressure system, also drives the airspeed indicator. The static pressure system is open to the aircraft's exterior through a small opening called the static port, which allows sensing the ambient atmospheric pressure at the altitude at which the aircraft is flying. In flight, the air pressure varies slightly ...
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Aerodynamics
Aerodynamics, from grc, ἀήρ ''aero'' (air) + grc, δυναμική (dynamics), is the study of the motion of air, particularly when affected by a solid object, such as an airplane wing. It involves topics covered in the field of fluid dynamics and its subfield of gas dynamics. The term ''aerodynamics'' is often used synonymously with gas dynamics, the difference being that "gas dynamics" applies to the study of the motion of all gases, and is not limited to air. The formal study of aerodynamics began in the modern sense in the eighteenth century, although observations of fundamental concepts such as aerodynamic drag were recorded much earlier. Most of the early efforts in aerodynamics were directed toward achieving Aircraft#Heavier than air – aerodynes, heavier-than-air flight, which was first demonstrated by Otto Lilienthal in 1891. Since then, the use of aerodynamics through mathematical analysis, empirical approximations, wind tunnel experimentation, and computer simu ...
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Calibrated Airspeed
Calibrated airspeed (CAS) is indicated airspeed corrected for instrument and position error. When flying at sea level under International Standard Atmosphere conditions (15 °C, 1013 hPa, 0% humidity) calibrated airspeed is the same as equivalent airspeed (EAS) and true airspeed (TAS). If there is no wind it is also the same as ground speed (GS). Under any other conditions, CAS may differ from the aircraft's TAS and GS. Calibrated airspeed in knots is usually abbreviated as ''KCAS'', while indicated airspeed is abbreviated as ''KIAS''. In some applications, notably British usage, the expression ''rectified airspeed'' is used instead of calibrated airspeed. Practical applications of CAS CAS has two primary applications in aviation: * for navigation, CAS is traditionally calculated as one of the steps between indicated airspeed and true airspeed; * for aircraft control, CAS (and EAS) are the primary reference points, since they describe the dynamic pressure acting on aircraf ...
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Air Data Computer
An air data computer (ADC) or central air data computer (CADC) computes altitude, vertical speed, air speed, and Mach number from pressure and temperature inputs. It is an essential avionics component found in modern aircraft. This computer, rather than individual instruments, can determine the calibrated airspeed, Mach number, altitude, and altitude trend data from an aircraft's pitot-static system. In some very high speed aircraft such as the Space Shuttle, equivalent airspeed is calculated instead of calibrated airspeed. Air data computers usually also have an input of total air temperature. This enables computation of static air temperature and true airspeed. In Airbus aircraft the air data computer is combined with altitude, heading and navigation sources in a single unit known as the Air Data Inertial Reference Unit (ADIRU) this has now been replaced by the Global Navigation Air Data Inertial Reference System (GNADIRS). On the Embraer Embraer E-Jet family the concept has ...
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Mach Number
Mach number (M or Ma) (; ) is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound. It is named after the Moravian physicist and philosopher Ernst Mach. : \mathrm = \frac, where: : is the local Mach number, : is the local flow velocity with respect to the boundaries (either internal, such as an object immersed in the flow, or external, like a channel), and : is the speed of sound in the medium, which in air varies with the square root of the thermodynamic temperature. By definition, at Mach1, the local flow velocity is equal to the speed of sound. At Mach0.65, is 65% of the speed of sound (subsonic), and, at Mach1.35, is 35% faster than the speed of sound (supersonic). Pilots of high-altitude aerospace vehicles use flight Mach number to express a vehicle's true airspeed, but the flow field around a vehicle varies in three dimensions, with corresponding variations in local Mach number. The local spe ...
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True Airspeed
The true airspeed (TAS; also KTAS, for ''knots true airspeed'') of an aircraft is the speed of the aircraft relative to the air mass through which it is flying. The true airspeed is important information for accurate navigation of an aircraft. Traditionally it is measured using an analogue TAS indicator, but as the Global Positioning System has become available for civilian use, the importance of such air-measuring instruments has decreased. Since ''indicated'', as opposed to ''true'', airspeed is a better indicator of margin above the stall, true airspeed is not used for controlling the aircraft; for these purposes the indicated airspeed – IAS or KIAS (knots indicated airspeed) – is used. However, since indicated airspeed only shows true speed through the air at standard sea level pressure and temperature, a TAS meter is necessary for navigation purposes at cruising altitude in less dense air. The IAS meter reads very nearly the TAS at lower altitude and at lower spe ...
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Isentropic Flow
In thermodynamics, an isentropic process is an idealized thermodynamic process that is both adiabatic and reversible. The work transfers of the system are frictionless, and there is no net transfer of heat or matter. Such an idealized process is useful in engineering as a model of and basis of comparison for real processes. This process is idealized because reversible processes do not occur in reality; thinking of a process as both adiabatic and reversible would show that the initial and final entropies are the same, thus, the reason it is called isentropic (entropy does not change). Thermodynamic processes are named based on the effect they would have on the system (ex. isovolumetric: constant volume, isenthalpic: constant enthalpy). Even though in reality it is not necessarily possible to carry out an isentropic process, some may be approximated as such. The word "isentropic" can be interpreted in another way, since its meaning is deducible from its etymology. It means a pro ...
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Heat Capacity Ratio
In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure () to heat capacity at constant volume (). It is sometimes also known as the ''isentropic expansion factor'' and is denoted by ( gamma) for an ideal gasγ first appeared in an article by the French mathematician, engineer, and physicist Siméon Denis Poisson: * On p. 332, Poisson defines γ merely as a small deviation from equilibrium which causes small variations of the equilibrium value of the density ρ. In Poisson's article of 1823 – * γ was expressed as a function of density D (p. 8) or of pressure P (p. 9). Meanwhile, in 1816 the French mathematician and physicist Pierre-Simon Laplace had found that the speed of sound depends on the ratio of the specific heats. * However, he didn't denote the ratio as γ. In 1825, Laplace stated that the speed of sound is ...
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Binomial Series
In mathematics, the binomial series is a generalization of the polynomial that comes from a binomial formula expression like (1+x)^n for a nonnegative integer n. Specifically, the binomial series is the Taylor series for the function f(x)=(1+x)^ centered at x = 0, where \alpha \in \Complex and , x, 0 and diverges to +\infty if \operatorname\alpha<0. If \operatorname\alpha=0, then n^ = e^ converges if and only if the sequence \operatorname\alpha\log n converges \bmod, which is certainly true if \alpha=0 but false if \operatorname\alpha \neq0: in the latter case the sequence is dense \bmod, due to the fact that \log n diverges and \log (n+1)-\log n converges to zero).


Summation of the binomial series

The usual argument to compute the sum of the binomial series goes as follows.
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