The P-800 Oniks ( Russian : П-800 Оникс ; English: Onyx ), marketed in export as the Yakhont ( Russian : Яхонт ; English: ruby ), is a Soviet / Russian supersonic anti-ship cruise missile developed by NPO Mashinostroyeniya as a ramjet version of P-80 Zubr . Its GRAU designation is 3M55 , the air launched Kh-61 variant was planned but never built. The missile has the NATO codename SS-N-26 " Strobile " . Development commenced in 1983, and in the 1990s the anti-ship missile was tested on the Project 1234.7 ship . In 2002 the missile passed the whole range of trials and was commissioned. It is reportedly a replacement for the P-270 Moskit , and possibly also of the P-700 Granit .
104-490: The Oniks flies aerodynamically using its cropped delta wings mounted in a cruciform at the middle of the missile's fuselage. It possesses a very distinctive launch sequence which it shares with the BrahMos ; the missile lifts up from its launch tubes, and engages a stabilizing sequence using brief pulses from rockets in its nosecone . The missile then reorients itself; a pair of more powerful rockets fire sequentially to turn
208-485: A white noise contribution obtained from the fluctuation-dissipation theorem of statistical mechanics is added to the viscous stress tensor and heat flux . The concept of pressure is central to the study of both fluid statics and fluid dynamics. A pressure can be identified for every point in a body of fluid, regardless of whether the fluid is in motion or not. Pressure can be measured using an aneroid, Bourdon tube, mercury column, or various other methods. Some of
312-455: A continuum, do not contain ionized species, and have flow velocities that are small in relation to the speed of light, the momentum equations for Newtonian fluids are the Navier–Stokes equations —which is a non-linear set of differential equations that describes the flow of a fluid whose stress depends linearly on flow velocity gradients and pressure. The unsimplified equations do not have
416-493: A fluid dynamics problem typically involves the calculation of various properties of the fluid, such as flow velocity , pressure , density , and temperature , as functions of space and time. Before the twentieth century, "hydrodynamics" was synonymous with fluid dynamics. This is still reflected in names of some fluid dynamics topics, like magnetohydrodynamics and hydrodynamic stability , both of which can also be applied to gases. The foundational axioms of fluid dynamics are
520-440: A function of the fluid velocity and have different values in frames of reference with different motion. To avoid potential ambiguity when referring to the properties of the fluid associated with the state of the fluid rather than its motion, the prefix "static" is commonly used (such as static temperature and static enthalpy). Where there is no prefix, the fluid property is the static condition (so "density" and "static density" mean
624-405: A general closed-form solution , so they are primarily of use in computational fluid dynamics . The equations can be simplified in several ways, all of which make them easier to solve. Some of the simplifications allow some simple fluid dynamics problems to be solved in closed form. In addition to the mass, momentum, and energy conservation equations, a thermodynamic equation of state that gives
728-420: A given airspeed depends on the shape of the airfoil, especially the amount of camber (curvature such that the upper surface is more convex than the lower surface, as illustrated at right). Increasing the camber generally increases the maximum lift at a given airspeed. Cambered airfoils generate lift at zero angle of attack. When the chord line is horizontal, the trailing edge has a downward direction and since
832-436: A lift force roughly proportional to the angle of attack. As the angle of attack increases, the lift reaches a maximum at some angle; increasing the angle of attack beyond this critical angle of attack causes the upper-surface flow to separate from the wing; there is less deflection downward so the airfoil generates less lift. The airfoil is said to be stalled . The maximum lift force that can be generated by an airfoil at
936-536: A model of the effects of the turbulent flow. Such a modelling mainly provides the additional momentum transfer by the Reynolds stresses , although the turbulence also enhances the heat and mass transfer . Another promising methodology is large eddy simulation (LES), especially in the form of detached eddy simulation (DES) — a combination of LES and RANS turbulence modelling. There are a large number of other possible approximations to fluid dynamic problems. Some of
1040-443: A point in a flow. All fluids are compressible to an extent; that is, changes in pressure or temperature cause changes in density. However, in many situations the changes in pressure and temperature are sufficiently small that the changes in density are negligible. In this case the flow can be modelled as an incompressible flow . Otherwise the more general compressible flow equations must be used. Mathematically, incompressibility
1144-463: A point is reached where the boundary layer can no longer remain attached to the upper surface. When the boundary layer separates, it leaves a region of recirculating flow above the upper surface, as illustrated in the flow-visualization photo at right. This is known as the stall , or stalling . At angles of attack above the stall, lift is significantly reduced, though it does not drop to zero. The maximum lift that can be achieved before stall, in terms of
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#17327918897431248-485: A pressure difference, and that the speed difference then leads to a pressure difference, by Bernoulli's principle. This implied one-way causation is a misconception. The real relationship between pressure and flow speed is a mutual interaction . As explained below under a more comprehensive physical explanation , producing a lift force requires maintaining pressure differences in both the vertical and horizontal directions. The Bernoulli-only explanations do not explain how
1352-419: A region of the flow called a control volume . A control volume is a discrete volume in space through which fluid is assumed to flow. The integral formulations of the conservation laws are used to describe the change of mass, momentum, or energy within the control volume. Differential formulations of the conservation laws apply Stokes' theorem to yield an expression that may be interpreted as the integral form of
1456-417: A steady flow without viscosity, lower pressure means higher speed, and higher pressure means lower speed. Thus changes in flow direction and speed are directly caused by the non-uniform pressure. But this cause-and-effect relationship is not just one-way; it works in both directions simultaneously. The air's motion is affected by the pressure differences, but the existence of the pressure differences depends on
1560-412: A streamlined airfoil, and with somewhat higher drag. Most simplified explanations follow one of two basic approaches, based either on Newton's laws of motion or on Bernoulli's principle . An airfoil generates lift by exerting a downward force on the air as it flows past. According to Newton's third law , the air must exert an equal and opposite (upward) force on the airfoil, which is lift. As
1664-439: A wide area, producing a pattern called a velocity field . When an airfoil produces lift, the flow ahead of the airfoil is deflected upward, the flow above and below the airfoil is deflected downward leaving the air far behind the airfoil in the same state as the oncoming flow far ahead. The flow above the upper surface is sped up, while the flow below the airfoil is slowed down. Together with the upward deflection of air in front and
1768-507: A wide range of applications, including calculating forces and moments on aircraft , determining the mass flow rate of petroleum through pipelines , predicting weather patterns , understanding nebulae in interstellar space and modelling fission weapon detonation . Fluid dynamics offers a systematic structure—which underlies these practical disciplines —that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to
1872-401: A wing in a wind tunnel) or whether both are moving (e.g. a sailboat using the wind to move forward). Lift is the component of this force that is perpendicular to the oncoming flow direction. Lift is always accompanied by a drag force, which is the component of the surface force parallel to the flow direction. Lift is mostly associated with the wings of fixed-wing aircraft , although it
1976-407: Is a result of pressure differences and depends on angle of attack, airfoil shape, air density, and airspeed. Pressure is the normal force per unit area exerted by the air on itself and on surfaces that it touches. The lift force is transmitted through the pressure, which acts perpendicular to the surface of the airfoil. Thus, the net force manifests itself as pressure differences. The direction of
2080-439: Is because the assumption of equal transit time is wrong when applied to a body generating lift. There is no physical principle that requires equal transit time in all situations and experimental results confirm that for a body generating lift the transit times are not equal. In fact, the air moving past the top of an airfoil generating lift moves much faster than equal transit time predicts. The much higher flow speed over
2184-503: Is difficult because the cause-and-effect relationships involved are subtle. A comprehensive explanation that captures all of the essential aspects is necessarily complex. There are also many simplified explanations , but all leave significant parts of the phenomenon unexplained, while some also have elements that are simply incorrect. An airfoil is a streamlined shape that is capable of generating significantly more lift than drag. A flat plate can generate lift, but not as much as
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#17327918897432288-466: Is expressed by saying that the density ρ of a fluid parcel does not change as it moves in the flow field, that is, where D / D t is the material derivative , which is the sum of local and convective derivatives . This additional constraint simplifies the governing equations, especially in the case when the fluid has a uniform density. For flow of gases, to determine whether to use compressible or incompressible fluid dynamics,
2392-543: Is given a special name—a stagnation point . The static pressure at the stagnation point is of special significance and is given its own name— stagnation pressure . In incompressible flows, the stagnation pressure at a stagnation point is equal to the total pressure throughout the flow field. In a compressible fluid, it is convenient to define the total conditions (also called stagnation conditions) for all thermodynamic state properties (such as total temperature, total enthalpy, total speed of sound). These total flow conditions are
2496-517: Is known as unsteady (also called transient ). Whether a particular flow is steady or unsteady, can depend on the chosen frame of reference. For instance, laminar flow over a sphere is steady in the frame of reference that is stationary with respect to the sphere. In a frame of reference that is stationary with respect to a background flow, the flow is unsteady. Turbulent flows are unsteady by definition. A turbulent flow can, however, be statistically stationary . The random velocity field U ( x , t )
2600-401: Is more widely generated by many other streamlined bodies such as propellers , kites , helicopter rotors , racing car wings , maritime sails , wind turbines , and by sailboat keels , ship's rudders , and hydrofoils in water. Lift is also used by flying and gliding animals , especially by birds , bats , and insects , and even in the plant world by the seeds of certain trees. While
2704-564: Is negligible. The lift force frequency is characterised by the dimensionless Strouhal number , which depends on the Reynolds number of the flow. For a flexible structure, this oscillatory lift force may induce vortex-induced vibrations. Under certain conditions – for instance resonance or strong spanwise correlation of the lift force – the resulting motion of the structure due to the lift fluctuations may be strongly enhanced. Such vibrations may pose problems and threaten collapse in tall man-made structures like industrial chimneys . In
2808-494: Is often represented via a Reynolds decomposition , in which the flow is broken down into the sum of an average component and a perturbation component. It is believed that turbulent flows can be described well through the use of the Navier–Stokes equations . Direct numerical simulation (DNS), based on the Navier–Stokes equations, makes it possible to simulate turbulent flows at moderate Reynolds numbers. Restrictions depend on
2912-404: Is proportional to the density of the air and approximately proportional to the square of the flow speed. Lift also depends on the size of the wing, being generally proportional to the wing's area projected in the lift direction. In calculations it is convenient to quantify lift in terms of a lift coefficient based on these factors. No matter how smooth the surface of an airfoil seems, any surface
3016-409: Is rough on the scale of air molecules. Air molecules flying into the surface bounce off the rough surface in random directions relative to their original velocities. The result is that when the air is viewed as a continuous material, it is seen to be unable to slide along the surface, and the air's velocity relative to the airfoil decreases to nearly zero at the surface (i.e., the air molecules "stick" to
3120-429: Is statistically stationary if all statistics are invariant under a shift in time. This roughly means that all statistical properties are constant in time. Often, the mean field is the object of interest, and this is constant too in a statistically stationary flow. Steady flows are often more tractable than otherwise similar unsteady flows. The governing equations of a steady problem have one dimension fewer (time) than
3224-428: Is tilted with respect to the vertical. Lift may also act as downforce on the wing of a fixed-wing aircraft at the top of an aerobatic loop , and on the horizontal stabiliser of an aircraft. Lift may also be largely horizontal, for instance on a sailing ship. The lift discussed in this article is mainly in relation to airfoils, although marine hydrofoils and propellers share the same physical principles and work in
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3328-492: Is to use two flow models: the Euler equations away from the body, and boundary layer equations in a region close to the body. The two solutions can then be matched with each other, using the method of matched asymptotic expansions . A flow that is not a function of time is called steady flow . Steady-state flow refers to the condition where the fluid properties at a point in the system do not change over time. Time dependent flow
3432-462: Is treated separately. Reactive flows are flows that are chemically reactive, which finds its applications in many areas, including combustion ( IC engine ), propulsion devices ( rockets , jet engines , and so on), detonations , fire and safety hazards, and astrophysics. In addition to conservation of mass, momentum and energy, conservation of individual species (for example, mass fraction of methane in methane combustion) need to be derived, where
3536-401: Is well beyond the limit of DNS simulation ( Re = 4 million). Transport aircraft wings (such as on an Airbus A300 or Boeing 747 ) have Reynolds numbers of 40 million (based on the wing chord dimension). Solving these real-life flow problems requires turbulence models for the foreseeable future. Reynolds-averaged Navier–Stokes equations (RANS) combined with turbulence modelling provides
3640-589: The Mach number of the flow is evaluated. As a rough guide, compressible effects can be ignored at Mach numbers below approximately 0.3. For liquids, whether the incompressible assumption is valid depends on the fluid properties (specifically the critical pressure and temperature of the fluid) and the flow conditions (how close to the critical pressure the actual flow pressure becomes). Acoustic problems always require allowing compressibility, since sound waves are compression waves involving changes in pressure and density of
3744-549: The Mach numbers , which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density , viscosity , speed of sound , and flow speed . The concepts of total pressure and dynamic pressure arise from Bernoulli's equation and are significant in the study of all fluid flows. (These two pressures are not pressures in the usual sense—they cannot be measured using an aneroid, Bourdon tube or mercury column.) To avoid potential ambiguity when referring to pressure in fluid dynamics, many authors use
3848-629: The Magnus effect , a lift force is generated by a spinning cylinder in a freestream. Here the mechanical rotation acts on the boundary layer, causing it to separate at different locations on the two sides of the cylinder. The asymmetric separation changes the effective shape of the cylinder as far as the flow is concerned such that the cylinder acts like a lifting airfoil with circulation in the outer flow. As described above under " Simplified physical explanations of lift on an airfoil ", there are two main popular explanations: one based on downward deflection of
3952-593: The conservation laws , specifically, conservation of mass , conservation of linear momentum , and conservation of energy (also known as the First Law of Thermodynamics ). These are based on classical mechanics and are modified in quantum mechanics and general relativity . They are expressed using the Reynolds transport theorem . In addition to the above, fluids are assumed to obey the continuum assumption . At small scale, all fluids are composed of molecules that collide with one another and solid objects. However,
4056-441: The no-slip condition generates a thin region of large strain rate, the boundary layer , in which viscosity effects dominate and which thus generates vorticity . Therefore, to calculate net forces on bodies (such as wings), viscous flow equations must be used: inviscid flow theory fails to predict drag forces , a limitation known as the d'Alembert's paradox . A commonly used model, especially in computational fluid dynamics ,
4160-446: The streamline curvature theorem , was derived from Newton's second law by Leonhard Euler in 1754: The left side of this equation represents the pressure difference perpendicular to the fluid flow. On the right side of the equation, ρ is the density, v is the velocity, and R is the radius of curvature. This formula shows that higher velocities and tighter curvatures create larger pressure differentials and that for straight flow (R → ∞),
4264-405: The stress due to these viscous forces is linearly related to the strain rate. Such fluids are called Newtonian fluids . The coefficient of proportionality is called the fluid's viscosity; for Newtonian fluids, it is a fluid property that is independent of the strain rate. Non-Newtonian fluids have a more complicated, non-linear stress-strain behaviour. The sub-discipline of rheology describes
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4368-549: The "Coandă effect" is applicable, calling it the "Coandă effect" does not provide an explanation, it just gives the phenomenon a name. The ability of a fluid flow to follow a curved path is not dependent on shear forces, viscosity of the fluid, or the presence of a boundary layer. Air flowing around an airfoil, adhering to both upper and lower surfaces, and generating lift, is accepted as a phenomenon in inviscid flow. There are two common versions of this explanation, one based on "equal transit time", and one based on "obstruction" of
4472-552: The Armed Forces of Ukraine Oleksandr Syrskyi for the first time announced data on how many weapons Russia has used since 2022, as well as how many were intercepted. The report said that only 12/211 (5.69%) of Onyx were intercepted by Ukraine’s air defense Radar homing head Standard batteries of the K-300 Bastion-P (Бастион-П- П одвижный): Aerodynamic lift When a fluid flows around an object,
4576-439: The air follows the trailing edge it is deflected downward. When a cambered airfoil is upside down, the angle of attack can be adjusted so that the lift force is upward. This explains how a plane can fly upside down. The ambient flow conditions which affect lift include the fluid density, viscosity and speed of flow. Density is affected by temperature, and by the medium's acoustic velocity – i.e. by compressibility effects. Lift
4680-537: The air is accelerated by the pressure difference. This is why the air's mass is part of the calculation, and why lift depends on air density. Fluid dynamics In physics , physical chemistry and engineering , fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases . It has several subdisciplines, including aerodynamics (the study of air and other gases in motion) and hydrodynamics (the study of water and other liquids in motion). Fluid dynamics has
4784-418: The air's motion. The relationship is thus a mutual, or reciprocal, interaction: Air flow changes speed or direction in response to pressure differences, and the pressure differences are sustained by the air's resistance to changing speed or direction. A pressure difference can exist only if something is there for it to push against. In aerodynamic flow, the pressure difference pushes against the air's inertia, as
4888-411: The airflow approaches the airfoil it is curving upward, but as it passes the airfoil it changes direction and follows a path that is curved downward. According to Newton's second law, this change in flow direction requires a downward force applied to the air by the airfoil. Then Newton's third law requires the air to exert an upward force on the airfoil; thus a reaction force, lift, is generated opposite to
4992-400: The airflow. The "equal transit time" explanation starts by arguing that the flow over the upper surface is faster than the flow over the lower surface because the path length over the upper surface is longer and must be traversed in equal transit time. Bernoulli's principle states that under certain conditions increased flow speed is associated with reduced pressure. It is concluded that
5096-490: The airfoil and behind also indicate that air passing through the low-pressure region above the airfoil is sped up as it enters, and slowed back down as it leaves. Air passing through the high-pressure region below the airfoil is slowed down as it enters and then sped back up as it leaves. Thus the non-uniform pressure is also the cause of the changes in flow speed visible in the flow animation. The changes in flow speed are consistent with Bernoulli's principle , which states that in
5200-462: The airfoil can impart downward turning to a much deeper swath of the flow than it actually touches. Furthermore, it does not mention that the lift force is exerted by pressure differences , and does not explain how those pressure differences are sustained. Some versions of the flow-deflection explanation of lift cite the Coandă effect as the reason the flow is able to follow the convex upper surface of
5304-408: The airfoil is pushed outward from the center of the high-pressure region. According to Newton's second law , a force causes air to accelerate in the direction of the force. Thus the vertical arrows in the accompanying pressure field diagram indicate that air above and below the airfoil is accelerated, or turned downward, and that the non-uniform pressure is thus the cause of the downward deflection of
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#17327918897435408-429: The airfoil's surfaces. Pressure in a fluid is always positive in an absolute sense, so that pressure must always be thought of as pushing, and never as pulling. The pressure thus pushes inward on the airfoil everywhere on both the upper and lower surfaces. The flowing air reacts to the presence of the wing by reducing the pressure on the wing's upper surface and increasing the pressure on the lower surface. The pressure on
5512-458: The airfoil. The conventional definition in the aerodynamics field is that the Coandă effect refers to the tendency of a fluid jet to stay attached to an adjacent surface that curves away from the flow, and the resultant entrainment of ambient air into the flow. More broadly, some consider the effect to include the tendency of any fluid boundary layer to adhere to a curved surface, not just
5616-501: The amount of constriction or obstruction do not predict experimental results. Another flaw is that conservation of mass is not a satisfying physical reason why the flow would speed up. Effectively explaining the acceleration of an object requires identifying the force that accelerates it. A serious flaw common to all the Bernoulli-based explanations is that they imply that a speed difference can arise from causes other than
5720-455: The boundary layer accompanying a fluid jet. It is in this broader sense that the Coandă effect is used by some popular references to explain why airflow remains attached to the top side of an airfoil. This is a controversial use of the term "Coandă effect"; the flow following the upper surface simply reflects an absence of boundary-layer separation, thus it is not an example of the Coandă effect. Regardless of whether this broader definition of
5824-400: The common meaning of the word " lift " assumes that lift opposes weight, lift can be in any direction with respect to gravity, since it is defined with respect to the direction of flow rather than to the direction of gravity. When an aircraft is cruising in straight and level flight, the lift opposes gravity. However, when an aircraft is climbing , descending , or banking in a turn the lift
5928-409: The continuum assumption assumes that fluids are continuous, rather than discrete. Consequently, it is assumed that properties such as density, pressure, temperature, and flow velocity are well-defined at infinitesimally small points in space and vary continuously from one point to another. The fact that the fluid is made up of discrete molecules is ignored. For fluids that are sufficiently dense to be
6032-559: The contract delivery to the Syrian government supplying missiles with an advanced radar to make them more effective to counter any future foreign military invasion. A warehouse containing the Bastion missiles was destroyed by an Israeli air strike on Latakia on 5 July 2013, but US intelligence analysts believe that some missiles had been removed before the attack. Oniks missiles were reportedly used in 2016 against ISIL targets. The P-800
6136-415: The directional change. In the case of an airplane wing, the wing exerts a downward force on the air and the air exerts an upward force on the wing. The downward turning of the flow is not produced solely by the lower surface of the airfoil, and the air flow above the airfoil accounts for much of the downward-turning action. This explanation is correct but it is incomplete. It does not explain how
6240-421: The downward deflection of the air immediately behind, this establishes a net circulatory component of the flow. The downward deflection and the changes in flow speed are pronounced and extend over a wide area, as can be seen in the flow animation on the right. These differences in the direction and speed of the flow are greatest close to the airfoil and decrease gradually far above and below. All of these features of
6344-422: The downward turning, but this is false. (see above under " Controversy regarding the Coandă effect "). The arrows ahead of the airfoil indicate that the flow ahead of the airfoil is deflected upward, and the arrows behind the airfoil indicate that the flow behind is deflected upward again, after being deflected downward over the airfoil. These deflections are also visible in the flow animation. The arrows ahead of
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#17327918897436448-452: The flight profile of the missile is of particular concern: "Onyx missiles are designed to destroy watercraft, and ships, it flies at a speed of 3000 km per hour, that is, very fast,... On the march [cruising], it can rise high, and when entering the target, it can actually fly 10–15 meters above the water to destroy the ship." He concluded that it was "impossible" to shoot them down with available anti-air means, but he mentioned that some success
6552-414: The flow (Newton's laws), and one based on pressure differences accompanied by changes in flow speed (Bernoulli's principle). Either of these, by itself, correctly identifies some aspects of the lifting flow but leaves other important aspects of the phenomenon unexplained. A more comprehensive explanation involves both downward deflection and pressure differences (including changes in flow speed associated with
6656-527: The flow is irrotational everywhere, Bernoulli's equation can completely describe the flow everywhere. Such flows are called potential flows , because the velocity field may be expressed as the gradient of a potential energy expression. This idea can work fairly well when the Reynolds number is high. However, problems such as those involving solid boundaries may require that the viscosity be included. Viscosity cannot be neglected near solid boundaries because
6760-409: The flow visible in the flow animation. To produce this downward turning, the airfoil must have a positive angle of attack or have sufficient positive camber. Note that the downward turning of the flow over the upper surface is the result of the air being pushed downward by higher pressure above it than below it. Some explanations that refer to the "Coandă effect" suggest that viscosity plays a key role in
6864-428: The fluid exerts a force on the object. Lift is the component of this force that is perpendicular to the oncoming flow direction. It contrasts with the drag force, which is the component of the force parallel to the flow direction. Lift conventionally acts in an upward direction in order to counter the force of gravity , but it is defined to act perpendicular to the flow and therefore can act in any direction. If
6968-436: The governing equations of the same problem without taking advantage of the steadiness of the flow field. Turbulence is flow characterized by recirculation, eddies , and apparent randomness . Flow in which turbulence is not exhibited is called laminar . The presence of eddies or recirculation alone does not necessarily indicate turbulent flow—these phenomena may be present in laminar flow as well. Mathematically, turbulent flow
7072-403: The law applied to an infinitesimally small volume (at a point) within the flow. In the above integral formulation of this equation, the term on the left is the net change of momentum within the volume. The first term on the right is the net rate at which momentum is convected into the volume. The second term on the right is the force due to pressure on the volume's surfaces. The first two terms on
7176-410: The lift by a modest amount and modifies the pressure distribution somewhat, which results in a viscosity-related pressure drag over and above the skin friction drag. The total of the skin friction drag and the viscosity-related pressure drag is usually called the profile drag . An airfoil's maximum lift at a given airspeed is limited by boundary-layer separation . As the angle of attack is increased,
7280-421: The lift coefficient, is generally less than 1.5 for single-element airfoils and can be more than 3.0 for airfoils with high-lift slotted flaps and leading-edge devices deployed. The flow around bluff bodies – i.e. without a streamlined shape, or stalling airfoils – may also generate lift, in addition to a strong drag force. This lift may be steady, or it may oscillate due to vortex shedding . Interaction of
7384-400: The lower portion of the body is immersed in a liquid flow, is used by motorboats, surfboards, windsurfers, sailboats, and water-skis. A fluid flowing around the surface of a solid object applies a force on it. It does not matter whether the object is moving through a stationary fluid (e.g. an aircraft flying through the air) or whether the object is stationary and the fluid is moving (e.g.
7488-403: The lower surface pushes up harder than the reduced pressure on the upper surface pushes down, and the net result is upward lift. The pressure difference which results in lift acts directly on the airfoil surfaces; however, understanding how the pressure difference is produced requires understanding what the flow does over a wider area. An airfoil affects the speed and direction of the flow over
7592-580: The macroscopic and microscopic fluid motion at large velocities comparable to the velocity of light . This branch of fluid dynamics accounts for the relativistic effects both from the special theory of relativity and the general theory of relativity . The governing equations are derived in Riemannian geometry for Minkowski spacetime . This branch of fluid dynamics augments the standard hydrodynamic equations with stochastic fluxes that model thermal fluctuations. As formulated by Landau and Lifshitz ,
7696-404: The magnitude of inertial effects compared to the magnitude of viscous effects. A low Reynolds number ( Re ≪ 1 ) indicates that viscous forces are very strong compared to inertial forces. In such cases, inertial forces are sometimes neglected; this flow regime is called Stokes or creeping flow . In contrast, high Reynolds numbers ( Re ≫ 1 ) indicate that the inertial effects have more effect on
7800-403: The medium through which they propagate. All fluids, except superfluids , are viscous, meaning that they exert some resistance to deformation: neighbouring parcels of fluid moving at different velocities exert viscous forces on each other. The velocity gradient is referred to as a strain rate ; it has dimensions T . Isaac Newton showed that for many familiar fluids such as water and air ,
7904-471: The missile 90 degrees so that it is parallel to the surface , and thus the rocket begins its flight, ditching its nosecone to open its ramjet intake to the air. In its initial flight, the Oniks utilizes thrust from a solid rocket booster mounted inside the combustion chamber of its ramjet to get up to cruise speed. Once the rocket engine is expended, the air pressure built up in the ramjet's intake kicks
8008-566: The more commonly used are listed below. While many flows (such as flow of water through a pipe) occur at low Mach numbers ( subsonic flows), many flows of practical interest in aerodynamics or in turbomachines occur at high fractions of M = 1 ( transonic flows ) or in excess of it ( supersonic or even hypersonic flows ). New phenomena occur at these regimes such as instabilities in transonic flow, shock waves for supersonic flow, or non-equilibrium chemical behaviour due to ionization in hypersonic flows. In practice, each of those flow regimes
8112-494: The net force implies that the average pressure on the upper surface of the airfoil is lower than the average pressure on the underside. These pressure differences arise in conjunction with the curved airflow. When a fluid follows a curved path, there is a pressure gradient perpendicular to the flow direction with higher pressure on the outside of the curve and lower pressure on the inside. This direct relationship between curved streamlines and pressure differences, sometimes called
8216-413: The object's flexibility with the vortex shedding may enhance the effects of fluctuating lift and cause vortex-induced vibrations . For instance, the flow around a circular cylinder generates a Kármán vortex street : vortices being shed in an alternating fashion from the cylinder's sides. The oscillatory nature of the flow produces a fluctuating lift force on the cylinder, even though the net (mean) force
8320-453: The power of the computer used and the efficiency of the solution algorithm. The results of DNS have been found to agree well with experimental data for some flows. Most flows of interest have Reynolds numbers much too high for DNS to be a viable option, given the state of computational power for the next few decades. Any flight vehicle large enough to carry a human ( L > 3 m), moving faster than 20 m/s (72 km/h; 45 mph)
8424-551: The pressure as a function of other thermodynamic variables is required to completely describe the problem. An example of this would be the perfect gas equation of state : where p is pressure , ρ is density , and T is the absolute temperature , while R u is the gas constant and M is molar mass for a particular gas. A constitutive relation may also be useful. Three conservation laws are used to solve fluid dynamics problems, and may be written in integral or differential form. The conservation laws may be applied to
8528-422: The pressure difference is zero. The angle of attack is the angle between the chord line of an airfoil and the oncoming airflow. A symmetrical airfoil generates zero lift at zero angle of attack. But as the angle of attack increases, the air is deflected through a larger angle and the vertical component of the airstream velocity increases, resulting in more lift. For small angles, a symmetrical airfoil generates
8632-435: The pressure differences in the vertical direction are sustained. That is, they leave out the flow-deflection part of the interaction. Although the two simple Bernoulli-based explanations above are incorrect, there is nothing incorrect about Bernoulli's principle or the fact that the air goes faster on the top of the wing, and Bernoulli's principle can be used correctly as part of a more complicated explanation of lift. Lift
8736-405: The pressure differences), and requires looking at the flow in more detail. The airfoil shape and angle of attack work together so that the airfoil exerts a downward force on the air as it flows past. According to Newton's third law, the air must then exert an equal and opposite (upward) force on the airfoil, which is the lift. The net force exerted by the air occurs as a pressure difference over
8840-467: The production/depletion rate of any species are obtained by simultaneously solving the equations of chemical kinetics . Magnetohydrodynamics is the multidisciplinary study of the flow of electrically conducting fluids in electromagnetic fields. Examples of such fluids include plasmas , liquid metals, and salt water . The fluid flow equations are solved simultaneously with Maxwell's equations of electromagnetism. Relativistic fluid dynamics studies
8944-428: The reduced pressure over the upper surface results in upward lift. While it is true that the flow speeds up, a serious flaw in this explanation is that it does not correctly explain what causes the flow to speed up. The longer-path-length explanation is incorrect. No difference in path length is needed, and even when there is a difference, it is typically much too small to explain the observed speed difference. This
9048-432: The right are negated since momentum entering the system is accounted as positive, and the normal is opposite the direction of the velocity u and pressure forces. The third term on the right is the net acceleration of the mass within the volume due to any body forces (here represented by f body ). Surface forces , such as viscous forces, are represented by F surf , the net force due to shear forces acting on
9152-509: The rocket engine out, clearing the combustion chamber and starting the missile's self-sustaining ramjet cycle. In 2010 Sergei Prikhodko, senior adviser to the Russian President, has said that Russia intends to deliver P-800 to Syria based on the contracts signed in 2007. Syria received two Bastion missile systems with 36 missiles each (72 in total). The missiles' test was broadcast by Syrian state TV. In May 2013, Russia continued
9256-507: The same way, despite differences between air and water such as density, compressibility, and viscosity. The flow around a lifting airfoil is a fluid mechanics phenomenon that can be understood on essentially two levels: There are mathematical theories , which are based on established laws of physics and represent the flow accurately, but which require solving equations. And there are physical explanations without math, which are less rigorous. Correctly explaining lift in these qualitative terms
9360-406: The streamlines to pinch closer together, making the streamtubes narrower. When streamtubes become narrower, conservation of mass requires that flow speed must increase. Reduced upper-surface pressure and upward lift follow from the higher speed by Bernoulli's principle , just as in the equal transit time explanation. Sometimes an analogy is made to a venturi nozzle , claiming the upper surface of
9464-440: The stress-strain behaviours of such fluids, which include emulsions and slurries , some viscoelastic materials such as blood and some polymers , and sticky liquids such as latex , honey and lubricants . The dynamic of fluid parcels is described with the help of Newton's second law . An accelerating parcel of fluid is subject to inertial effects. The Reynolds number is a dimensionless quantity which characterises
9568-432: The surface instead of sliding along it), something known as the no-slip condition . Because the air at the surface has near-zero velocity but the air away from the surface is moving, there is a thin boundary layer in which air close to the surface is subjected to a shearing motion. The air's viscosity resists the shearing, giving rise to a shear stress at the airfoil's surface called skin friction drag . Over most of
9672-416: The surface is just part of this pressure field. The non-uniform pressure exerts forces on the air in the direction from higher pressure to lower pressure. The direction of the force is different at different locations around the airfoil, as indicated by the block arrows in the pressure field around an airfoil figure. Air above the airfoil is pushed toward the center of the low-pressure region, and air below
9776-428: The surface of most airfoils, the boundary layer is naturally turbulent, which increases skin friction drag. Under usual flight conditions, the boundary layer remains attached to both the upper and lower surfaces all the way to the trailing edge, and its effect on the rest of the flow is modest. Compared to the predictions of inviscid flow theory, in which there is no boundary layer, the attached boundary layer reduces
9880-431: The surrounding fluid is air, the force is called an aerodynamic force . In water or any other liquid, it is called a hydrodynamic force . Dynamic lift is distinguished from other kinds of lift in fluids. Aerostatic lift or buoyancy , in which an internal fluid is lighter than the surrounding fluid, does not require movement and is used by balloons, blimps, dirigibles, boats, and submarines. Planing lift , in which only
9984-405: The term static pressure to distinguish it from total pressure and dynamic pressure. Static pressure is identical to pressure and can be identified for every point in a fluid flow field. A point in a fluid flow where the flow has come to rest (that is to say, speed is equal to zero adjacent to some solid body immersed in the fluid flow) is of special significance. It is of such importance that it
10088-414: The terminology that is necessary in the study of fluid dynamics is not found in other similar areas of study. In particular, some of the terminology used in fluid dynamics is not used in fluid statics . Dimensionless numbers (or characteristic numbers ) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena . They include the Reynolds and
10192-414: The upper surface can be clearly seen in this animated flow visualization . Like the equal transit time explanation, the "obstruction" or "streamtube pinching" explanation argues that the flow over the upper surface is faster than the flow over the lower surface, but gives a different reason for the difference in speed. It argues that the curved upper surface acts as more of an obstacle to the flow, forcing
10296-445: The velocity field also appear in theoretical models for lifting flows. The pressure is also affected over a wide area, in a pattern of non-uniform pressure called a pressure field . When an airfoil produces lift, there is a diffuse region of low pressure above the airfoil, and usually a diffuse region of high pressure below, as illustrated by the isobars (curves of constant pressure) in the drawing. The pressure difference that acts on
10400-497: The velocity field than the viscous (friction) effects. In high Reynolds number flows, the flow is often modeled as an inviscid flow , an approximation in which viscosity is completely neglected. Eliminating viscosity allows the Navier–Stokes equations to be simplified into the Euler equations . The integration of the Euler equations along a streamline in an inviscid flow yields Bernoulli's equation . When, in addition to being inviscid,
10504-423: The volume surface. The momentum balance can also be written for a moving control volume. The following is the differential form of the momentum conservation equation. Here, the volume is reduced to an infinitesimally small point, and both surface and body forces are accounted for in one total force, F . For example, F may be expanded into an expression for the frictional and gravitational forces acting at
10608-525: The wing acts like a venturi nozzle to constrict the flow. One serious flaw in the obstruction explanation is that it does not explain how streamtube pinching comes about, or why it is greater over the upper surface than the lower surface. For conventional wings that are flat on the bottom and curved on top this makes some intuitive sense, but it does not explain how flat plates, symmetric airfoils, sailboat sails, or conventional airfoils flying upside down can generate lift, and attempts to calculate lift based on
10712-510: Was found when using electronic warfare against them; he mentioned that a missile attack on 23 September 2023 missed a military target and destroyed a "recreational area", adding that "something affected its flight." Russian sources reported on 27 March 2024 that the missile received a new active homing head in order to hit ground targets more precisely. On 20 August 2024, at the Congress of Local and Regional Authorities, Commander-in-Chief of
10816-529: Was used in the Russo-Ukrainian War. The Russian Defense Ministry announced that it had used the missile in 1 May 2022; reportedly a number of Oniks missiles were used to destroy military equipment around the city of Odesa . On 19 July 2023, Oniks missiles were used to target Ukraine's grain storage facility in the Black Sea region. Ukrainian Air Force Spokesperson Yurii Ihnat mentioned that
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