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40-415: BrahMos-II or BrahMos-2 or BrahMos Mark II is a hypersonic scramjet -propelled missile currently under joint development by India 's Defence Research and Development Organisation and Russia 's NPO Mashinostroyenia , which have together formed BrahMos Aerospace Private Limited . The BrahMos-II is expected to have a range of 1,500 kilometres (930 mi; 810 nmi) and a speed of Mach 8. During

80-492: A chemical equilibrium the dissociation constant K d is the ratio of dissociated to undissociated compound where the brackets denote the equilibrium concentrations of the species. The dissociation degree α {\displaystyle \alpha } is the fraction of original solute molecules that have dissociated. It is usually indicated by the Greek symbol α. More accurately, degree of dissociation refers to

120-472: A MTCR signatory in 2014, the parameters for Brahmos 2 will get enhanced. Its top speed will be double that of the current BrahMos-I, and it has been described as the fastest cruise missile in the world. Testing was planned to start in 2020 but has been delayed. Fourth-generation multi-purpose Russian Naval destroyers ( Project 21956 ) are also likely to be equipped with the BrahMos II. BrahMos Aerospace named

160-459: A body's Mach number increases, the density behind a bow shock generated by the body also increases, which corresponds to a decrease in volume behind the shock due to conservation of mass . Consequently, the distance between the bow shock and the body decreases at higher Mach numbers. As Mach numbers increase, the entropy change across the shock also increases, which results in a strong entropy gradient and highly vortical flow that mixes with

200-478: A more explicit description is provided by the Brønsted–Lowry acid–base theory , which specifies that the proton H+ does not exist as such in solution but is instead accepted by (bonded to) a water molecule to form the hydronium ion H 3 O . The reaction can therefore be written as and better described as an ionization or formation of ions (for the case when HA has no net charge). The equilibrium constant

240-517: A number of similarity parameters , which allow the simplification of a nearly infinite number of test cases into groups of similarity. For transonic and compressible flow , the Mach and Reynolds numbers alone allow good categorization of many flow cases. Hypersonic flows, however, require other similarity parameters. First, the analytic equations for the oblique shock angle become nearly independent of Mach number at high (~>10) Mach numbers. Second,

280-419: A number of regimes. The selection of these regimes is rough, due to the blurring of the boundaries where a particular effect can be found. In this regime, the gas can be regarded as an ideal gas . Flow in this regime is still Mach number dependent. Simulations start to depend on the use of a constant-temperature wall, rather than the adiabatic wall typically used at lower speeds. The lower border of this region

320-574: A similarity parameter, similar to the Whitcomb area rule , which allowed similar configurations to be compared. In the study of hypersonic flow over slender bodies, the product of the freestream Mach number M ∞ {\displaystyle M_{\infty }} and the flow deflection angle θ {\displaystyle \theta } , known as the hypersonic similarity parameter: K = M ∞ θ {\displaystyle K=M_{\infty }\theta }

360-411: A substance that contains free ions and can be used as an electrically conductive medium. Most of the solute does not dissociate in a weak electrolyte, whereas in a strong electrolyte a higher ratio of solute dissociates to form free ions. A weak electrolyte is a substance whose solute exists in solution mostly in the form of molecules (which are said to be "undissociated"), with only a small fraction in

400-774: A weak electrolyte. Strong acids and bases are good examples, such as HCl and H 2 SO 4 . These will all exist as ions in an aqueous medium. The degree of dissociation in gases is denoted by the symbol α , where α refers to the percentage of gas molecules which dissociate. Various relationships between K p and α exist depending on the stoichiometry of the equation. The example of dinitrogen tetroxide ( N 2 O 4 ) dissociating to nitrogen dioxide ( NO 2 ) will be taken. N 2 O 4 ↽ − − ⇀ 2 NO 2 {\displaystyle {\ce {N2O4 <=> 2NO2}}} If

440-600: Is (1 – α ) + 2 α , which is equivalent to 1 + α . Thus, substituting the mole fractions with actual values in term of α and simplifying; K p = p T ( 4 α 2 ) ( 1 + α ) ( 1 − α ) = p T ( 4 α 2 ) 1 − α 2 {\displaystyle K_{p}={\frac {p_{T}(4\alpha ^{2})}{(1+\alpha )(1-\alpha )}}={\frac {p_{T}(4\alpha ^{2})}{1-\alpha ^{2}}}} This equation

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480-411: Is a solute that exists in solution completely or nearly completely as ions. Again, the strength of an electrolyte is defined as the percentage of solute that is ions, rather than molecules. The higher the percentage, the stronger the electrolyte. Thus, even if a substance is not very soluble, but does dissociate completely into ions, the substance is defined as a strong electrolyte. Similar logic applies to

520-555: Is around Mach 5, where ramjets become inefficient, and the upper border around Mach 10–12. This is a subset of the perfect gas regime, where the gas can be considered chemically perfect, but the rotational and vibrational temperatures of the gas must be considered separately, leading to two temperature models. See particularly the modeling of supersonic nozzles, where vibrational freezing becomes important. In this regime, diatomic or polyatomic gases (the gases found in most atmospheres) begin to dissociate as they come into contact with

560-491: Is called the transonic range. Aircraft designed to fly at supersonic speeds show large differences in their aerodynamic design because of the radical differences in the behavior of flows above Mach 1. Sharp edges, thin aerofoil -sections, and all-moving tailplane / canards are common. Modern combat aircraft must compromise in order to maintain low-speed handling; "true" supersonic designs, generally incorporating delta wings, are rarer. The categorization of airflow relies on

600-449: Is considered to be an important governing parameter. The slenderness ratio of a vehicle τ = d / l {\displaystyle \tau =d/l} , where d {\displaystyle d} is the diameter and l {\displaystyle l} is the length, is often substituted for θ {\displaystyle \theta } . Hypersonic flow can be approximately separated into

640-423: Is in accordance with Le Chatelier's principle . K p will remain constant with temperature. The addition of pressure to the system will increase the value of p T , so α must decrease to keep K p constant. In fact, increasing the pressure of the equilibrium favours a shift to the left favouring the formation of dinitrogen tetroxide (as on this side of the equilibrium there is less pressure since pressure

680-431: Is less than Mach 1. The critical Mach number (Mcrit) is lowest free stream Mach number at which airflow over any part of the aircraft first reaches Mach 1. So the subsonic speed range includes all speeds that are less than Mcrit. The transonic speed range is that range of speeds within which the airflow over different parts of an aircraft is between subsonic and supersonic. So the regime of flight from Mcrit up to Mach 1.3

720-411: Is proportional to number of moles) hence decreasing the extent of dissociation α . The reaction of an acid in water solvent is often described as a dissociation where HA is a proton acid such as acetic acid, CH 3 COOH. The double arrow means that this is an equilibrium process, with dissociation and recombination occurring at the same time. This implies that the acid dissociation constant However

760-414: Is then where [ H 2 O ] {\displaystyle {\ce {[H_2O]}}} is not included because in dilute solution the solvent is essentially a pure liquid with a thermodynamic activity of one. K a is variously named a dissociation constant , an acid ionization constant , an acidity constant or an ionization constant . It serves as an indicator of

800-425: The boundary layer . A portion of the large kinetic energy associated with flow at high Mach numbers transforms into internal energy in the fluid due to viscous effects. The increase in internal energy is realized as an increase in temperature. Since the pressure gradient normal to the flow within a boundary layer is approximately zero for low to moderate hypersonic Mach numbers, the increase of temperature through

840-447: The bow shock generated by the body. Surface catalysis plays a role in the calculation of surface heating, meaning that the type of surface material also has an effect on the flow. The lower border of this regime is where any component of a gas mixture first begins to dissociate in the stagnation point of a flow (which for nitrogen is around 2000 K). At the upper border of this regime, the effects of ionization start to have an effect on

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880-810: The partial pressure . Hence, through the definition of partial pressure and using p T to represent the total pressure and x to represent the mole fraction ; K p = p T 2 ( x NO 2 ) 2 p T ⋅ x N 2 O 4 = p T ( x NO 2 ) 2 x N 2 O 4 {\displaystyle K_{p}={\frac {p_{T}^{2}{\bigl (}x\,{\ce {NO2}}{\bigr )}^{2}}{p_{T}\cdot x\,{\ce {N2O4}}}}={\frac {p_{T}{\bigl (}x\,{\ce {NO2}}{\bigr )}^{2}}{x\,{\ce {N2O4}}}}} The total number of moles at equilibrium

920-658: The BrahMos-II (K) will be based. Hypersonic In aerodynamics , a hypersonic speed is one that exceeds five times the speed of sound , often stated as starting at speeds of Mach 5 and above. The precise Mach number at which a craft can be said to be flying at hypersonic speed varies, since individual physical changes in the airflow (like molecular dissociation and ionization ) occur at different speeds; these effects collectively become important around Mach 5–10. The hypersonic regime can also be alternatively defined as speeds where specific heat capacity changes with

960-402: The acid strength: stronger acids have a higher K a value (and a lower p K a value). Fragmentation of a molecule can take place by a process of heterolysis or homolysis . Receptors are proteins that bind small ligands . The dissociation constant K d is used as indicator of the affinity of the ligand to the receptor. The higher the affinity of the ligand for the receptor

1000-468: The amount of solute dissociated into ions or radicals per mole. In case of very strong acids and bases, degree of dissociation will be close to 1. Less powerful acids and bases will have lesser degree of dissociation. There is a simple relationship between this parameter and the van 't Hoff factor i {\displaystyle i} . If the solute substance dissociates into n {\displaystyle n} ions, then For instance, for

1040-562: The boundary layer coincides with a decrease in density. This causes the bottom of the boundary layer to expand, so that the boundary layer over the body grows thicker and can often merge with the shock wave near the body leading edge. High temperatures due to a manifestation of viscous dissipation cause non-equilibrium chemical flow properties such as vibrational excitation and dissociation and ionization of molecules resulting in convective and radiative heat-flux . Although "subsonic" and "supersonic" usually refer to speeds below and above

1080-620: The cruise stage of flight, the missile will be propelled by a scramjet airbreathing jet engine . Other details, including production cost and physical dimensions of the missile, are yet to be published. The planned operational range of the BrahMos-II had initially been restricted to 290 kilometres as Russia is a signatory to the Missile Technology Control Regime (MTCR), which prohibits it from helping other countries develop missiles with ranges above 300 kilometres (190 mi; 160 nmi). However, subsequent to India becoming

1120-420: The flow. In this regime the ionized electron population of the stagnated flow becomes significant, and the electrons must be modeled separately. Often the electron temperature is handled separately from the temperature of the remaining gas components. This region occurs for freestream flow velocities around 3–4 km/s. Gases in this region are modeled as non-radiating plasmas . Above around 12 km/s,

1160-413: The following dissociation As n = 2 {\displaystyle n=2} , we would have that i = 1 + α {\displaystyle i=1+\alpha } . The dissociation of salts by solvation in a solution , such as water , means the separation of the anions and cations . The salt can be recovered by evaporation of the solvent. An electrolyte refers to

1200-496: The form of ions. Simply because a substance does not readily dissolve does not make it a weak electrolyte. Acetic acid ( CH 3 COOH ) and ammonium ( NH + 4 ) are good examples. Acetic acid is extremely soluble in water, but most of the compound dissolves into molecules, rendering it a weak electrolyte. Weak bases and weak acids are generally weak electrolytes. In an aqueous solution there will be some CH 3 COOH and some CH 3 COO and H . A strong electrolyte

1240-508: The formation of strong shocks around aerodynamic bodies means that the freestream Reynolds number is less useful as an estimate of the behavior of the boundary layer over a body (although it is still important). Finally, the increased temperature of hypersonic flow mean that real gas effects become important. Research in hypersonics is therefore often called aerothermodynamics , rather than aerodynamics . The introduction of real gas effects means that more variables are required to describe

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1280-479: The full state of a gas. Whereas a stationary gas can be described by three variables ( pressure , temperature , adiabatic index ), and a moving gas by four ( flow velocity ), a hot gas in chemical equilibrium also requires state equations for the chemical components of the gas, and a gas in nonequilibrium solves those state equations using time as an extra variable. This means that for nonequilibrium flow, something between 10 and 100 variables may be required to describe

1320-465: The heat transfer to a vehicle changes from being conductively dominated to radiatively dominated. The modeling of gases in this regime is split into two classes: The modeling of optically thick gases is extremely difficult, since, due to the calculation of the radiation at each point, the computation load theoretically expands exponentially as the number of points considered increases. Dissociation (chemistry) For reversible dissociations in

1360-547: The initial concentration of dinitrogen tetroxide is 1  mole per litre , this will decrease by α at equilibrium giving, by stoichiometry, α moles of NO 2 . The equilibrium constant (in terms of pressure) is given by the equation K p = p ( NO 2 ) 2 p N 2 O 4 {\displaystyle K_{p}={\frac {p{\bigl (}{\ce {NO2}}{\bigr )}^{2}}{p\,{\ce {N2O4}}}}} where p represents

1400-595: The local speed of sound respectively, aerodynamicists often use these terms to refer to particular ranges of Mach values. When an aircraft approaches transonic speeds (around Mach 1), it enters a special regime. The usual approximations based on the Navier–Stokes equations , which work well for subsonic designs, start to break down because, even in the freestream, some parts of the flow locally exceed Mach 1. So, more sophisticated methods are needed to handle this complex behavior. The "supersonic regime" usually refers to

1440-538: The missile BrahMos-II (K) in honour of the former President of India , APJ Abdul Kalam . The CEO of the joint Indo-Russian BrahMos programme, Atul Rane, stated in 2022, a future BrahMos-II will likely have similar characteristics to the 3M22 Zircon . According to reports published in April 2023, India has requested Russia for the transfer of technology (ToT) for the Russian 3M22 Zircon hypersonic cruise missile, upon which

1480-420: The previously-operated Space Shuttle ; various reusable spacecraft in development such as SpaceX Starship and Rocket Lab Electron ; and (theoretical) spaceplanes . In the following table, the "regimes" or "ranges of Mach values" are referenced instead of the usual meanings of "subsonic" and "supersonic". The subsonic speed range is that range of speeds within which, all of the airflow over an aircraft

1520-455: The set of Mach numbers for which linearised theory may be used; for example, where the ( air ) flow is not chemically reacting and where heat transfer between air and vehicle may be reasonably neglected in calculations. Generally, NASA defines "high" hypersonic as any Mach number from 10 to 25, and re-entry speeds as anything greater than Mach 25. Among the spacecraft operating in these regimes are returning Soyuz and Dragon space capsules ;

1560-437: The state of the gas at any given time. Additionally, rarefied hypersonic flows (usually defined as those with a Knudsen number above 0.1) do not follow the Navier–Stokes equations . Hypersonic flows are typically categorized by their total energy, expressed as total enthalpy (MJ/kg), total pressure (kPa-MPa), stagnation pressure (kPa-MPa), stagnation temperature (K), or flow velocity (km/s). Wallace D. Hayes developed

1600-470: The temperature of the flow as kinetic energy of the moving object is converted into heat. While the definition of hypersonic flow can be quite vague and is generally debatable (especially due to the absence of discontinuity between supersonic and hypersonic flows), a hypersonic flow may be characterized by certain physical phenomena that can no longer be analytically discounted as in supersonic flow. The peculiarities in hypersonic flows are as follows: As

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