Math 2.0

Fluid mechanics Definition

Detonation

Builds on Shock wave in gasesSpeed of soundCombustion theory

Definition

Consider a combustible gas mixture that can react and release heat, as in combustion theory. A combustion wave is a front that moves into the unburnt mixture and leaves burnt gas behind it. Let DD be the speed of the front relative to the unburnt gas and let c1c_1 be the speed of sound in the unburnt gas. The wave is a detonation if the following hold.

  1. It moves supersonically into the unburnt gas: D>c1D > c_1.
  2. It is led by a shock wave that compresses the unburnt gas and starts the reaction.
  3. The pressure and density of the burnt gas are higher than those of the unburnt gas.

Remarks

In the simplest model the whole wave is a discontinuity across which mass, momentum and total energy, including chemical energy, are conserved. The burnt states then lie on the reactive Hugoniot curve of the unburnt state, which has two branches. On the detonation branch the pressure rises and the wave is supersonic; on the deflagration branch the pressure falls and the wave is subsonic.

Example: a steady planar Chapman–Jouguet detonation in a hydrogen and oxygen mixture runs at a speed of the order of kilometres per second. This is far above the sound speed of the unburnt gas.

Non-example: a premixed laminar flame, as on a gas stove, moves into the fresh gas at well below the speed of sound and the pressure drops slightly across it. It fails clause 1 and is a deflagration.

Reading path

To understand this page from the ground up, read these 4 pages in order. The foundations come first.

Show the path as a graph
Combustion theory, concept, no evidence levelCombustion theoryconceptShock wave in gases, concept, no evidence levelShock wave in gasesconceptSpeed of sound, concept, no evidence levelSpeed of soundconceptDetonation, definition, no evidence levelDetonationdefinition
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Combustion theory concept
  2. Shock wave in gases concept
  3. Speed of sound concept
  4. Detonation definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Detonation
About this page
TagGAS1A4ZYYF
URIm2://GAS1A4ZYYF
Kinddefinition
WritingW0 stub
MSC76L05, 80A25, 76V05
DefinesDetonation
UsesShock wave in gases, Speed of sound, Combustion theory
Changed3 November 2026

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