### Re: What are the temp. pressure & speed of sound in center of TNT explosion?

Date: Mon Feb 25 13:16:04 2008
Posted By: Joseph Weeks, Engineer
Area of science: Physics
ID: 1201836936.Ph
Message:

From a theoretical standpoint, the maximum pressure and temperature in an explosion are defined by the Chapman-Jouguet point or simply C-J point. At the C-J point, "the detonation proceeds at a velocity at which the reacting gases just reach sonic velocity (in the frame of the lead shock) as the reaction ceases." (See http://en.wikipedia.org/wiki/Chapman-Jouguet_condition).

The C-J point can be calculated for explosive mixtures and gives the theoretical value for the maximum pressure and temperature and velocity that would be reached for that particular explosive. In reality, the actual detonation pressures and temperatures are somewhat less.

The C-J pressure for TNT is 19.09 GPa and temperature is 3712K as reported by ATK (http://www.dtic.mil/ndia/2003insensitive/dewey.pdf) and as 19 GPa and 3700K in this book: Synthesis, Properties and Applications of Ultrananocrystalline Diamond By Dieter page 191. Measured pressure for TNT detonation was reported as 187.2 kilobars, which is 18.92 GPa by N.L. Coleburn at the Naval Ordinance Lab (http://stinet.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=AD0603540)

The detonation velocity of TNT is approximately 22,300 feet per second (6800 meters/sec) (see http://www.globalsecurity.org/military/systems/munitions/explosives-nitroaromatics.htm) The exit velocity of the gases from the shuttle main engine are reported to be about 4500 meters/sec (see http://batman.mech.ubc.ca/~mech380/notes/node34.html).

So, you can see that the detonation velocity of TNT is approximately 2,300 meters/sec higher than the gas velocity exiting from the shuttle main engine, and the detonation pressures are many orders of magnitude higher than produced by the shuttle. The pressure from an explosive blast decreases as the cube of the distance from the explosion, so if you knew the weight of the explosive, you could calculate the overpressure as a function of distance from the blast. But, considering that the rocket nozzles are operating very close to the maximum pressure that they can sustain without rupturing, it wouldn't take much of a shock wave or overpressure to interfere with the the gas exiting the nozzle, bringing the shuttle launch to an abrupt end. A clever plot by SPECTRE that may finally bring Bond to his doom.

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