Riemann problem - Revision history

2A02:1811:318D:3100:7954:7011:8DE2:4F14: /* The Riemann problem in linearized gas dynamics */

2014-12-12T22:04:19Z

The Riemann problem in linearized gas dynamics

← Older revision		Revision as of 00:04, 13 December 2014
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	'~~''Oxygen balance''' ('''OB''', or '''OB%''')~~ is ~~an expression that~~ is ~~used to indicate the degree to which~~ an ~~explosive can be oxidized~~. If an explosive molecule contains just enough oxygen to form [[carbon dioxide]] from [[carbon]], water from [[hydrogen]] molecules, all of its [[sulfur dioxide]] from [[sulfur]], and all metal oxides from metals with no excess, the molecule is said to ~~have a '''zero oxygen balance'''~~. The ~~molecule~~ is ~~said~~ to ~~have a '''positive oxygen balance''' if it contains more oxygen than is needed~~ and a '''negative oxygen balance''' if it contains less oxygen than is needed; the combustion will then be incomplete, and large amount of toxic gases like [[carbon monoxide]] will be present. The sensitivity, [[strength (~~explosive)\|strength]], and~~ [~~[brisance]] of an explosive are all somewhat dependent upon oxygen balance and tend to approach their maxima as oxygen balance approaches zero~~.

	The oxygen balance is calculated from the empirical formula of a compound in percentage of oxygen required for complete conversion of carbon to carbon dioxide, hydrogen to water, and metal to metal oxide.

	The procedure for calculating oxygen balance in terms of 100 grams of the explosive material is to determine the number of [[Mole (unit)\|mole]]s of oxygen that are excess or deficient for 100 grams of a compound.

	~~:<math>OB\%~~ = ~~\frac{~~-~~1600}{Mol~~. wt. ~~of compound} \times (2X + (Y/2) + M - Z~~)~~</math>~~

	~~where~~

	'~~'X'' = number of atoms of carbon, ''Y'' = number of atoms of hydrogen, ''Z'' = number of atoms of oxygen, and ''M'' = number of atoms of metal (metallic oxide produced)~~.

	~~In the case of [[trinitrotoluene\|TNT]] (C~~<~~sub~~>6<~~/sub~~>~~H<sub>2</sub>(NO<sub>2</sub>)<sub>3<~~/~~sub>CH<sub>3<~~/~~sub>),~~

	~~Molecular weight = 227~~.1

	~~''X'' = 7 (number of carbon atoms)~~

	~~''Y'' = 5 (number of hydrogen atoms)~~

	~~''Z'' = 6 (number of oxygen atoms)~~

	~~Therefore~~

	~~:<math>OB\% = \frac{-1600}{227~~.~~1} \times (14 + 2~~.~~5 - 6)<~~/~~math>~~

	~~:OB% =~~ -~~74% for TNT~~

	Because sensitivity, [[brisance]], and strength are properties resulting from a complex explosive chemical reaction, a simple relationship such as oxygen balance cannot be depended upon to yield universally consistent results. When using oxygen balance to predict properties of one explosive relative to another, it is to be expected that one with an oxygen balance closer to zero will be the more brisant, powerful, and sensitive; however, many exceptions to this rule do exist. More complicated predictive calculations, such as those discussed in the next section of the [[explosive materials]] article, result in more accurate predictions.

	One area in which oxygen balance can be applied is in the processing of mixtures of explosives. The family of explosives called [[amatol]]s are mixtures of [[ammonium nitrate]] and [[trinitrotoluene\|TNT]]. Ammonium nitrate has an oxygen balance of +20% and TNT has an oxygen balance of −74%, so it would appear that the mixture yielding an oxygen balance of zero would also result in the best explosive properties. In actual practice a mixture of 80% ammonium nitrate and 20% TNT by weight yields an oxygen balance of +1%, the best properties of all mixtures, and an increase in strength of 30% over TNT.

	~~Examples of materials with negative oxygen balance are e.g. [[trinitrotoluene]] (~~-~~74%), [[aluminium]] powder (~~-~~89%), [[sulfur]] (~~-~~100%), or [[carbon]] (~~-~~266.7%).~~

	~~Examples of materials with positive oxygen balance are e.g. [[ammonium nitrate]] (+20%), [[ammonium perchlorate]~~] (~~+34%),~~ [~~[potassium chlorate]] (+39~~.~~2%), [[sodium chlorate]] (+45%), [[sodium nitrate]] (+47%), [[tetranitromethane]] (+49%), [[lithium perchlorate]] (+60%), or [[nitroglycerine]] (+3~~.~~5%)~~.

	~~The theoretical compound [[trinitrotriazine]] has an oxygen balance of zero.~~

	Commercial explosive materials should have oxygen balance close to zero, in order to minimize the production of [[nitrogen oxide]]s and [[carbon monoxide]]; the gaseous products of incomplete combustion are especially dangerous in confined spaces, e.g. ~~[[coal mine]]s~~.

	~~{{DEFAULTSORT:Oxygen Balance}}~~
	~~[[Category:Explosives engineering]~~]

132.206.200.137: /* The Riemann problem in linearized gas dynamics */

2013-05-17T20:32:16Z

The Riemann problem in linearized gas dynamics

← Older revision		Revision as of 22:32, 17 May 2013
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	~~Andera~~ is ~~what you~~ can ~~call her but she never really favored that title~~. ~~She functions as~~ a ~~journey agent but soon she~~'ll be ~~on her personal~~. ~~Playing badminton~~ is a ~~thing that he~~ is ~~completely addicted~~ to. I'~~ve usually loved living in Kentucky but now I~~'~~m contemplating other options~~.<br><br>~~Feel free~~ to ~~visit my blog~~ ... ~~clairvoyants~~ ([~~http://conniecolin~~.~~com/xe/community/24580 http://conniecolin~~.~~com~~])		{{Unreferenced\|date=February 2007}}
			'''Oxygen balance''' ('''OB''', or '''OB%''') is an expression that is used to indicate the degree to which an explosive can be oxidized. If an explosive molecule contains just enough oxygen to form [[carbon dioxide]] from [[carbon]], water from [[hydrogen]] molecules, all of its [[sulfur dioxide]] from [[sulfur]], and all metal oxides from metals with no excess, the molecule is said to have a '''zero oxygen balance'''. The molecule is said to have a '''positive oxygen balance''' if it contains more oxygen than is needed and a '''negative oxygen balance''' if it contains less oxygen than is needed; the combustion will then be incomplete, and large amount of toxic gases like [[carbon monoxide]] will be present. The sensitivity, [[strength (explosive)\|strength]], and [[brisance]] of an explosive are all somewhat dependent upon oxygen balance and tend to approach their maxima as oxygen balance approaches zero.

			The oxygen balance is calculated from the empirical formula of a compound in percentage of oxygen required for complete conversion of carbon to carbon dioxide, hydrogen to water, and metal to metal oxide.

			The procedure for calculating oxygen balance in terms of 100 grams of the explosive material is to determine the number of [[Mole (unit)\|mole]]s of oxygen that are excess or deficient for 100 grams of a compound.

			:<math>OB\% = \frac{-1600}{Mol. wt. of compound} \times (2X + (Y/2) + M - Z)</math>

			where

			''X'' = number of atoms of carbon, ''Y'' = number of atoms of hydrogen, ''Z'' = number of atoms of oxygen, and ''M'' = number of atoms of metal (metallic oxide produced).

			In the case of [[trinitrotoluene\|TNT]] (C<sub>6</sub>H<sub>2</sub>(NO<sub>2</sub>)<sub>3</sub>CH<sub>3</sub>),

			Molecular weight = 227.1

			''X'' = 7 (number of carbon atoms)

			''Y'' = 5 (number of hydrogen atoms)

			''Z'' = 6 (number of oxygen atoms)

			Therefore

			:<math>OB\% = \frac{-1600}{227.1} \times (14 + 2.5 - 6)</math>

			:OB% = -74% for TNT

			Because sensitivity, [[brisance]], and strength are properties resulting from a complex explosive chemical reaction, a simple relationship such as oxygen balance cannot be depended upon to yield universally consistent results. When using oxygen balance to predict properties of one explosive relative to another, it is to be expected that one with an oxygen balance closer to zero will be the more brisant, powerful, and sensitive; however, many exceptions to this rule do exist. More complicated predictive calculations, such as those discussed in the next section of the [[explosive materials]] article, result in more accurate predictions.

			One area in which oxygen balance can be applied is in the processing of mixtures of explosives. The family of explosives called [[amatol]]s are mixtures of [[ammonium nitrate]] and [[trinitrotoluene\|TNT]]. Ammonium nitrate has an oxygen balance of +20% and TNT has an oxygen balance of −74%, so it would appear that the mixture yielding an oxygen balance of zero would also result in the best explosive properties. In actual practice a mixture of 80% ammonium nitrate and 20% TNT by weight yields an oxygen balance of +1%, the best properties of all mixtures, and an increase in strength of 30% over TNT.

			Examples of materials with negative oxygen balance are e.g. [[trinitrotoluene]] (-74%), [[aluminium]] powder (-89%), [[sulfur]] (-100%), or [[carbon]] (-266.7%).

			Examples of materials with positive oxygen balance are e.g. [[ammonium nitrate]] (+20%), [[ammonium perchlorate]] (+34%), [[potassium chlorate]] (+39.2%), [[sodium chlorate]] (+45%), [[sodium nitrate]] (+47%), [[tetranitromethane]] (+49%), [[lithium perchlorate]] (+60%), or [[nitroglycerine]] (+3.5%).

			The theoretical compound [[trinitrotriazine]] has an oxygen balance of zero.

			Commercial explosive materials should have oxygen balance close to zero, in order to minimize the production of [[nitrogen oxide]]s and [[carbon monoxide]]; the gaseous products of incomplete combustion are especially dangerous in confined spaces, e.g. [[coal mine]]s.

			{{DEFAULTSORT:Oxygen Balance}}
			[[Category:Explosives engineering]]

67.82.136.60: /* The Riemann problem in linearized gas dynamics */

2012-07-29T16:13:16Z

The Riemann problem in linearized gas dynamics

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