https://en.formulasearchengine.com/index.php?action=history&feed=atom&title=Tensor_operatorTensor operator - Revision history2026-05-06T05:06:34ZRevision history for this page on the wikiMediaWiki 1.43.0-wmf.28https://en.formulasearchengine.com/index.php?title=Tensor_operator&diff=29897&oldid=preven>Mark viking: Added wl2014-01-11T01:54:04Z<p>Added wl</p>
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Normal shocks is a fundamental type of [[Shock wave]].The [[Shock wave]] which are perpendicular to the flow is called Normal shocks. It happen only when the flow is supersonic. When the flow is flowing at higher mach no the presence of obstacle is identified before the speed of sound which makes the molecule return after sensing the obstacle. While returning, the molecule get coalescent at certain point. This thin film of molecules act as a normal shocks.<br />
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== Thermodynamic relation across the normal shocks==<br />
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===Relation of Mach number across the normal shocks===<br />
The [[Mach number]] in the upstream is given by<math>{M_x}</math> and the mach number in the downstream is given by<math>{M_y}</math><br />
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{{NumBlk|:|<math>{M^2_y=\frac{{\frac{2}{\gamma-1}}+M^2_x}{\frac{2\gamma}{\gamma-1}M^2_x-1}}</math>|{{EquationRef|1}}}}<br />
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===Static pressure relation===<br />
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{{NumBlk|:|<math>{\frac{P_y}{P_x}=\frac{2\gamma}{\gamma+1}M^2_x-{\frac{\gamma-1}{\gamma+1}}}</math>|{{EquationRef|2}}}}<br />
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===Static temperature relation===<br />
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{{numBlk|:|<math>{\frac{T_y}{T_x}=\frac{\left(1+\frac{\gamma-1}{2}M^2_x\right)\left(\frac{2\gamma}{\gamma-1}M^2_x-1\right)}{\frac{1}{2}\frac{\left(\gamma+1\right)^2}{\left(\gamma-1\right)}M^2_x}}</math>|{{EquationRef|3}}}}<br />
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===Stagnation pressure ratio===<br />
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{{NumBlk|:|<math>{\frac{P_oy}{P_ox}=\left(\frac{\frac{\gamma+1}{2}M^2_x}{1+\frac{\gamma-1}{2}M^2_x}\right)^\frac{\gamma}{\left(\gamma-1\right)}\left(\frac{2\gamma}{\gamma+1}M^2_x-\frac{\gamma-1}{\gamma+1}\right)}</math>|{{EquationRef|4}}}}<br />
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===Entropy change across the normal shocks===<br />
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{{NumBlk|:|<math>{\frac{\Delta S}{R}=\frac{\gamma}{\gamma-1}\ln\left(\frac{2}{\left(\gamma+1\right)M^2_x}+\frac{\gamma-1}{\gamma+1}\right)+\frac{1}{\gamma-1}\ln\left(\frac{2\gamma}{\gamma+1}M^2_x-\frac{\gamma-1}{\gamma+1}\right)}</math>|{{EquationRef|5}}}}<br />
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==Reference list==<br />
*{{cite book|last=Yaha|first=S.M|title=Fundamentals of compressible flow|year=2010|publisher=New age international publishers|isbn=9788122426687|edition=4th edition.}}<br />
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[[Category:Shock waves]]</div>en>Mark viking