Benedict-Webb-Rubin equation of state
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Term information
The Benedict Rubin equation (BWR) is an equation of state used in fluid dynamics. :<math>P=\rho RT + \left(B_0 RT-A_0 - \frac{C_0}{T^2} \right) \rho^2 + \left(bRT-a\right) \rho^3 + \alpha a \rho^6 + \frac{c\rho^3}{T^2}\left(1 + \gamma\rho^2\right)\exp\left(-\gamma\rho^2\right)</math> source: http://en.wikipedia.org/wiki/Benedict%E2%80%93Webb%E2%80%93Rubin_equation
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> <apply> <eq/> <ci>P</ci> <apply> <plus/> <apply> <times/> <ci>ρ</ci> <ci>R</ci> <ci>T</ci> </apply> <apply> <times/> <apply> <minus/> <apply> <minus/> <apply> <times/> <ci> <msub> <mi>B</mi> <mn>0</mn> </msub> </ci> <ci>R</ci> <ci>T</ci> </apply> <ci> <msub> <mi>A</mi> <mn>0</mn> </msub> </ci> </apply> <apply> <divide/> <ci> <msub> <mi>C</mi> <mn>0</mn> </msub> </ci> <apply> <power/> <ci>T</ci> <cn>2</cn> </apply> </apply> </apply> <apply> <power/> <ci>ρ</ci> <cn>2</cn> </apply> </apply> <apply> <times/> <apply> <minus/> <apply> <times/> <ci>b</ci> <ci>R</ci> <ci>T</ci> </apply> <ci>a</ci> </apply> <apply> <power/> <ci>ρ</ci> <cn>3</cn> </apply> </apply> <apply> <times/> <ci>α</ci> <ci>a</ci> <apply> <power/> <ci>ρ</ci> <cn>6</cn> </apply> </apply> <apply> <times/> <apply> <times/> <apply> <divide/> <apply> <times/> <ci>c</ci> <apply> <power/> <ci>ρ</ci> <cn>3</cn> </apply> </apply> <apply> <power/> <ci>T</ci> <cn>2</cn> </apply> </apply> <apply> <plus/> <cn>1</cn> <apply> <times/> <eulergamma/> <apply> <power/> <ci>ρ</ci> <cn>2</cn> </apply> </apply> </apply> </apply> <apply> <exp/> <apply> <minus/> <apply> <times/> <eulergamma/> <apply> <power/> <ci>ρ</ci> <cn>2</cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </math>
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> <mrow> <mi>P</mi> <mo>=</mo> <mrow> <mrow> <mi>ρ</mi> <mo>⁢</mo> <mi>R</mi> <mo>⁢</mo> <mi>T</mi> </mrow> <mo>+</mo> <mrow> <mfenced close=")" open="("> <mrow> <mrow> <mrow> <msub> <mi>B</mi> <mn>0</mn> </msub> <mo>⁢</mo> <mi>R</mi> <mo>⁢</mo> <mi>T</mi> </mrow> <mo>-</mo> <msub> <mi>A</mi> <mn>0</mn> </msub> </mrow> <mo>-</mo> <mfrac> <msub> <mi>C</mi> <mn>0</mn> </msub> <msup> <mi>T</mi> <mn>2</mn> </msup> </mfrac> </mrow> </mfenced> <mo>⁢</mo> <msup> <mi>ρ</mi> <mn>2</mn> </msup> </mrow> <mo>+</mo> <mrow> <mfenced close=")" open="("> <mrow> <mrow> <mi>b</mi> <mo>⁢</mo> <mi>R</mi> <mo>⁢</mo> <mi>T</mi> </mrow> <mo>-</mo> <mi>a</mi> </mrow> </mfenced> <mo>⁢</mo> <msup> <mi>ρ</mi> <mn>3</mn> </msup> </mrow> <mo>+</mo> <mrow> <mi>α</mi> <mo>⁢</mo> <mi>a</mi> <mo>⁢</mo> <msup> <mi>ρ</mi> <mn>6</mn> </msup> </mrow> <mo>+</mo> <mrow> <mrow> <mfrac> <mrow> <mi>c</mi> <mo>⁢</mo> <msup> <mi>ρ</mi> <mn>3</mn> </msup> </mrow> <msup> <mi>T</mi> <mn>2</mn> </msup> </mfrac> <mo>⁢</mo> <mfenced close=")" open="("> <mrow> <mn>1</mn> <mo>+</mo> <mrow> <mi>γ</mi> <mo>⁢</mo> <msup> <mi>ρ</mi> <mn>2</mn> </msup> </mrow> </mrow> </mfenced> </mrow> <mo>⁢</mo> <mrow> <mi>exp</mi> <mo>⁡</mo> <mfenced close=")" open="("> <mrow> <mo>-</mo> <mrow> <mi>γ</mi> <mo>⁢</mo> <msup> <mi>ρ</mi> <mn>2</mn> </msup> </mrow> </mrow> </mfenced> </mrow> </mrow> </mrow> </mrow> </math>
P=\rho RT + \left(B_0 RT-A_0 - \frac{C_0}{T^2} \right) \rho^2 + \left(bRT-a\right) \rho^3 + \alpha a \rho^6 + \frac{c\rho^3}{T^2}\left(1 + \gamma\rho^2\right)\exp\left(-\gamma\rho^2\right)
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> <semantics> <mrow> <mi>P</mi> <mo>=</mo> <mi>ρ</mi> <mi>R</mi> <mi>T</mi> <mo>+</mo> <mfenced close=")" open="("> <mrow> <msub> <mi>B</mi> <mn>0</mn> </msub> <mi>R</mi> <mi>T</mi> <mo>-</mo> <msub> <mi>A</mi> <mn>0</mn> </msub> <mo>-</mo> <mfrac> <msub> <mi>C</mi> <mn>0</mn> </msub> <msup> <mi>T</mi> <mn>2</mn> </msup> </mfrac> </mrow> </mfenced> <msup> <mi>ρ</mi> <mn>2</mn> </msup> <mo>+</mo> <mfenced close=")" open="("> <mrow> <mi>b</mi> <mi>R</mi> <mi>T</mi> <mo>-</mo> <mi>a</mi> </mrow> </mfenced> <msup> <mi>ρ</mi> <mn>3</mn> </msup> <mo>+</mo> <mi>α</mi> <mi>a</mi> <msup> <mi>ρ</mi> <mn>6</mn> </msup> <mo>+</mo> <mfrac> <mrow> <mi>c</mi> <msup> <mi>ρ</mi> <mn>3</mn> </msup> </mrow> <msup> <mi>T</mi> <mn>2</mn> </msup> </mfrac> <mfenced close=")" open="("> <mrow> <mn>1</mn> <mo>+</mo> <mi>γ</mi> <msup> <mi>ρ</mi> <mn>2</mn> </msup> </mrow> </mfenced> <mi>exp</mi> <mfenced close=")" open="("> <mrow> <mo>-</mo> <mi>γ</mi> <msup> <mi>ρ</mi> <mn>2</mn> </msup> </mrow> </mfenced> </mrow> <annotation encoding="SnuggleTeX">\[ P=\rho RT + \left(B_0 RT-A_0 - \frac{C_0}{T^2} \right) \rho^2 + \left(bRT-a\right) \rho^3 + \alpha a \rho^6 + \frac{c\rho^3}{T^2}\left(1 + \gamma\rho^2\right)\exp\left(-\gamma\rho^2\right) \]</annotation> </semantics> </math>