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| c(p) = \frac{1}{p} - \frac{1}{Z} \frac{dZ}{dp} |
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| Z(p) = \frac{Z_0}{p_0} \cdot p \cdot \exp \left[ - \int_{p_0}^p c(p) dp \right] |
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| c = \frac{1}{\rho} \frac{d\rho}{dp} = \frac{d \ln \rho}{dp} = \frac{d }{dp} \left( \ln \left(\frac{p}{Z} \right) \right) = \frac{Z}{p} \cdot \frac{d }{dp} \left(\frac{p}{Z} \right) = \frac{Z}{p} \cdot \left( \frac{1}{Z} + p \cdot \frac{d }{dp} \left( \frac{1}{Z} \right) \right) = \frac{1}{p} - \frac{1}{Z} \frac{dZ}{dp} |
Integrating | LaTeX Math Block Reference |
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one arrives to | LaTeX Math Block Reference |
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The Z-factor value is trending towards unit value (
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for incompressible fluids and linear pressure dependence (| LaTeX Math Inline |
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| body | Z \rightarrow a \cdot p |
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for strongly compressible Fluids.
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