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c(T,p) = \frac{1}{\rho} \left( \frac{\partial \rho}{\partial p} \right)_T = - \frac{1}{V_m} \left( \frac{\partial V_m}{\partial p} \right)_T |
There is no universal ffull-range analytical model for Fluid Compressibility but there is a good number of approximations which can be effectively used in engineering practice.
Approximations
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Incompressible fluid | Compressible fluid |
Full-Range Proxy Model |
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| Slightly compressible fluid | Strongly Compressible Fluid |
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| Real Gas | Ideal Gas |
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| c(T, p) = 0 |
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| c(T, p) = c_0 = \rm const |
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| c(T, p) = \frac{1}{p} |
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| c(T, p) = \frac{c_0(T,p)}{1+c_0(T,p) \cdot p} |
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| \rho(T, p) = \rho_0(T) |
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| \rho(T, p) = \rho_0 \cdot \exp \left[ c_0(T) \cdot (p-p_0) \right] |
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| \rho(T, p) = \frac{\rho_0(T)}{p_0} \cdot p |
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| \rho(T, p) = \rho_0(T) \cdot \frac{1+c_0(T,p) \, p}{1+c_0(T,p) \, p_0} |
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| Z(T, p) = \frac{p}{p_0} |
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| Z(T, p) =\frac{p}{p_0}\cdot \exp \left[ - c_0(T) \cdot (p-p_0) \right] |
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| Z(T, p) = 1 |
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| Z(T, p) = \frac{p}{p_0} \cdot \frac{1+c_0(T, p) \, p_0}{1 + c_0(T,p) \, p} |
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where
Mathematical models of Fluid Compressibility are reviewed in Fluid Compressibility @model.
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