Outputs
LaTeX Math Inline |
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body | --uriencoded--\%7B s_\alpha \%7D_%7B\alpha=1..n%7D |
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| phase holdup |
LaTeX Math Inline |
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body | --uriencoded--\%7B q_\alpha \%7D_%7B\alpha=1..n%7D |
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| phase volumetric flowrate |
Inputs
| pipe cross-sectional area |
LaTeX Math Inline |
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body | --uriencoded--\%7B \dot m_\alpha \%7D_%7B\alpha = 1..n%7D |
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| phase mass flowrates |
LaTeX Math Inline |
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body | --uriencoded--\%7B \rho_\alpha \%7D_%7B\alpha = 1..n%7D |
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| phase densities |
Solver
LaTeX Math Block |
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| s_\alpha = \frac{\dot m_\alpha}{\rho_\alpha \, u_\alpha} \cdot \left( \sum_\beta \frac{\dot m_\beta}{\rho_\beta \, u_\beta} \right)^{-1} |
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LaTeX Math Block |
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| q_\alpha = s_\alpha \, u_\alpha \, A |
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Derivation
Given the multiphase flow of
phases: and mass flowrates LaTeX Math Block |
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\dot m = \sum_\alpha \dot m_\alpha |
...
LaTeX Math Block |
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q_\alpha = \dot m_\alpha / \rho_\alpha = A_\alpha \, u_\alpha \Rightarrow \dot m_\alpha = \rho_\alpha \, A_\alpha \, u_\alpha |
LaTeX Math Block |
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anchor | ORI6M |
alignment | left | s_\alpha = \frac{\dot m_\alpha}{\rho_\alpha \, u_\alpha} \cdot \left( \sum_\beta \frac{\dot m_\beta}{\rho_\beta \, u_\beta} \right)^{-1} |
For homogeneous pipe flow:
LaTeX Math Inline |
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body | u_\alpha = u_m, \, \forall \alpha \in [1..n] |
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and volumetric shares are going to be:
...