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