Outputs
\{ s_\alpha \}_{\alpha=1..n} | phase holdup |
\{ q_\alpha \}_{\alpha=1..n} | phase volumetric flowrate |
| pipe cross-sectional area |
\{ \dot m_\alpha \}_{\alpha = 1..n} | phase mass flowrates |
\{ \rho_\alpha \}_{\alpha = 1..n} | phase densities |
Solver
| (1) |
s_\alpha = \frac{\dot m_\alpha}{\rho_\alpha \, u_\alpha} \cdot \left( \sum_\beta \frac{\dot m_\beta}{\rho_\beta \, u_\beta} \right)^{-1} |
|
| (2) |
q_\alpha = s_\alpha \, u_\alpha \, A |
|
Derivation
Given the multiphase flow of
n phases:
\alpha = 1..n and mass flowrates
\dot m_\alpha
| (3) |
\dot m = \sum_\alpha \dot m_\alpha |
| (4) |
A = \sum_\alpha A_\alpha |
| (5) |
s_\alpha = A_\alpha/A |
| (6) |
\sum_\alpha s_\alpha = 1 |
| (7) |
u_m = \sum_\alpha s_\alpha \cdot \dot u_\alpha |
| (8) |
q_\alpha = \dot m_\alpha / \rho_\alpha = A_\alpha \, u_\alpha \Rightarrow \dot m_\alpha = \rho_\alpha \, A_\alpha \, u_\alpha |
For homogeneous pipe flow:
u_\alpha = u_m, \, \forall \alpha \in [1..n] and volumetric shares are going to be:
| (9) |
s_\alpha = \frac{\dot m_\alpha}{\rho_\alpha} \cdot \left( \sum_\beta \frac{\dot m_\beta}{\rho_\beta} \right)^{-1} |
See also
Physics / Mechanics / Continuum mechanics / Fluid Mechanics / Fluid Dynamics / Fluid Flow / Pipe Flow / Pipe Flow Dynamics / Pipe Flow Simulation
[ Pipe ] [ Pipeline ] [ Pipeline Engineering ]
