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(1) |
\dot m = \dot m_1 + \dot m_2 |
(3) |
\begin{cases}
s_1 = A_1/A
\\
s_2 = A_2/A
\end{cases} |
(5) |
u_m = s_1 \cdot \dot u_1 + s_2 \cdot \dot u_2 |
(6) |
\begin{cases}
q_1 = \dot m_1 / \rho_1 = A_1 \, u_1 \Rightarrow \dot m_1 = \rho_1 \, A_1 \, u_1
\\
q_2 = \dot m_2 / \rho_2 = A_2 \, u_2 \Rightarrow \dot m_2 = \rho_2 \, A_2 \, u_2
\end{cases} |
The areas ratio:
(7) |
\omega_{12} = \frac{A_1}{A_2} = \frac{\dot m_1 \, \rho_2 \, u_2}{\dot m_2 \, \rho_1 \, u_1} |
(8) |
\begin{cases}
A_1 = \frac{\omega_{12}}{1+\omega_{12}} \cdot A
\\
A_2 = \frac{1}{1+\omega_{12}} \cdot A
\end{cases} |
For homogeneous 2-phase pipe flow:
u_1 = u_2 = u_m and areas ratio are going to be:
(9) |
\omega_{12} = \frac{\dot m_1 \, \rho_2 }{\dot m_2 \, \rho_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 ]