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LaTeX Math Block
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\dot m = \dot m_1 +sum_\alpha \dot m_2\alpha


LaTeX Math Block
anchor1
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A = A_1 + A_2
LaTeX Math Block
anchor4UAJQ
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s_1 = A_1/A 

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anchor4UAJQ
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\sum_\alpha A_\alpha


LaTeX Math Block
anchor29G9B
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s_1 +\sum_\alpha s_2\alpha = 1


LaTeX Math Block
anchorIKGRE
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u_m = s\sum_1 \cdot \dot u_1 +\alpha s_2\alpha \cdot \dot u_2\alpha


LaTeX Math Block
anchor4UAJQ
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q_

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\alpha = \dot m_

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\alpha / \rho_

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\alpha = A_

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\alpha \, u_

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\alpha \Rightarrow \dot m_

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\alpha = \rho_

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alpha \, A_

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anchor4UAJQ
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\alpha \, u_

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\

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alpha 


LaTeX Math Block
anchorORI6M
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s_

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\alpha =  \frac{\dot m_

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\alpha}{\

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rho_

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\

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alpha \

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, u

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_

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\

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alpha} \

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cdot \

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anchorORI6M
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left( \sum_\beta \frac{\dot m_

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\beta}{\

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rho_

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\beta \, u_

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\beta} \right)^{-1}



For homogeneous For homogeneous 2-phase pipe flow: 

LaTeX Math Inline
bodyu_1 = u_2 \alpha = u_m, \, \forall \alpha
 and volumetric shares are going to be:

LaTeX Math Block
anchor

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LTRUS
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s_

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\alpha =  \frac{\dot m_

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\alpha}{\rho_

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\alpha \

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cdot \

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anchorORI6M
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left( \sum_\beta \frac{\dot m_

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\beta}{\rho_

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\beta} \right)^{-1}



See also

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Physics / Mechanics / Continuum mechanics / Fluid Mechanics / Fluid Dynamics / Fluid Flow / Pipe Flow / Pipe Flow Dynamics / Pipe Flow Simulation

Pipe ] [ Pipeline ] [ Pipeline Engineering ]


LaTeX Math Block
anchor4UAJQ
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s_\alpha = A_\alpha/A