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A share of total pipe cross-section area occupied by moving 

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body\alpha
-phase is called an 
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body\alpha
-phase phase hold-up and defined as: 

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s_\alpha = \frac{A_\alpha}{A}

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The actual average cross-sectional velocity of moving 

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body\alpha
-phase is called in-situ velocity  velocity and defined as:

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u_\alpha = \frac{q_\alpha}{A_\alpha}

where 

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bodyq_\alpha
 is the volumetric 
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body\alpha
-phase flowrate through cross-sectional area 
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bodyA_\alpha
.


The  superficial velocity  velocity of 

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body\alpha
-phase is defined as the 

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The difference between velocities of 

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body\alpha_1
-phase and 
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body\alpha_2
-phase is called interfacial phase slippage:

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u_{\alpha_1 \alpha_2} = u_{\alpha_1} - u_{\alpha_2}

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