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LaTeX Math Block
anchordp
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\Delta p = p_{in} - p_{out} =  \frac{ \rho \cdot (1- \beta^4)}{0.125 \, \pi^2 \, d^4 \, C_d^2 \, \epsilon^2} \cdot  q^2

where

LaTeX Math Inline
body\rho

fluid  density

LaTeX Math Inline
bodyd

orifice diameter

LaTeX Math Inline
bodyD

pipe diameter 

LaTeX Math Inline
body\beta = \frac{d}{D}

orifice narrowing ratio

LaTeX Math Inline
bodyC_d

LaTeX Math Inline
body\epsilon

expansion factor



LaTeX Math Block
anchor1
alignmentleft
p_{outwf, k} = p_{wfout} - + \rho \, g \, z_k


LaTeX Math Block
anchorJR5B7
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q = \sum_k \frac{B_w(p_{e, k})}{B_w(p_{out})} \cdot J_k \cdot \left[ p_{out} + \rho \, g \, z_k  - p_{e, k} \right] 

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which is equivalent to 

LaTeX Math Block Reference
anchordp
.

See Also

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Petroleum Industry / Upstream / Well / Water injector