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The discharge coefficient 

LaTeX Math Inline
bodyC_d
 is a function of a choke narrowing ratio 
LaTeX Math Inline
body\beta
and Reynolds number 
LaTeX Math Inline
body{\rm Re}
 in the pipe:

LaTeX Math Block
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C_d = C_d(\beta, {\rm Re})

where

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{\rm Re} = \frac{v \cdot D}{\nu} = \frac{4 \, q}{\pi \, D \, \nu}

where

LaTeX Math Inline
body\nu

kinematic viscosity


It can be estimated for popular popular choke types or tabulated in laboratory.

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