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Stationary flowHomogenous flowIsothermal or Quasi-isothermal conditions

Constant cross-section pipe area

LaTeX Math Inline
bodyA
along hole

LaTeX Math Inline
body\theta (l) = \theta = \rm const

LaTeX Math Inline
bodyf(l) = f = \rm const

LaTeX Math Inline
body--uriencoded--\rho = \rho%5e* \cdot ( 1 + c%5e* \cdot p)

LaTeX Math Inline
bodyA(l) = A = \rm const


Equations

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Pressure profile along the pipe


LaTeX Math Block
anchorPressureProfile
alignmentleft
L = \frac{1}{2 \, G \, c^*  \rho^*}  \cdot \ln \frac{G \, \rho^2-F}{G \, \rho_0^2-F}
-\frac{d}{f} \cdot \ln \frac{F/\rho^2 - G}{ F/\rho_0^2-G}



LaTeX Math Block
anchor1
alignmentleft
 \cos \theta \neq 0



LaTeX Math Block
anchorG0
alignmentleft
L = \frac{1}{2F\, c^* \rho^*} \cdot (\rho_0^2 - \rho^2)
 - \frac{2d}{f} \cdot \ln \frac{\rho_0}{\rho}



LaTeX Math Block
anchor1
alignmentleft
 \cos \theta = 0


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