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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_0 \cdot ( 1 + c c%5e* \cdot p/p_0)



Equations

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Pressure profile along the pipe


LaTeX Math Block
anchorPressureProfile
alignmentleft
L = \intfrac{p_0}{2 \, G \, c^* \, \rho_0}^{\rho}  \cdot \ln \frac{G \rho, \, dprho_0^2(1+c^* p/p_0)-F}{G \, \rho^2 - rho_0^2(1+c^*)-F} 
-\frac{j_m^2}{2} \, \ln \frac{F/\rho^2 - G}{ F/\rho_0^2-G}


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