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Pressure profile along the pipe


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L = \frac{p_0}{2 \, G \, c^* \, \rho_0}  \cdot \ln \frac{G \, \rho_0^2(1+c^* p/p_0)-F}{G \, \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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 \cos \theta \leqneq 0



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L = \frac{\rho_0}{j_m^2 \cdot f/(2d)} 
\left[ (p_0-p) + \frac{c^*}{2 p_0} \left( p_0^2 - p^2 \right) \right]
 - j_m^2 \, \ln \frac{\rho_0}{\rho}



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 \cos \theta = 0


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