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Pressure profile in static fluid column, no flow:

LaTeX Math Inline
body\dot m = 0, \, q_0 = 0

LaTeX Math Block
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p(L) = \frac{1}{c^*} \cdot \left[ -1 + (1+c^* \, p_0) \cdot \exp(c^*  \rho^*  G \, L)  \right]
LaTeX Math Block
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p(L) = p_0 +  \frac{1}{c_0} \cdot \left[ -1 + \exp(c_0 \,  \rho_0 \,  G \, L)  \right]

where

LaTeX Math Inline
bodyG = g \cdot \cos \theta

gravity acceleration along pipe 
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