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| \left[\rho(p) - j_m^2 \cdot c(p) \right] \frac{dp}{dl} = \rho^2(p) \, g \, \cos \theta(l) - \frac{ j_m^2 }{2 d} \cdot f(p) |
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| p(l=0) = p_0 |
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u(l) = \frac{j_m}{\rho(l)} |
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q(l) =A \cdot u(l) |
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and assume constant pipe inclination:
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| anchor | PressureProfile |
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| alignment | left |
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L = \int_{\rho_0}^{\rho} \frac{1/c- j_m^2 / \rho}{G \, \rho^2 - F} \, d \rho
=\int_{\rho_0}^{\rho} \frac{\rho \, dp}{G \, \rho^2 - F} -\frac{j_m^2}{2} \, \ln \frac{F/\rho^2 - G}{ F/\rho_0^2-G} |
where
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| body | --uriencoded--\displaystyle F = \frac%7B j_m%5e2 %7D%7B2 d%7D \cdot f(p) |
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See also
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Physics / Fluid Dynamics / Pipe Flow Dynamics / Pipe Flow Simulation / Pressure Profile in Homogeneous Steady-State Pipe Flow @model / Pressure Profile in G-Proxy Pipe Flow @model
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