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The integration of the left side of
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with the boundary condition | LaTeX Math Block Reference |
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leads to:
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| anchor | PressureProfile |
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L = \int_{\rho_0}^{\rho} \frac{ 1/c(\rho) - j_m^2 / \rho }{G \, \rho^2 - F(\rho)} \, d \rho
=\int_{p_0}^{p} \frac{ \rho(p) - j_m^2 \, c(p) }{G \, \rho^2(p) - F(\rho(p))} \, dp =
\int_{p_0}^{\rhop} \frac{ \rho \, dp}{G \, \rho^2 - F(\rho)}
- j_m^2 \cdot \int_{\rho_0}^{\rho} \frac{j_m^21}{2\rho} \, \lnfrac{d \frac{F/rho}{G \, \rho^2 - G}{ F/(\rho_0^2-G)}
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where
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| body | --uriencoded--\displaystyle F(\rho) = \frac%7B j_m%5e2 %7D%7B2 d%7D \cdot f(p\rho) |
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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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