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Inputs & Outputs
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pipeline trajectory | LaTeX Math Inline |
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| body | {\bf r} = {\bf r}(l) = \{ x(l), \, y(l), \, z(l) \} |
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| along-pipe stabilized pressure distribution |
| along-pipe stabilized flowrate distribution |
Along-pipe temperature profile | along-pipe stabiliszed average flow velocity distribution |
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| Inner pipe wall roughness |
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Assumptions
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Equations
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| LaTeX Math Block |
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| \bigg( 1 - \frac{c(p) \, \rho_0^2 \, q_0^2}{A^2} \bigg ) \frac{dp}{dl} = \rho(p) \, g \, \frac{dz}{dl} - \frac{\rho_0^2 \, q_0^2 }{2 A^2 d} \frac{f(p)}{\rho(p)} |
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| LaTeX Math Block |
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| u(l) = \frac{\rho_0 \cdot q_0}{\rho(p) \cdot A(l)} |
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| LaTeX Math Block |
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| q(l) = \frac{\rho_0 \cdot q_0}{\rho(p)} |
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The first term in
| LaTeX Math Block Reference |
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defines the hydrostatic column of static fluid while the last term defines the friction losses under fluid movement:
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