Motivation
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One of the key challenges in Pipe Flow Dynamics is to predict the pressure distribution along the pipe during the steady-state fluid transport.
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Pipeline Flow Pressure Model is addressing this problem with account of the varying pipeline trajectory, gravity effects and fluid friction with pipeline walls.
Outputs
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Assumptions
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| Steady-State flow | Quasi-isothermal flow |
| LaTeX Math Inline |
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| body | --uriencoded--\displaystyle \frac%7B\partial p%7D%7B\partial t%7D = 0 \rightarrow p(t,l) = p(l) |
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| | LaTeX Math Inline |
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| body | --uriencoded--\displaystyle \frac%7B\partial T%7D%7B\partial t%7D =0 \rightarrow T(t,l) = T(l) |
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| Homogenous flow | |
| LaTeX Math Inline |
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| body | --uriencoded--\displaystyle \frac%7B\partial p%7D%7B\partial \tau_x%7D =\frac%7B\partial p%7D%7B\partial \tau_y%7D =0 \rightarrow p(\tau_x,\tau_y,l) = p(l) |
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Equations
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| LaTeX Math Block |
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| \left( \rho(p) - j_m^2 \cdot c(p) \right) \cdot \frac{dp}{dl} = \rho^2(p) \, g \, \cos \theta(l) - \frac{ j_m^2 }{2 d} \cdot f(p) |
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| LaTeX Math Block |
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| p(l=0) = p_0 |
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| LaTeX Math Block |
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| u(l) = \frac{j_m}{\rho(l)} |
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| LaTeX Math Block |
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| q(l) =A \cdot u(l) |
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