Motivation
Proxy model of Pressure Profile in Homogeneous Steady-State Pipe Flow @model in the form of algebraic equation for fast computation.
Outputs
Assumptions
| 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 |
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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(t, \tau_x,\tau_y,l) = p(l) |
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| Constant inclination | Linear density |
| LaTeX Math Inline |
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| body | --uriencoded--\displaystyle \theta(l) = \theta = %7B\rm const%7D \rightarrow \cos \theta = \frac%7Bdz%7D%7Bdl%7D = %7B\rm const%7D |
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| | LaTeX Math Inline |
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| body | --uriencoded--\rho = \rho%5e* \cdot ( 1 + c%5e* \cdot p) |
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Equation
Pressure profile in static fluid column, no flow: | LaTeX Math Inline |
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| body | \dot m = 0, \, q_0 = 0 |
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| LaTeX Math Block |
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| anchor | static |
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| alignment | left |
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| p(L) = \frac{1}{c^*} \cdot \left[ -1 + (1+c^* \, p_0) \cdot \exp(c^* \rho^* G \, L) \right] |
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| borderColor | wheat |
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| bgColor | mintcream |
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| borderWidth | 7 |
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| See ... |
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See also
References
| Show If |
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| bgColor | papayawhip |
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| title | ARAX |
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