Motivation
Explicit solution of Pressure Profile in Homogeneous Steady-State Pipe Flow @model
Outputs
Assumptions
Equations
Pressure profile along the pipe |
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anchor | PressureProfile |
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alignment | left |
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| L = \frac{p_0}{2 \, G \, c^* \, \rho_0} \cdot \ln \frac{G \, \rho_0^2(1+c^* p/p_0)-F}{G \, \rho_0^2(1+c^*)-F}
-\frac{d}{f} \cdot \ln \frac{F/\rho^2 - G}{ F/\rho_0^2-G} |
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| \cos \theta \neq 0 |
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LaTeX Math Block |
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anchor | PressureProfile |
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alignment | left |
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| L = \frac{\rho_0}{j_m^2 \cdot f/(2d)}
\left[ (p_0-p) + \frac{c^*}{2 p_0} \left( p_0^2 - p^2 \right) \right]
- \frac{2d}{f} \cdot \ln \frac{\rho_0}{\rho} |
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| \cos \theta = 0 |
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where
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body | --uriencoded--\displaystyle j_m = \frac%7B \dot m %7D%7B A%7D |
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| mass flux |
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body | --uriencoded--\displaystyle \dot m = \frac%7Bdm %7D%7B dt%7D |
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| mass flowrate |
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body | --uriencoded--\displaystyle q_0 = \frac%7BdV_0%7D%7Bdt%7D = \frac%7B \dot m %7D%7B \rho_0%7D |
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| Intake volumetric flowrate |
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body | \rho_0 = \rho(T_0, p_0) |
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| Intake fluid density |
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body | \Delta z(l) = z(l)-z(0) |
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| elevation drop along pipe trajectory |
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body | --uriencoded--f(T,p) = f(%7B\rm Re%7D(T,p), \, \epsilon) |
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| Darcy friction factor |
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body | --uriencoded--\displaystyle %7B\rm Re%7D(T,p) = \frac%7Bu(l) \cdot d%7D%7B\nu(l)%7D = \frac%7Bj_m \cdot d%7D%7B\mu(T,p)%7D |
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| Reynolds number in Pipe Flow |
| dynamic viscosity as function of fluid temperature and pressure |
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body | --uriencoded--\displaystyle d = \sqrt%7B \frac%7B4 A%7D%7B\pi%7D%7D |
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| characteristic linear dimension of the pipe (or exactly a pipe diameter in case of a circular pipe) |
| gravity acceleration along pipe |
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body | --uriencoded--F = j_m%5e2 \cdot f/(2d) |
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See also
References
Show If |
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Panel |
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bgColor | papayawhip |
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title | ARAX |
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