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Assumptions
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| Stationary Steady-State flow | Isothermal or 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 | |
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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 | Constant friction along hole |
| 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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Alternative forms
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| Density form |
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| LaTeX Math Block |
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| L = L(\rho) =\int_{\rho_0}^{\rho} \frac{ 1}{G \, \rho^2 - F} \, \frac{ d\rho}{c(\rho)} -\frac{d}{f} \cdot \ln \frac{F/\rho^2 - G}{ F/\rho_0^2-G}
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Approximations
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| LaTeX Math Block |
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| \rho(p) = \tilde \rho \cdot \sqrt{ 1- \frac{f}{2d} \frac{j_m^2}{G} ( \rho_0^2 - {\tilde \rho}^2) }
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| LaTeX Math Block |
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| \int_{\rho_0}^{\tilde \rho} \frac{d \rho}{ \rho^2 \, c(\rho)} = G \cdot L
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where
| no-flow pressure at the pipe end ( | LaTeX Math Inline |
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| body | --uriencoded--%7B\tilde j%7D_m = 0 |
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) |
See also
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