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| Steady-State flow | Quasi-isothermal flow |
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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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Alternative forms
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| LaTeX Math Block |
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| \frac{dp}{dl} = \left( \frac{dp}{dl} \right)_G + \left( \frac{dp}{dl} \right)_K + \left( \frac{dp}{dl} \right)_f |
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where
| LaTeX Math Inline |
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| body | --uriencoded--\displaystyle \left( \frac%7Bdp%7D%7Bdl%7D \right)_G = \rho \cdot g \cdot \cos \theta |
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gravity losses which represent pressure losses for upward flow and pressure gain for downward flow |
| LaTeX Math Inline |
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| body | --uriencoded--\displaystyle \left( \frac%7Bdp%7D%7Bdl%7D \right)_K = u%5e2 \cdot \frac%7Bd \rho%7D%7Bdl%7D |
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kinematic losses, which grow contribution at high velocities
and high fluid compressibility (like turbulent gas flow) |
| LaTeX Math Inline |
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| body | --uriencoded--\displaystyle \left( \frac%7Bdp%7D%7Bdl%7D \right)_f = - \frac%7B j_m%5e2%7D%7B2 d%7D \cdot \frac%7Bf%7D%7B\rho%7D |
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friction losses which are always negative along the flow direction |
Approximations
See also
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