The pressure drop in pipe flow due to fluid friction with pipe walls depends on mass flux density and friction factor distribution along the pipe.
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\left( \frac{dp}{dl} \right)_f = - \frac{ j_m^2}{2 d} \cdot \frac{f}{\rho} |
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where
| mass flux |
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| body | \dot m (l) = \dot m = \rm const |
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| mass flowrate |
| pipe diameter |
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| body | --uriencoded--A = 0.25 \, \pi \, d%5e2 |
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| pipe cross-section area |
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| body | --uriencoded--f= f(%7B\rm Re%7D, \epsilon) |
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| Darcy friction factor |
| inner pipe walls roughness |
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| body | --uriencoded--\displaystyle %7B\rm Re%7D = \frac%7Bj_m \, d%7D%7B\mu%7D |
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| Reynolds number |
| dynamic viscosity as function of fluid temperature and pressure |
The accurate calculations require solving of a self-consistent equation of Pressure Profile in Homogeneous Quasi-Isothermal Steady-State Pipe Flow @model.
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