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| body | --uriencoded--f(%7B\rm Re%7D, \, \epsilon) |
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| Darcy friction factor |
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| body | --uriencoded--\displaystyle %7B\rm Re%7D = \frac%7Bu(l) \cdot d%7D%7B\nu(l)%7D = \frac%7B4 \rho_s q_s%7D%7B\pi d%7D \frac%7B1%7D%7B\mu(T, p)%7D |
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| Reynolds number |
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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) |
See Derivation of Pressure Profile in Stationary Isothermal Homogenous Pipe Flow @model.
Alternative forms
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-\frac{1}{c} \frac{d}{dl} \left( \frac{1}{\rho} \right) + \frac{\rho_s^2 q_s^2}{2A^2} \frac{d}{dl} \left( \frac{1}{\rho^2} \right) + \frac{\rho_s^2 q_s^2}{2A^2} \frac{f}{d} \left( \frac{1}{\rho^2} \right) - g \frac{dz}{dl} = 0 |
See derivation at
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| displaytext | derivation here |
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| anchor | drho |
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| page | Derivation of Pressure Profile in Stationary Quasi-Isothermal Homogenous Pipe Flow @model |
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Approximations
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Incompressible pipe flow
with constant viscosity ...
