polykin.transport.flow¤
fD_Colebrook ¤
fD_Colebrook(Re: float, er: float) -> float
Calculate the Darcy friction factor using Colebrook's equation.
For turbulent flow, i.e., \(Re \gtrsim 2300\), the friction factor is given by the following implicit expression:
\[ \frac{1}{\sqrt{f}}= -2 \log \left( \frac {\epsilon/D} {3.7} +
\frac {2.51} {Re \sqrt{f}} \right) \]
This equation is a historical landmark but has the disadvantage of being implicit, requiring an iterative solution.
References
- Colebrook, C F (1939). "Turbulent Flow in Pipes, with Particular Reference to the Transition Region Between the Smooth and Rough Pipe Laws", Journal of the Institution of Civil Engineers. 11 (4): 133-156.
PARAMETER | DESCRIPTION |
---|---|
Re
|
Reynolds number.
TYPE:
|
er
|
Relative pipe roughness, \(\epsilon/D\).
TYPE:
|
RETURNS | DESCRIPTION |
---|---|
float
|
Darcy friction factor. |
See also
fD_Haaland
: alternative method.
Examples:
Calculate the friction factor for water flowing at 2 m/s through a PVC pipe with an internal diameter of 25 mm.
>>> from polykin.transport import fD_Colebrook
>>> rho = 1e3 # kg/m³
>>> mu = 1e-3 # Pa·s
>>> D = 25e-3 # m
>>> v = 2. # m/s
>>> Re = rho*v*D/mu
>>> er = 0.0015/25 # from pipe table
>>> fD = fD_Colebrook(Re, er)
>>> print(f"fD = {fD:.3f}")
fD = 0.021
Source code in src/polykin/transport/flow.py
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