CÁLCULO DEL FACTOR DE FRICCIÓN EN TUBOS SEGÚN ECUACIONES PRINCIPALES
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Description
Friction Factor in Pipes – Comparison of Principal Equations
What it does
This workbook calculates the Darcy–Weisbach friction factor (f) for fluid flow in a circular pipe, then computes it ten different ways using the principal published correlations and benchmarks each one against the reference Colebrook equation. It lets an engineer see, for a single real flow case, how much scatter exists between the various explicit approximations and the implicit “exact” solution.
The interface is multi-language, selectable from the dropdown in cell E6.
Inputs
The user specifies the physical case, and the sheet derives the flow parameters automatically:
- Tube material, nominal diameter and schedule → outer and inner diameter are looked up from the pipe dimension tables.
- Fluid and temperature → density (ρ) and dynamic viscosity (μ) are looked up from the fluid-property tables.
- Volume flow → mass flow, mean pipe velocity, and the Reynolds number are calculated.
- Absolute roughness (e) of the material → the relative (effective) roughness ε/D is calculated.
The two governing dimensionless quantities that feed every friction-factor equation are therefore the Reynolds number (Re) and the relative roughness (ε/D).
Methodology – the ten equations
Each correlation estimates the turbulent friction factor from Re and ε/D. They are listed with their published validity ranges:
| Equation | Year | Type | Notes |
|---|---|---|---|
| Colebrook | 1937 | Implicit | Reference standard; solved iteratively |
| Moody | 1947 | Explicit | 4000 ≤ Re ≤ 107, ε/D ≤ 0.01 |
| Altshul | 1952 | Explicit | 4000 ≤ Re ≤ 107 |
| Jain | 1976 | Explicit | 5000 < Re < 107 |
| Churchill | 1977 | Explicit | Valid for any Re and ε/D (laminar → turbulent) |
| Round | 1980 | Explicit | |
| Pavlov | 1981 | Explicit | 4000 < Re < 107 |
| Zigrang & Sylvester | 1982 | Explicit | 4000 < Re < 108 |
| Serghides | 1984 | Explicit | Re > 2100, any ε/D; three-substitution form |
| Manadilli | 1997 | Explicit | 4000 < Re, 0 < ε/D < 0.05 |
The Colebrook equation is treated as the benchmark because it is the accepted implicit relationship underlying the Moody chart. All the others are explicit approximations developed to avoid its iterative solution.
Output – accuracy comparison
The results block collects each computed friction factor and reports the percentage difference from Colebrook. For the default sample case (Re ≈ 2.8×105, ε/D ≈ 1.2×10-4), the explicit correlations fall within roughly ±0.1% to ±3.7% of Colebrook – Altshul being the outlier and Serghides/Jain being nearly exact. The practical takeaway: most modern explicit forms reproduce Colebrook closely enough for engineering use, so the iterative solution is rarely necessary.
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