0 psi
- Head loss
- 0 ft
- In bar
- 0 bar
- Re
- 0
- f (Colebrook)
- 0
Darcy-Weisbach Calculator
The general case. Pick the fluid, dial the temperature, see how the explicit friction-factor approximations compare to a full Colebrook iteration.
System
Friction-factor correlations — head-to-head
Same Re and ε/D, three different solvers. Δ vs Colebrook is the absolute error of each explicit form.
Colebrook (iterative)
0.0224
Canonical reference. Implicit, ~6 iterations.Haaland (explicit)
0.0222
Δ = -0.25e-3 (-1.11%)Swamee-Jain (explicit)
0.0226
Δ = 0.15e-3 (0.69%)Moody — operating point
How this works
Darcy-Weisbach: hf = f · (L/D) · v² / (2g) Colebrook–White (implicit): 1/√f = −2·log₁₀(ε/3.7D + 2.51/(Re·√f)) Haaland (explicit): 1/√f = −1.8·log₁₀((ε/3.7D)1.11 + 6.9/Re)
Darcy-Weisbach is physically grounded — it works for any Newtonian fluid given (ρ, μ). The hard part is the friction factor, which has no closed-form solution in the turbulent regime. Colebrook–White is the industry standard; the explicit forms exist because in the 1970s an iteration cost real CPU time. Today the cost difference is irrelevant; we use Colebrook everywhere by default.
The flagship pressure-drop calculator dispatches automatically: laminar exact (64/Re) below Re=2,300, linear interpolation across the transitional band, Colebrook for fully turbulent. This page simply runs all three in parallel so you can see how close the explicit forms are.
| Form | Accuracy vs Colebrook | Cost | |
|---|---|---|---|
| Colebrook–White (1939) | Implicit; iterate to 1e-10 | Reference | ~6 iterations |
| Swamee-Jain (1976) | Explicit | ±1% in 5e3 ≤ Re ≤ 1e8 | Constant |
| Haaland (1983) | Explicit | ±2% | Constant |
| 64/Re (laminar) | Exact | N/A — laminar only | Constant |
Common questions
Which friction-factor correlation should I trust?
Colebrook–White is the textbook reference and what we use as the dispatcher in the flagship. Haaland and Swamee-Jain are explicit approximations; both stay within ±2% of Colebrook for typical engineering ranges. The display here lets you see the disagreement directly.
How does temperature change the answer?
Through ν = μ/ρ. Water viscosity drops sharply with temperature (≈1.79e-3 Pa·s at 0 °C, ≈0.28e-3 at 100 °C). For a fixed velocity that means Re rises with temperature, friction factor falls slightly, and head loss falls — by 10-20 % across the residential hot/cold range.
Why override roughness?
If you have a manufacturer roughness or a measured value (e.g. internal pipe-coating spec), supply it directly. Otherwise the material library is a good default (Moody-based).