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. New to the regimes? The Reynolds number guide explains why 2,000–4,000 is the transition and how to tell laminar from turbulent in the field.
| 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).