When should I use Darcy-Weisbach instead of Hazen-Williams?

Use Darcy-Weisbach for any pipe-flow problem where accuracy matters or fluid is anything other than cold water. It's based on physics (Reynolds number, friction factor) and works for any fluid. Hazen-Williams is empirical, valid only for water at typical temperatures and turbulent flow.

What is the Swamee-Jain friction factor?

Swamee-Jain (1976) is an explicit approximation of the Colebrook equation, accurate to within 1% for turbulent flow. It avoids the iteration required by the implicit Colebrook formula and is the standard for hand calculation and spreadsheet implementation.

What roughness value should I use?

Commercial steel: 0.00015 ft (0.046 mm). Galvanized iron: 0.0005 ft. Concrete: 0.001–0.01 ft. PVC: 0.000005 ft (smooth). For aged pipes, multiply by 2–4× to reflect tuberculation and biofilm growth.

What is the friction factor for laminar flow?

For Re < 2,300, flow is laminar and f = 64/Re, independent of pipe roughness. The Darcy-Weisbach equation reduces to the Hagen-Poiseuille form: h_f = 32·μ·V·L / (ρ·g·D²).

How does the Moody diagram relate?

The Moody diagram plots friction factor f against Reynolds number Re for various values of relative roughness ε/D. Swamee-Jain reproduces the Moody diagram analytically. For ε/D = 0 (smooth pipe), the Blasius equation f = 0.316/Re^0.25 applies for Re < 10⁵.

What about minor losses (fittings, valves)?

This calculator handles only friction loss along the pipe. Add minor losses for fittings: h_minor = K·V²/(2g). Typical K-values: gate valve open ~0.15, ball valve open ~0.05, 90° elbow ~0.30, tee through ~0.60, sudden expansion (1−A1/A2)² ranges 0.5–1.0.

What is the friction factor for fully rough turbulent flow?

At very high Re (fully rough turbulent), friction factor depends only on relative roughness ε/D, not Re. The von Karman equation: 1/√f = 2·log₁₀(3.7·D/ε). This is the asymptote of the Moody diagram on the right side.

Darcy-Weisbach Equation Calculator — Pipe Head Loss

Pipe head loss from friction. Friction factor is computed from Reynolds number and pipe roughness using the Swamee-Jain explicit form of the Colebrook equation.

When to use Darcy-Weisbach

The Darcy-Weisbach equation is the dimensionally correct, fluid-and-temperature-aware way to compute pipe friction loss. It applies to any Newtonian fluid in any flow regime, in pipes of any roughness. For water-supply work in the typical pressure-and-temperature range, Hazen-Williams is the simpler shortcut — but Hazen-Williams is calibrated for water at common conditions and falls apart for hot water, low-Reynolds flow, or non-water fluids.

Absolute pipe roughness ε — full reference table

Roughness is the most uncertain parameter in Darcy-Weisbach for new pipe; for old pipe it dominates everything else. New-pipe values come from the Crane manual; aged values reflect 20–30 years of tuberculation, scaling, and biofilm.

Absolute roughness ε for common pipe materials
Material / condition	ε (in)	ε (mm)	ε (ft)
Drawn tubing (copper, brass)	0.000059	0.0015	5×10⁻⁶
Glass	0.000059	0.0015	5×10⁻⁶
PVC, HDPE (new)	0.000059	0.0015	5×10⁻⁶
Commercial steel (new)	0.0018	0.046	1.5×10⁻⁴
Wrought iron	0.0018	0.046	1.5×10⁻⁴
Galvanized iron	0.006	0.15	5×10⁻⁴
Asphalted cast iron	0.0048	0.12	4×10⁻⁴
Cast iron (uncoated, new)	0.0102	0.26	8.5×10⁻⁴
Concrete pipe (smooth, precast)	0.012	0.30	1.0×10⁻³
Concrete pipe (rough, formed)	0.12	3.0	1.0×10⁻²
Riveted steel	0.036–0.36	0.9–9.0	3×10⁻³–3×10⁻²
Cast iron, aged 30 yr	0.04	1.0	3.3×10⁻³
Cast iron, aged 40+ yr (tuberculated)	0.10–0.50	2.5–12.5	8×10⁻³–4×10⁻²

Source: Crane Technical Paper No. 410, Flow of Fluids Through Valves, Fittings, and Pipe. Aged-pipe values from Lamont (1981) and field measurements summarized in AWWA M11.

Kinematic viscosity ν of water and common fluids

Kinematic viscosity for common fluids in pipe-flow problems
Fluid / temperature	ν (US ft²/s)	ν (SI m²/s)
Water, 40°F (4°C)	1.66×10⁻⁵	1.55×10⁻⁶
Water, 60°F (16°C)	1.21×10⁻⁵	1.13×10⁻⁶
Water, 70°F (21°C) — STD	1.06×10⁻⁵	9.84×10⁻⁷
Water, 80°F (27°C)	9.30×10⁻⁶	8.64×10⁻⁷
Water, 100°F (38°C)	7.39×10⁻⁶	6.87×10⁻⁷
Air, 60°F	1.58×10⁻⁴	1.47×10⁻⁵
SAE 10W oil, 60°F	1.0×10⁻³	9.3×10⁻⁵
Glycerin, 70°F	6.5×10⁻³	6.0×10⁻⁴

Worked examples

Example 1 — 8-inch new commercial steel pipe, 2000 ft, 1000 gpm

Given: D = 8 in, L = 2000 ft, Q = 1000 gpm, new commercial steel (ε = 0.0018 in), water at 60°F (ν = 1.21×10⁻⁵ ft²/s).

Find: Friction head loss h_f.

D = 8/12 = 0.667 ft; A = π·(0.667)²/4 = 0.349 ft²

Q = 1000/448.83 = 2.228 cfs; V = 2.228/0.349 = 6.38 ft/s

Re = V·D/ν = 6.38·0.667/(1.21×10⁻⁵) = 3.52×10⁵ (turbulent)

ε/D = 0.0018/8 = 2.25×10⁻⁴

f = 0.25 / [log₁₀(2.25×10⁻⁴/3.7 + 5.74/(3.52×10⁵)^0.9)]² = 0.25 / [log₁₀(6.08×10⁻⁵ + 6.45×10⁻⁵)]² = 0.0181

h_f = 0.0181 · (2000/0.667) · (6.38)²/64.4 = 0.0181 · 2999 · 0.632

h_f = 34.3 ft (over 2000 ft of pipe)

Example 2 — Laminar flow check (small-diameter chemical line)

Given: 1-inch line, V = 0.5 ft/s, glycerin at 70°F (ν = 6.5×10⁻³ ft²/s), L = 50 ft.

Find: Friction head loss.

D = 1/12 = 0.0833 ft; Re = 0.5·0.0833/(6.5×10⁻³) = 6.4 (LAMINAR)

f = 64/Re = 64/6.4 = 10.0

h_f = 10.0 · (50/0.0833) · (0.5)²/64.4 = 10.0 · 600 · 0.00388

h_f = 23.3 ft of glycerin

Kinematic viscosity for water

Water at 60°F (15.6°C) has ν ≈ 1.08 × 10⁻⁵ ft²/s (1.13 × 10⁻⁶ m²/s). At 40°F use 1.66 × 10⁻⁵ ft²/s; at 80°F use 0.93 × 10⁻⁵ ft²/s. Viscosity changes ~50% between 40°F and 100°F, which matters for laminar-flow calculations but is usually negligible for fully turbulent water-distribution work.

Reynolds number regimes

Re < 2,300: laminar — friction factor is f = 64/Re, independent of roughness.
2,300 ≤ Re ≤ 4,000: transitional — friction factor uncertain.
Re > 4,000: turbulent — Swamee-Jain (or Colebrook) applies.

Reference: Crane Technical Paper No. 410, Flow of Fluids Through Valves, Fittings, and Pipe. Swamee, P.K., Jain, A.K. (1976). "Explicit equations for pipe-flow problems." J. Hydraulic Div., ASCE, 102 (5), 657–664.