Darcy vs Hazen-Williams: A Practical Guide to Pipe Friction Loss

Friction loss is where pump sizing usually goes wrong. Not because the math is hard — it is not — but because engineers pick the wrong equation for the fluid, forget fittings, or under-count elevation. This guide is the version of the pipe-friction chapter every plant engineer wishes they had on day one.

1. Two equations, two worlds

Darcy–Weisbach is the general form:

h_f = f × (L/D) × V² / (2g)

It works for any Newtonian fluid at any temperature. The only tricky part is the friction factor f, which depends on Reynolds number and relative roughness. We use the Swamee–Jain explicit correlation because it is within 1% of the implicit Colebrook equation and does not need iteration.

Hazen–Williams is a shortcut:

h_f = 10.67 × L × (Q/C)^1.852 / D^4.87

It is only valid for water at ambient temperature. Not for glycol, not for hot condensate, not for oil. C is the pipe roughness coefficient — 150 for PVC, 130 for new steel, 100 for old cast iron.

Rule of thumb: default to Darcy–Weisbach. Use Hazen–Williams only for ambient-water sizing when speed matters more than precision (fire-protection sketches, quick building-service loops).

2. Reynolds number decides everything

Re = V × D / ν

Where ν is kinematic viscosity. For water at 60°F, ν ≈ 1.21 × 10⁻⁵ ft²/s; at 200°F it drops to about 3.4 × 10⁻⁶ ft²/s. That is why the same flow in the same pipe has different friction loss at different temperatures.

• Re < 2000: laminar flow, f = 64/Re. Rare in commercial water piping.
• 2000 < Re < 4000: transitional — avoid designing here, results are unpredictable.
• Re > 4000: turbulent — use Swamee–Jain or a Moody chart.

3. Roughness is not fudge

Relative roughness ε/D moves the friction factor by a factor of 2–3× at high Re. Do not guess.

Material	Absolute roughness ε (ft)
PVC / smooth plastic	0.000005
Copper	0.000005
New commercial steel	0.00015
Galvanized iron	0.0005
Cast iron (uncoated)	0.00085
Old / corroded steel	0.003 – 0.01

Old pipe roughens with age. A 20-year-old steel line may have effectively doubled its ε. That is why nameplate hydraulics from 1998 no longer match reality.

4. Fittings: equivalent length vs K-factors

Minor losses can be handled two ways:

Equivalent length

Express each fitting as feet of straight pipe of the same diameter. Rules of thumb (L_eq / D):

Fitting	L_eq / D
90° elbow (standard)	30
45° elbow	16
Tee, straight-through	20
Tee, branch	60
Gate valve (full open)	8
Globe valve	340
Butterfly	30 – 50
Swing check	100

Multiply by pipe internal diameter (in feet), sum, and add to the straight-pipe length. Easy to hand-calculate, slightly conservative.

K-factor

More accurate: h_f_fitting = K × V²/(2g). Use K when the piping is fitting-heavy relative to straight run (short skid piping, valve stations). For long runs, equivalent length is fine.

5. Where engineers usually get it wrong

1. Ignoring viscosity change with temperature — most tables assume 60°F. Fix ν for hot fluids.
2. Applying Hazen–Williams to non-water fluids — it is only calibrated for water. Glycol and oil give wildly wrong answers.
3. Forgetting elevation — friction loss is added to static head, not part of it.
4. Using nameplate roughness on old pipe — audit, or add 25% margin.
5. Skipping the fitting count on suction piping — that is where NPSH usually dies.

Do the math

Run the Pipe Friction Loss Calculator — it uses Swamee–Jain and lets you enter fittings as equivalent length. Then feed the answer into the Pump Sizing Calculator or the NPSH Calculator to close the loop.