What is the Darcy-Weisbach equation and why is it preferred?

hf = f·L/D·v²/2g is preferred because it is dimensionally consistent, applies to all fluids and flow regimes, and the friction factor is well-characterised by the Colebrook-White equation.

What is the Colebrook-White equation?

1/√f = −2·log(ε/3.7D + 2.51/Re√f). It requires iteration to solve for f. The explicit Swamee-Jain approximation is accurate within ±3% for most practical cases.

What is the Reynolds number and what does it tell me?

Re = vD/ν. Re 4000: turbulent — use Colebrook-White.

How do minor losses compare to major losses in typical pipe systems?

In long runs (L/D > 1,000), major losses dominate. In short systems with many fittings, minor losses can equal or exceed major losses.

Pipe Head Loss Calculator

Calculate pipe head loss and pressure drop using the Darcy-Weisbach equation with Colebrook iterative friction factor. Includes major losses (pipe friction), minor losses (fittings K-factors), Reynolds number, flow regime, and pump head requirement.

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What This Calculator Does

The pipe head loss calculator uses the Darcy-Weisbach equation with the Colebrook-White iterative friction factor — the industry-standard method used in ASHRAE, AWWA, and hydraulic engineering practice. It computes major losses (pipe wall friction), minor losses from fittings using K-factors, the Reynolds number and flow regime (laminar/turbulent/transitional), and the total pump head required to overcome resistance. Results are shown in metres of head, Pa, kPa, and psi.

It combines Pipe Internal Diameter, Pipe Length, Flow Rate, Pipe Roughness ε to estimate Total Head Loss, Pressure Drop, Flow Velocity.

Formula & Method

Darcy-Weisbach equation:

h_f = f \cdot \frac{L}{D} \cdot \frac{v^2}{2g}

where

f

is the Darcy friction factor,

L

is pipe length (m),

D

is internal diameter (m),

v

is mean flow velocity (m/s), and

g = 9.81\,\text{m/s}^2

. Reynolds number:

Re = \frac{vD}{\nu}

where

\nu

is kinematic viscosity. Colebrook-White equation (iterative):

\frac{1}{\sqrt{f}} = -2\log\!\left(\frac{\varepsilon}{3.7D} + \frac{2.51}{Re\sqrt{f}}\right)

For laminar flow (

Re < 2300

f = 64/Re

. Minor losses:

h_m = K \cdot \frac{v^2}{2g}

where

K

is the fitting loss coefficient.

Notation used in the formulas: $R$ = Total Head Loss; $x_{1}$ = Pipe Internal Diameter; $x_{2}$ = Pipe Length; $x_{3}$ = Flow Rate; $x_{4}$ = Pipe Roughness ε; $x_{5}$ = Fluid Density ρ; $x_{6}$ = Kinematic Viscosity ν.

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use this calculator for quick scenario analysis. Start with baseline values, change one driver at a time, and compare how sensitive the results are to each input shown above.

Worked Examples

50mm steel pipe — 30 m long, 2 L/s water

Inputs: D = 0.050 m, L = 30 m, Q = 2 L/s = 0.002 m³/s, ε = 0.046 mm (drawn steel), ν = 1×10⁻⁶ m²/s (water at 20°C) Step 1: Flow velocity A = π(0.025)² = 1.963×10⁻³ m² v = Q/A = 0.002 / 1.963×10⁻³ = 1.019 m/s Step 2: Reynolds number Re = vD/ν = 1.019 × 0.050 / 1×10⁻⁶ = 50,950 → turbulent Step 3: Friction factor (Colebrook iteration, converges in ~5 iterations) ε/D = 0.046/50 = 0.00092 f ≈ 0.0232 (Colebrook converged) Step 4: Major head loss hf = 0.0232 × (30/0.050) × (1.019)²/(2×9.81) = 0.0232 × 600 × 0.0529 = 0.736 m Pressure drop = ρgh = 1000 × 9.81 × 0.736 = 7,220 Pa = 7.22 kPa = 1.05 psi

100mm cast iron main — 500 m, 15 L/s with fittings

Inputs: D = 0.100 m, L = 500 m, Q = 15 L/s = 0.015 m³/s, ε = 0.26 mm (cast iron) Fittings: two 90° elbows (K = 1.5 each) + one gate valve open (K = 0.2) v = 0.015 / (π × 0.0025) = 1.910 m/s Re = 1.910 × 0.100 / 1×10⁻⁶ = 191,000 f (Colebrook) ≈ 0.0262 Major loss: hf = 0.0262 × (500/0.1) × (1.91)²/19.62 = 12.32 m Minor loss: hm = (2×1.5 + 0.2) × (1.91)²/19.62 = 3.2 × 0.186 = 0.60 m Total head loss = 12.32 + 0.60 = 12.92 m (126.7 kPa, 18.4 psi)

Pipe Roughness Values Reference

Pipe Material	Roughness ε (mm)	Typical Use
Smooth bore (drawn tubing, PVC)	0.0015	Domestic plumbing, hydraulic lines
Drawn steel / copper	0.046	HVAC, process piping
Wrought iron	0.046	Older industrial systems
Galvanised steel	0.15	General-purpose industrial
Cast iron (unlined)	0.26	Water mains (older)
Concrete (smooth)	0.3	Culverts, sewers
Concrete (rough)	3.0	Large-diameter culverts
HDPE	0.007	Water supply, drainage

Minor Loss K-Factors for Common Fittings

Fitting / Component	K-Factor	Notes
Gate valve — fully open	0.2	Low resistance when open
Gate valve — half open	5.6	Avoid throttling gate valves
Ball valve — fully open	0.05	Lowest-resistance valve type
Globe valve — fully open	10.0	High resistance; use for throttling
Check valve — swing type	2.5	Backflow prevention
90° elbow — standard radius	1.5	Most common elbow
90° elbow — long radius	0.7	Lower loss, larger footprint
45° elbow	0.4	Gradual direction change
Tee — branch flow	1.8	Flow turns 90°
Tee — straight through	0.4	Minimal loss
Sharp entrance (tank → pipe)	0.5	Reentrant = 0.8–1.0
Rounded entrance	0.04	Well-formed bell mouth
Exit (pipe → tank)	1.0	All kinetic energy lost

Common Mistakes

Using pipe outer diameter instead of internal diameter — especially important for thick-wall pipes where the difference is significant.
Forgetting to convert flow rate units consistently — enter Q in m³/s for SI calculations. 1 L/s = 0.001 m³/s; 1 US gal/min = 6.309×10⁻⁵ m³/s.
Using flywheel friction factor f = 0.02 as a constant — the Colebrook friction factor varies significantly with Reynolds number and roughness. f ranges from 0.010 (smooth turbulent) to 0.06 (rough, fully turbulent).
Ignoring minor losses in short systems — in systems with many fittings and short pipe runs, minor losses can equal or exceed major losses.
Not checking the flow regime — Hagen-Poiseuille (f = 64/Re) applies only for laminar flow (Re < 2300). Using Colebrook for laminar flow gives incorrect results.

Frequently Asked Questions

What is the Darcy-Weisbach equation and why is it preferred?: hf = f·L/D·v²/2g is preferred because it is dimensionally consistent, applies to all fluids and flow regimes, and the friction factor is well-characterised by the Colebrook-White equation.
What is the Colebrook-White equation?: 1/√f = −2·log(ε/3.7D + 2.51/Re√f). It requires iteration to solve for f. The explicit Swamee-Jain approximation is accurate within ±3% for most practical cases.
What is the Reynolds number and what does it tell me?: Re = vD/ν. Re < 2300: laminar (f = 64/Re). 2300–4000: transitional. Re > 4000: turbulent — use Colebrook-White.
How do minor losses compare to major losses in typical pipe systems?: In long runs (L/D > 1,000), major losses dominate. In short systems with many fittings, minor losses can equal or exceed major losses.

Inputs Used

Pipe Internal Diameter: Internal (bore) diameter of the pipe — not the outer diameter.
Pipe Length: Total length of the straight pipe run (not including fittings).
Flow Rate: Volumetric flow rate in litres per second.
Pipe Roughness ε: Absolute surface roughness. Drawn steel/copper: 0.046; galvanised: 0.15; cast iron: 0.26. See table below.
Fluid Density ρ: Water at 20°C: 998 kg/m³. Water at 60°C: 983 kg/m³. Light oil: ~850 kg/m³.
Kinematic Viscosity ν: 1 cSt = 10⁻⁶ m²/s. Water at 20°C: 1.0 cSt. Water at 60°C: 0.47 cSt. SAE 30 oil: ~110 cSt.
Total Minor Loss K: Sum of K-factors for all fittings/valves. See the K-factor table. Zero to ignore minor losses.

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Pipe Head Loss Calculator

What This Calculator Does

Formula & Method

Worked Examples

50mm steel pipe — 30 m long, 2 L/s water

100mm cast iron main — 500 m, 15 L/s with fittings

Pipe Roughness Values Reference

Minor Loss K-Factors for Common Fittings

Common Mistakes

Frequently Asked Questions

Inputs Used

See Also

Related Calculators