Calculate the Darcy friction factor using the Moody chart relationships. Supports laminar flow, Swamee-Jain, Haaland and iterative Colebrook-White equations.
Moody chart region determined by Reynolds number and relative roughness ε/D
Flow Regime
TURBULENT
Laminar (Re < 2300) · Transitional · Turbulent (Re > 4000)
SI units preferred
Mean flow velocity in the pipe.
Internal diameter of the pipe.
For water at 20 °C ≈ 1.0×10⁻⁶ m²/s.
Pipe wall absolute roughness.
Common materials (click to apply)
Darcy Friction Factor f
Regime: turbulent
Reynolds Number
250,000
Relative Roughness ε/D
4.500e-4
Laminar (Re < 2300)
f = 64 / ReSwamee-Jain (turbulent)
f = 0.25 / [log₁₀(ε/D / 3.7 + 5.74 / Re0.9)]²Colebrook-White
1/√f = −2 log₁₀(ε/(3.7D) + 2.51/(Re√f))import math
def friction_factor_swamee_jain(Re, rel_rough):
"""
Swamee-Jain explicit approximation of Colebrook-White
"""
if Re < 2300:
return 64 / Re
term = rel_rough / 3.7 + 5.74 / Re**0.9
return 0.25 / (math.log10(term))**2
# Example
V = 2.5 # m/s
D = 100 / 1000 # m
nu = 1.0e-6 # m²/s
eps = 0.045 / 1000 # m
Re = V * D / nu
rel_rough = eps / D
f = friction_factor_swamee_jain(Re, rel_rough)
print(f"Reynolds number: {Re:.0f}")
print(f"Relative roughness: {rel_rough:.6f}")
print(f"Friction factor f: {f:.5f}")function f = friction_factor_sj(Re, rel_rough)
if Re < 2300
f = 64 / Re;
else
term = rel_rough/3.7 + 5.74/Re^0.9;
f = 0.25 / (log10(term))^2;
end
end
% Example
V = 2.5;
D = 100/1000;
nu = 1.0e-6;
eps = 0.045/1000;
Re = V*D/nu;
rr = eps/D;
f = friction_factor_sj(Re, rr);
fprintf('Re = %.0f, f = %.5f\n', Re, f);=IF(Re<2300,64/Re,0.25/(LOG10(epsD/3.7+5.74/Re^0.9))^2)Quickly calculate and analyze parameters for your ohms law requirements.
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An engineer used a smooth-pipe friction factor for a 20-year-old cast-iron main. Actual friction was almost twice as high, causing the selected pump to deliver far less flow than required.
Always use realistic roughness values that account for pipe age, scaling and material. When in doubt, be conservative.
A viscous oil line was designed assuming turbulent flow. At the actual operating temperature the Reynolds number dropped into the laminar regime, completely changing the pressure-drop calculation.
Always calculate Reynolds number first. The friction-factor formula changes dramatically between laminar and turbulent regimes.
The Darcy friction factor is four times the Fanning friction factor (f_Darcy = 4 × f_Fanning). This calculator returns the Darcy factor used in the classic Darcy-Weisbach equation.
Swamee-Jain is excellent for most engineering work. Haaland is slightly more accurate near the smooth-pipe limit. Use Colebrook-White when maximum precision is required.
New commercial steel ≈ 0.045 mm. Aged or corroded steel can be 0.15–0.5 mm or higher. Always consider the expected condition of the pipe over its service life.