Darcy Weisbach Calculator
Calculate friction head loss in pipes using the Darcy-Weisbach equation. Enter values for instant results with step-by-step formulas.
Reviewed by Daniel Agrici, Founder & Lead Developer
Formula
hf = f x (L/D) x (V^2 / 2g)
Where hf is friction head loss (ft), f is the Darcy friction factor (dimensionless), L is pipe length (ft), D is pipe inside diameter (ft), V is mean flow velocity (ft/s), and g is gravitational acceleration (32.174 ft/s^2). The friction factor f is determined from the Reynolds number and relative roughness using the Colebrook-White equation or Swamee-Jain approximation.
Worked Examples
Example 1: Industrial Steel Pipe Head Loss
Problem:Water at 60 degrees F flows at 8 ft/s through a 6-inch commercial steel pipe (roughness = 0.00015 ft) over 200 feet. Calculate friction factor and head loss.
Solution:D = 6/12 = 0.5 ft\nRe = VD/nu = (8 x 0.5) / 1.217e-5 = 328,677 (turbulent)\nRelative roughness = 0.00015 / 0.5 = 0.0003\nSwamee-Jain: f = 0.25 / [log10(0.0003/3.7 + 5.74/328677^0.9)]^2\nf = 0.25 / [log10(8.108e-5 + 3.217e-5)]^2 = 0.25 / [-4.148]^2 = 0.01453\n\nhf = f(L/D)(V^2/2g) = 0.01453 x (200/0.5) x (64/64.348)\nhf = 0.01453 x 400 x 0.9946 = 5.78 ft
Result:f = 0.01453 | Re = 328,677 | Head Loss = 5.78 ft (2.50 psi) | Turbulent flow
Example 2: Comparing Pipe Materials for Same Flow
Problem:Compare head loss for 100 ft of 4-inch pipe at 4 ft/s for PVC (epsilon = 0.000005 ft) versus old cast iron (epsilon = 0.005 ft).
Solution:D = 4/12 = 0.333 ft, Re = (4 x 0.333) / 1.217e-5 = 109,450\n\nPVC: e/D = 0.000005/0.333 = 1.5e-5\nf = 0.25/[log10(1.5e-5/3.7 + 5.74/109450^0.9)]^2 = 0.01776\nhf = 0.01776 x (100/0.333) x (16/64.348) = 1.33 ft\n\nOld Cast Iron: e/D = 0.005/0.333 = 0.015\nf = 0.25/[log10(0.015/3.7 + 5.74/109450^0.9)]^2 = 0.04438\nhf = 0.04438 x 300 x 0.2487 = 3.31 ft\n\nOld cast iron has 2.49x more head loss.
Result:PVC: hf = 1.33 ft | Old Cast Iron: hf = 3.31 ft | Cast iron has 2.49x more friction loss
Frequently Asked Questions
What is the Darcy-Weisbach equation and why is it considered the most accurate pipe friction formula?
The Darcy-Weisbach equation is a theoretically-derived formula that calculates friction head loss in pipes: hf = f x (L/D) x (V^2/(2g)), where f is the Darcy friction factor, L is pipe length, D is pipe diameter, V is flow velocity, and g is gravitational acceleration. Unlike empirical formulas such as Hazen-Williams, the Darcy-Weisbach equation is derived from fundamental fluid mechanics principles and is valid for any Newtonian fluid (water, oil, air, chemicals), any pipe material, any pipe size, and any flow regime (laminar or turbulent). It is considered the gold standard of pipe friction calculations because it accounts for the actual physics of fluid-wall interaction through the friction factor, which depends on both the Reynolds number and the relative pipe roughness. Modern computational hydraulics exclusively uses Darcy-Weisbach because of its universal applicability and theoretical rigor.
How is the Darcy friction factor determined using the Moody diagram?
The Moody diagram (developed by Lewis Moody in 1944) is a graphical representation of the Colebrook-White equation that plots the Darcy friction factor against Reynolds number for various values of relative roughness (epsilon/D). To use the Moody diagram, first calculate the Reynolds number Re = VD/nu and the relative roughness epsilon/D. Then locate the Reynolds number on the horizontal axis, follow the curve for your relative roughness value, and read the friction factor from the vertical axis. In the laminar flow region (Re < 2000), all curves collapse to the single line f = 64/Re. In the transition zone (2000 < Re < 4000), flow is unstable and the friction factor is uncertain. In the fully turbulent rough zone, the friction factor depends only on relative roughness and not on Reynolds number. Modern practice uses explicit approximations like the Swamee-Jain equation or iterative solutions of the Colebrook-White equation instead of reading from the diagram.
How is the Darcy-Weisbach equation used for non-circular conduits?
For non-circular conduits (rectangular ducts, annular spaces, open channels), the Darcy-Weisbach equation uses the hydraulic diameter Dh = 4A/P (where A is cross-sectional area and P is wetted perimeter) in place of the pipe diameter D. For a circular pipe, Dh equals the actual diameter. For a rectangular duct with width W and height H, Dh = 2WH/(W+H). For an annular space between pipes of outer diameter D1 and inner diameter D2, Dh = D1 - D2. The friction factor is then calculated using the Reynolds number based on hydraulic diameter (Re = V x Dh / nu) and the relative roughness epsilon/Dh. This approach works well for turbulent flow but requires correction factors for laminar flow in non-circular cross-sections because the velocity profile shape differs from that in circular pipes. For HVAC ductwork design, this method is standard practice using the ASHRAE Duct Fitting Database for both friction and fitting losses.
What are the advantages of using Darcy-Weisbach over Hazen-Williams or Manning?
Darcy-Weisbach offers several fundamental advantages over empirical formulas. First, it applies to any Newtonian fluid (water, oil, air, glycol, chemicals), while Hazen-Williams only works for water and Manning only for open channels. Second, it is valid for any flow regime (laminar, transitional, turbulent), whereas Hazen-Williams assumes turbulent flow. Third, the roughness parameter (epsilon) has a clear physical meaning (average height of wall irregularities in feet or mm) that can be measured, unlike the dimensionless C factor or n value. Fourth, it accounts for temperature effects through the kinematic viscosity, which affects the Reynolds number and thus the friction factor. Fifth, it is dimensionally consistent and does not require unit-specific constants (unlike the 1.486 in Manning equation or the varying coefficients in Hazen-Williams depending on unit system). The main disadvantage is the need to calculate the friction factor, but modern computers make this trivial.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy