Haaland Darcy Friction Factor Calculator
Calculate Haaland Darcy friction factor from turbulent Reynolds number and pipe relative roughness. Do not substitute the Fanning convention.
Calculate Haaland Darcy friction factor from turbulent Reynolds number and pipe relative roughness. Do not substitute the Fanning convention.
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Calculation context and source notes
Estimate the Darcy friction factor for fully developed turbulent Newtonian pipe flow from Reynolds number and relative roughness. Haaland is an explicit approximation to the implicit Colebrook relation, not a laminar-flow or drilling-mud rheology model.
Establish Reynolds number and divide pipe-wall roughness by the inside diameter using the same length units. Transfer the resulting Darcy factor only to a pressure-loss equation that uses the Darcy convention, rather than the Fanning convention.
Solves for
f_D (dimensionless)
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Formula, variables, and sourceReproduce a turbulent pipe check
For Re = 100,000 and relative roughness 0.001, the Haaland relation gives Darcy factor 0.0219662. Solving the implicit Colebrook equation for the same inputs gives approximately 0.0221745. The difference illustrates an approximation check, not a universal error guarantee.
The corresponding Fanning factor is 0.00549155, one quarter of the Haaland Darcy result. Inserting the wrong convention into a pressure-loss calculation introduces a factor-of-four error even when every length, velocity and density input is otherwise correct.
Select the flow model before the friction factor
Use the friction model that matches the flow regime and fluid behavior. The calculator deliberately rejects Re at or below 4,000 rather than silently applying a turbulent correlation to a laminar or transitional case. For non-Newtonian drilling fluids, the required rheology and annular geometry are outside this pipe model.
Relative roughness is dimensionless: 0.1 mm roughness divided by 100 mm inside diameter is 0.001. This example does not prescribe a roughness for a particular material or condition. Establish roughness and diameter from the actual pipe specification, condition and engineering basis.
Learn, compare and practice
Worked explanations, controlled studies and printable exercises connected to this calculation.
Formula, variables, and default calculation
Reproducible default result
With the default values shown below, the calculation returns f_D = 0.021966 dimensionless. Defaults demonstrate the implementation; they are not recommended field values.
100000
0.001
Input definitions
Re
dimensionlessReynolds Number (Turbulent Flow Only)
eps_D
dimensionlessPipe Roughness Divided by Inside Diameter
Output definitions
f_D
Darcy (Not Fanning) Friction Factor
Engineering use, assumptions, and limits
Establish Reynolds number and divide pipe-wall roughness by the inside diameter using the same length units. Transfer the resulting Darcy factor only to a pressure-loss equation that uses the Darcy convention, rather than the Fanning convention.
Assumptions
- The fluid is single-phase Newtonian and flow is fully developed in a pipe.
- Reynolds number is strictly between 4,000 and 100 million; relative roughness is between zero and 0.05 in this implementation.
Limitations
- Not a laminar, transitional, non-Newtonian mud, annular or multiphase friction model.
- Does not calculate Reynolds number or pressure loss; the roughness screening bound is not a guarantee of field accuracy.
Common mistakes
- Entering absolute roughness instead of roughness divided by diameter, or mixing the two length units.
- Using natural logarithm rather than log10, or using Darcy factor where a Fanning factor is required.
Frequently asked questions
What inputs does the Haaland Darcy Friction Factor calculator need?
The calculation uses Reynolds Number (Turbulent Flow Only) (Re), Pipe Roughness Divided by Inside Diameter (eps_D). Enter values on the units shown beside each field.
What result does this calculator return?
The primary result is darcy (not fanning) friction factor in dimensionless. The formula section shows the declared relationship, variables, and a reproducible default calculation.
What should I check before using the result?
Confirm the unit basis, source applicability, and input quality. Not a laminar, transitional, non-Newtonian mud, annular or multiphase friction model. Entering absolute roughness instead of roughness divided by diameter, or mixing the two length units.
Source and record status
Source metadata identifies the relationship implemented by the calculator. Check the cited edition, unit basis, and scope against the engineering case before operational use.
COMSOL Pipe Flow Module User's Guide 6.3, equations 2-13 and 2-14, page 50: Haaland Darcy friction factor. The calculator restricts relative roughness to 0-0.05 as an implementation screening range, not a quoted source validity limit.
Open source reference