Learn: Laminar Darcy friction factor
At sufficiently low Reynolds number, liquid in a circular pipe moves in orderly layers. For fully developed laminar flow, the Darcy friction factor has a simple inverse relationship with Reynolds number.
What the formula is saying
Divide 64 by Re. The factor 64 belongs to the Darcy convention for a circular pipe; it follows from the laminar velocity profile, not from a roughness chart.
Read the symbols in plain language
- Re
- Reynolds number
Inertial-to-viscous flow parameter based on mean velocity and internal pipe diameter; choose the flow-regime equation accordingly.
Reynolds number (no unit)Use Reynolds number as the base unit shown here. Re and f are dimensionless. Enter the Reynolds number as a number, not a percentage. There is no length unit in this step because density, viscosity, speed and diameter are already combined in Re.
- f
- Result to find
Laminar Darcy friction factor. The coefficient sixty-four is specific to the Darcy convention for fully developed circular-pipe flow.
ratio / no unit
Sort out the units first
Re and f are dimensionless. Enter the Reynolds number as a number, not a percentage. There is no length unit in this step because density, viscosity, speed and diameter are already combined in Re.
Assumptions before calculating
Use a Newtonian liquid in a circular full pipe with fully developed laminar flow. This lesson accepts 0 < Re < 2300 as its teaching range; disturbances and entrance effects can affect real transition.
Let’s solve one together
Read the given values, follow each operation, then check what the result means.
Read the supplied values as one complete study case. Find f and explain the result in the stated output unit.
- Re · Reynolds number
- 1000 Reynolds number (no unit)
Take the reciprocal of Reynolds number
The laminar Darcy factor varies inversely with the supplied Reynolds number.
1 ÷ (1000) = 0.001Apply the circular-pipe coefficient
The coefficient sixty-four is specific to the Darcy convention for fully developed circular-pipe flow.
64 × (0.001) = 0.064
Does this worked answer make sense?
Doubling Re halves f while both values remain within the laminar range. Although f decreases, the complete head-loss expression also contains velocity squared.
A second worked example — different values
A second case uses different data. Predict which way the answer will change, then calculate it without reusing the first answer.
- Re · Reynolds number
- 1600 Reynolds number (no unit)
Take the reciprocal of Reynolds number
The laminar Darcy factor varies inversely with the supplied Reynolds number.
1 ÷ (1600) = 0.000625Apply the circular-pipe coefficient
The coefficient sixty-four is specific to the Darcy convention for fully developed circular-pipe flow.
64 × (0.000625) = 0.04
Now try your own values
Change a value or its unit. The same method will show your calculation, step by step.
Results update only when you calculate. The lesson example above stays unchanged.
Your turn — check your understanding
Solve this separate case yourself. Use only the values below; the two worked examples use different data. Give the requested result in the selected unit.
- Re · Reynolds number
- 800 Reynolds number (no unit)
Find: Learn: Laminar Darcy friction factor
A hint, not the answer
Divide 64 by Re. The factor 64 belongs to the Darcy convention for a circular pipe; it follows from the laminar velocity profile, not from a roughness chart.
Re and f are dimensionless. Enter the Reynolds number as a number, not a percentage. There is no length unit in this step because density, viscosity, speed and diameter are already combined in Re.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Take the reciprocal of Reynolds number
The laminar Darcy factor varies inversely with the supplied Reynolds number.
1 ÷ (800) = 0.00125Apply the circular-pipe coefficient
The coefficient sixty-four is specific to the Darcy convention for fully developed circular-pipe flow.
64 × (0.00125) = 0.08
Avoid the common trap
Using 16/Re gives the Fanning factor, not Darcy. A Reynolds number of zero makes the algebraic factor undefined; the calculator rejects it instead of returning an infinite usable coefficient.
When this method applies — and when it does not
Do not extrapolate this equation into transitional or turbulent flow. It is not the corresponding formula for every noncircular duct or non-Newtonian fluid, and it does not compute total pipe loss by itself.
For study and understanding, not approval of a real structure, site operation or design. Apply the correct standard, National Annex and professional review to actual engineering work.
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Sources & further reading
References open in a new tab and explain the underlying principles. The teaching text and examples here are SimpleFlick’s own; the source organisations have not endorsed this calculator.
Reading focus: Laminar Darcy friction factor. Water-measurement principles; for discharge devices, read the orifice/weir chapters and the installation and head-measurement conditions, not only the coefficient formula.
- U.S. Bureau of Reclamation — Water Measurement Manual, 3rd edition (1997; revised reprint 2001)
- Dawei Han, University of Bristol — Concise Hydraulics (2008, Ventus Publishing)
Lesson updated: · Both examples and the separate practice case are checked against an independent high-precision numerical implementation. This verifies arithmetic for the stated model, not engineering certification.