Calculator Inputs
Example Data Table
This sample row demonstrates a turbulent water-flow case in a small commercial pipe.
| Diameter (m) | Length (m) | Velocity (m/s) | Density (kg/m³) | Viscosity (Pa·s) | Roughness (m) | Reynolds Number | Darcy Factor | Pressure Drop (Pa) | Head Loss (m) |
|---|---|---|---|---|---|---|---|---|---|
| 0.050000 | 25.000 | 1.800 | 998.000 | 0.001002 | 0.000045 | 89,640.72 | 0.02223584 | 17,975.01 | 1.836614 |
Formula Used
1) Reynolds Number
Re = (ρ × V × D) / μWhere ρ is density, V is average velocity, D is pipe diameter, and μ is dynamic viscosity.
2) Relative Roughness
ε / DHere ε is absolute roughness and D is internal diameter.
3) Laminar Flow Relation
f = 64 / ReThis applies to fully developed laminar flow in circular pipes.
4) Colebrook-White Equation
1 / √f = -2 log10[(ε / 3.7D) + (2.51 / (Re √f))]This is solved iteratively for turbulent flow.
5) Swamee-Jain Equation
f = 0.25 / [log10((ε / 3.7D) + (5.74 / Re^0.9))]^2This explicit form is fast and practical for turbulent flow estimates.
6) Haaland Equation
1 / √f = -1.8 log10[( (ε / 3.7D)^1.11 ) + (6.9 / Re)]Haaland gives another efficient explicit turbulent approximation.
7) Churchill Equation
f = 8[(8/Re)^12 + 1/(A + B)^(3/2)]^(1/12)Churchill offers a smooth all-range formula useful across many regimes.
8) Darcy-Weisbach Pressure Drop
ΔP = f × (L / D) × (ρV² / 2)The calculator also reports head loss using:
hf = f × (L / D) × (V² / 2g)How to Use This Calculator
- Choose whether Reynolds number should be calculated from fluid properties or entered directly.
- Enter pipe diameter, length, velocity, density, viscosity, roughness, and gravity in SI units.
- Select a friction-factor model. Colebrook is robust, while explicit models are faster.
- Click Calculate Friction Factor.
- Read the results block that appears below the header and above the form.
- Review friction factor, flow regime, pressure drop, head loss, and the graph.
- Use the CSV or PDF buttons to export your result summary.
Frequently Asked Questions
1) What does friction factor represent?
It is a dimensionless measure of wall resistance in pipe flow. This page returns the Darcy friction factor and also shows the Fanning value as one quarter of Darcy.
2) When is f = 64 / Re valid?
Use it for fully developed laminar flow, usually below Reynolds 2300 in straight circular pipes. Strong entrance effects or unusual fluids can shift the practical limit.
3) Why does roughness matter?
Higher wall roughness disturbs near-wall flow and increases resistance. Its effect becomes stronger in turbulent conditions and is captured through relative roughness, ε/D.
4) Which method should I choose?
Colebrook is a dependable iterative choice for turbulent flow. Swamee-Jain and Haaland are fast explicit approximations. Churchill is convenient when you want one continuous formula.
5) What is the difference between Darcy and Fanning factors?
Darcy friction factor equals four times the Fanning friction factor. Many hydraulic and pipe-loss equations use Darcy, so always confirm the convention in your reference.
6) Why is transitional flow harder to predict?
Between Reynolds 2300 and 4000, flow may alternate between laminar and turbulent structures. Any single estimate is approximate, so this calculator blends values for practical screening.
7) Can I use other units?
This page assumes SI units. Convert diameter and roughness to meters, density to kilograms per cubic meter, viscosity to pascal-seconds, and velocity to meters per second.
8) How is pressure drop calculated here?
After computing friction factor, the page applies Darcy-Weisbach for pressure drop. It also converts the same resistance into head loss using gravitational acceleration.