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Formula used
Re = ρVD/μ = VD/ν fDarcy = 64/Re fFanning = 16/Re ΔPmajor = f(L/D)(ρV²/2) Q = πD⁴ΔP/(128μL) V = Q/A τw = ΔPmajorD/(4L) Vmax = 2V Le ≈ 0.05ReD Ploss = ΔPfrictionQ
These equations assume steady, fully developed Newtonian flow. Density and viscosity remain constant throughout the pipe. Circular-pipe relations are exact under those assumptions.
How to use this calculator
- Select the unknown quantity from the solve menu.
- Choose circular or hydraulic-diameter geometry.
- Enter pipe dimensions and optional series sections.
- Select a fluid preset or enter custom properties.
- Choose pressure and flow input methods.
- Enter elevation, fittings, and parallel-pipe information.
- Calculate, review warnings, then export the results.
Example input data
| Example | Fluid | Diameter | Length | Known condition | Suggested solve mode |
|---|---|---|---|---|---|
| Small laboratory tube | Water | 4 mm | 2 m | 0.03 L/min | Pressure drop |
| Hydraulic oil line | Hydraulic oil | 10 mm | 8 m | 0.8 L/min | Pressure drop |
| Glycerine transfer | Glycerine | 25 mm | 5 m | 60 kPa available | Flow rate |
| Allowable diameter | Water | Unknown | 20 m | 5 L/min and 30 kPa | Diameter |
| Allowable run length | Oil | 12 mm | Unknown | 1 L/min and 100 kPa | Length |
| Viscosity experiment | Custom | 3 mm | 1 m | Flow and pressure measured | Viscosity |
Assumptions and engineering limits
Flow must remain steady and incompressible. The fluid must behave as Newtonian. Viscosity should remain nearly constant.
Pipe flow should become fully developed. Entrance effects may matter in short pipes. The calculator estimates entrance length automatically.
Laminar friction does not depend directly on roughness. Roughness still appears for useful comparison. Transitional results require another validated method.
Frequently asked questions
What defines laminar pipe flow?
Laminar flow has orderly fluid layers. Circular-pipe flow is usually laminar below Reynolds 2300. Local disturbances can shift this boundary.
Why is the Darcy factor 64 divided by Reynolds number?
The relationship follows the exact laminar momentum solution. It applies to fully developed circular flow. Other duct shapes may use different constants.
Does pipe roughness affect laminar pressure loss?
Fully developed laminar friction ignores ordinary wall roughness. Viscous effects dominate the resistance. Extreme roughness can disturb the ideal assumptions.
What is the difference between Darcy and Fanning factors?
The Darcy factor is four times larger. Both describe the same wall resistance. Always confirm which convention an equation uses.
Why is centreline velocity twice average velocity?
Fully developed laminar velocity forms a parabola. Velocity reaches zero at the wall. Area integration gives the two-to-one ratio.
When should entrance length be checked?
Check it whenever pipes are short. Developing flow has a changing velocity profile. Its pressure loss can exceed predictions.
Can this calculator analyse gases?
It can provide an incompressible estimate. Large gas pressure changes require compressible equations. A warning appears for gas selections.
Can I use a non-circular duct?
Yes, enter area and wetted perimeter. The calculator uses hydraulic diameter. Results remain approximate for unusual shapes.
Why can viscosity change the answer strongly?
Laminar pressure loss is directly proportional to viscosity. Temperature can change viscosity considerably. Use measured properties whenever accuracy matters.