Calculator
Example data table
| Field | Value | Result | Value |
|---|---|---|---|
| Inside diameter (D) | 0.150000 m | Relative roughness (ε/D) | 0.00030000 |
| Adjusted roughness (ε) | 0.000045000 m | Reynolds number (Re) | 300,000.00 |
| Friction factor (Colebrook) | 0.016974 | Head loss (hf) | 1.1539 m |
| Pressure drop (ΔP) | 11,293.5 Pa | Flow regime | Turbulent |
Typical roughness guide
| Material | Typical ε (mm) | Notes |
|---|---|---|
| Drawn tubing | 0.0015 | Very smooth internal surface. |
| Glass | 0.0015 | Often treated as hydraulically smooth. |
| Plastic / PVC | 0.0015 | Smooth polymers; aging can increase ε. |
| Copper | 0.0015 | Typically smooth when clean. |
| Commercial steel | 0.045 | Common design value for new steel. |
| Galvanized iron | 0.15 | Coating irregularities raise ε. |
| Cast iron | 0.26 | Rougher surface; deposits matter. |
| Concrete | 1.0 | Very rough; strong dependence on finish. |
| Riveted steel | 0.9 | Legacy piping; roughness dominates losses. |
Formula used
- Relative roughness: ε/D
- Reynolds number (using ν): Re = V·D/ν
- Laminar friction factor: f = 64/Re
- Colebrook–White (turbulent): 1/√f = −2·log₁₀( (ε/D)/3.7 + 2.51/(Re·√f) )
- Swamee–Jain (turbulent): f = 0.25 / [log₁₀( (ε/D)/3.7 + 5.74/Re⁰·⁹ )]²
- Darcy–Weisbach head loss: hf = f·(L/D)·(V²/(2g))
- Pressure drop: ΔP = ρ·g·hf
How to use this calculator
- Enter the inside diameter and choose its unit.
- Select a material, or switch to manual ε entry.
- Apply a roughness factor if the pipe is aged or scaled.
- Choose Reynolds input: compute it or enter directly.
- For head loss, provide pipe length and velocity.
- Press Submit to view results above the form.
- Use the download buttons to export CSV or PDF.
What Roughness Represents
Pipe roughness is the texture on the inner wall that disturbs the near wall flow. It is modeled as an equivalent sand grain height, written as epsilon. Even when a pipe looks smooth, corrosion, weld seams, deposits, or liners introduce texture. In turbulent flow the wall texture increases shear stress, raising the Darcy friction factor and the energy required to move fluid. Higher roughness boosts near wall mixing.
Absolute Versus Relative
Design calculations use absolute roughness in meters and relative roughness, epsilon divided by diameter. Relative roughness controls how texture affects turbulence on the Moody chart. A small epsilon can dominate when the diameter is small, such as instrument lines. As diameter grows, the same epsilon becomes less important, but old pipes often grow epsilon because of scaling, pitting, and biofilm. At high Reynolds numbers, flow may become fully rough.
Link to Friction Factor
Friction factor depends on Reynolds number and relative roughness. In laminar flow it is independent of roughness and equals sixty four divided by Reynolds. In turbulent flow, the Colebrook White relation couples friction factor on both sides and is solved iteratively. The Swamee Jain approximation is faster and accurate for engineering ranges, so this calculator can compute both. In the fully rough limit, friction factor weakly depends on Reynolds.
Data Inputs That Matter
Choose a material to load a typical epsilon, then apply a roughness factor to represent aging. Switch to manual entry when you have manufacturer data or measurements. To compute Reynolds number you need diameter, velocity, and kinematic viscosity, or you may enter Reynolds directly. For head loss and pressure drop, add pipe length and fluid density. Keep units consistent, and remember viscosity varies with temperature, especially for oils.
Interpreting The Output
The results show epsilon, relative roughness, Reynolds number, the friction factor, and head loss and pressure drop when requested. Compare laminar and turbulent methods to confirm the regime. If the friction factor changes little when you vary epsilon, the flow is dominated by Reynolds number. If it changes a lot, surface condition is driving losses and cleaning or lining may save pumping power. Use pressure data to validate assumptions.
FAQs
What is pipe roughness, epsilon?
Epsilon is an equivalent wall texture height used in friction calculations. It represents corrosion, seams, deposits, or liner texture, and is usually expressed in meters or micrometers.
Which friction factor method should I choose?
Use Colebrook when you want the classic iterative solution, especially for reporting. Use Swamee Jain for fast design estimates across common turbulent ranges. In laminar flow, the calculator uses f = 64/Re automatically.
Does roughness affect laminar flow?
In fully laminar flow, friction factor depends mainly on Reynolds number and not on roughness. Roughness becomes important after transition to turbulence, where it increases shear stress and energy loss.
How can I estimate kinematic viscosity?
You can use fluid property tables at the operating temperature, or compute it from dynamic viscosity divided by density. Water near room temperature is about 1e-6 m²/s, while oils can be much higher.
Why is relative roughness important?
Relative roughness, epsilon divided by diameter, scales wall texture to pipe size. It is the key roughness input in the Moody chart and in Colebrook type relations for turbulent friction factor.
Why do head loss and pressure drop stay blank?
Head loss and pressure drop require length and velocity. Pressure drop also needs fluid density. If you leave those fields empty, the calculator still reports roughness, relative roughness, Reynolds number, and friction factor.