Hydraulic Calculations Reference
Reference information for pipe flow, pressure drop, and fluid flow calculations.
This page provides reference information only. For interactive calculation tools, please visit the calculators section.
Pipe Flow Equations
Key equations for pipe flow calculations
Darcy-Weisbach Equation
hL = f × (L/D) × (v²/2g)
Where:
hL = Head loss due to friction (m or ft)
f = Darcy friction factor
L = Pipe length (m or ft)
D = Pipe inside diameter (m or ft)
v = Flow velocity (m/s or ft/s)
g = Gravitational acceleration (9.81 m/s² or 32.2 ft/s²)
Colebrook-White Equation
1/√f = -2.0 × log₁₀(ε/3.7D + 2.51/Re√f)
Where:
f = Darcy friction factor
ε = Pipe roughness (m or ft)
D = Pipe inside diameter (m or ft)
Re = Reynolds number
Reynolds Number
Re = ρvD/μ
Where:
Re = Reynolds number
ρ = Fluid density (kg/m³ or lb/ft³)
v = Flow velocity (m/s or ft/s)
D = Pipe inside diameter (m or ft)
μ = Fluid dynamic viscosity (Pa·s or lb/ft·s)
Pipe Roughness Values
Typical absolute roughness values for different pipe materials
| Pipe Material | Roughness (mm) | Roughness (inches) |
|---|---|---|
| Drawn tubing (brass, copper, plastic) | 0.0015 | 0.00006 |
| Commercial steel or wrought iron | 0.046 | 0.0018 |
| Galvanized iron | 0.15 | 0.006 |
| Cast iron | 0.26 | 0.010 |
| Concrete | 0.3 - 3.0 | 0.012 - 0.12 |
| Riveted steel | 0.9 - 9.0 | 0.035 - 0.35 |
Flow Regimes
Classification of flow based on Reynolds number
Laminar Flow
Re < 2000
- Smooth, orderly flow
- Fluid particles move in straight lines
- Pressure drop proportional to velocity
- Friction factor = 64/Re
Transitional Flow
2000 < Re < 4000
- Unstable flow regime
- Mixture of laminar and turbulent characteristics
- Difficult to predict behavior
Turbulent Flow
Re > 4000
- Chaotic, irregular flow
- Random motion and mixing
- Pressure drop approximately proportional to velocity squared
- Friction factor determined using Colebrook-White equation or Moody diagram
Minor Losses
Head loss due to fittings and components
Minor losses are calculated using the K-value method:
hL = K × (v²/2g)
Where:
hL = Head loss (m or ft)
K = Loss coefficient
v = Flow velocity (m/s or ft/s)
g = Gravitational acceleration (9.81 m/s² or 32.2 ft/s²)
Typical K Values
| Fitting/Component | K Value |
|---|---|
| 90° elbow, standard | 0.9 |
| 90° elbow, long radius | 0.6 |
| 45° elbow | 0.4 |
| Tee, flow through run | 0.3 |
| Tee, flow through branch | 1.0 |
| Gate valve, fully open | 0.2 |
| Globe valve, fully open | 10.0 |
| Check valve, swing | 2.0 |
| Sudden expansion | 1.0 |
| Sudden contraction | 0.5 |