Hydraulic Calculations Reference

Reference information for pipe flow, pressure drop, and fluid flow calculations.

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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 MaterialRoughness (mm)Roughness (inches)
Drawn tubing (brass, copper, plastic)0.00150.00006
Commercial steel or wrought iron0.0460.0018
Galvanized iron0.150.006
Cast iron0.260.010
Concrete0.3 - 3.00.012 - 0.12
Riveted steel0.9 - 9.00.035 - 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/ComponentK Value
90° elbow, standard0.9
90° elbow, long radius0.6
45° elbow0.4
Tee, flow through run0.3
Tee, flow through branch1.0
Gate valve, fully open0.2
Globe valve, fully open10.0
Check valve, swing2.0
Sudden expansion1.0
Sudden contraction0.5