hydraulics

Hydraulics Engineering Skill

Friction Factor Calculations

• Always use Darcy-Weisbach with Colebrook equation
• Never use Hazen-Williams (project decision per PRD)
• Friction factor function: fluids.friction.friction_factor(Re, eD)

Colebrook Equation

1/√f = -2.0 × log₁₀((ε/D)/3.7 + 2.51/(Re×√f))

• Implicit equation solved iteratively
• ε = absolute roughness (ft or m)
• D = pipe inner diameter (ft or m)
• Re = Reynolds number (dimensionless)

K-Factor Resolution Order

1. User-specified value (if provided)
2. Crane TP-410 correlation (preferred)
3. Fluids library default
4. Error if no value available

Standard L/D Values (Crane TP-410)

K-Factor Calculation from L/D:

K = f × (L/D)

where f is the Darcy friction factor

Pipe Material Roughness (ft)

Unit Conversions

Flow

• 1 GPM = 6.309e-5 m³/s
• 1 GPM = 1/448.831 ft³/s
• 1 GPM = 0.227 m³/h
• 1 GPM = 0.0631 L/s

Pressure

• 1 psi = 6894.76 Pa
• 1 psi = 2.31 ft H₂O
• 1 psi = 0.703 m H₂O
• 1 bar = 14.504 psi

Length

• 1 ft = 0.3048 m
• 1 in = 0.0254 m = 25.4 mm

Velocity

• 1 ft/s = 0.3048 m/s

Darcy-Weisbach Head Loss

Pipe Friction Loss

h_f = f × (L/D) × (v²/2g)

where:

• h_f = head loss (ft or m)
• f = Darcy friction factor
• L = pipe length (ft or m)
• D = pipe inner diameter (ft or m)
• v = flow velocity (ft/s or m/s)
• g = gravitational acceleration (32.174 ft/s² or 9.807 m/s²)

Minor Losses

h_m = K × (v²/2g)

where:

• h_m = minor head loss (ft or m)
• K = loss coefficient (dimensionless)
• Sum all K-factors for all fittings in series

Total Head Loss

h_total = h_pipe + Σh_fittings + Σh_components

Reynolds Number

Re = (ρ × v × D) / μ = (v × D) / ν

where:

• ρ = density (lb/ft³ or kg/m³)
• μ = dynamic viscosity (lb/(ft·s) or Pa·s)
• ν = kinematic viscosity (ft²/s or m²/s)

Flow Regimes

• Laminar: Re < 2,300
• Transition: 2,300 ≤ Re ≤ 4,000
• Turbulent: Re > 4,000

Most hydraulic systems operate in turbulent flow.

NPSH Calculations

NPSH Available

NPSH_a = (P_atm - P_vapor) / (ρ×g) + h_static - h_friction_suction

where:

• P_atm = atmospheric pressure (absolute)
• P_vapor = vapor pressure of fluid at operating temperature
• h_static = static height of fluid above pump centerline (positive if above, negative if below)
• h_friction_suction = friction loss in suction piping

NPSH Margin

NPSH_margin = NPSH_a - NPSH_r

• Minimum margin: 3 ft (0.91 m) for most applications
• Recommended margin: 5 ft (1.52 m) for continuous operation
• Warn if margin < 3 ft (configurable)

Pump Curve Handling

Interpolation

• Use cubic spline for smooth curve
• Scipy: scipy.interpolate.CubicSpline
• Ensure curve is monotonically decreasing (head decreases as flow increases)

Extrapolation

• Use with warning only
• Linear extrapolation acceptable for small extensions (< 10%)
• Flag to user if operating point is outside curve range

Operating Point

• Find intersection of pump curve and system curve
• Use root-finding: scipy.optimize.brentq or scipy.optimize.fsolve
• System curve: total head loss vs flow

Affinity Laws (Variable Speed)

Q₂/Q₁ = N₂/N₁
H₂/H₁ = (N₂/N₁)²
P₂/P₁ = (N₂/N₁)³

where:

• Q = flow rate
• H = head
• P = power
• N = pump speed (RPM)

Velocity Limits (Design Guidelines)

Note: These are guidelines. User can override in project settings.

Pressure Drop Limits

• Suction line: Minimize pressure drop to avoid cavitation
• Discharge line: Typically < 5 psi per 100 ft (11.3 kPa per 30 m)

Common Gotchas

1. Units consistency: Always convert to consistent unit system before calculations
2. Absolute vs gauge pressure: NPSH calculations require absolute pressure
3. Temperature effects: Fluid properties vary with temperature
4. Closed valve: Treat as infinite K-factor or broken connection
5. Zero flow: Avoid division by zero; handle as special case
6. Reverse flow: Friction calculations still use absolute velocity

Reference Standards

• Crane TP-410: Flow of Fluids Through Valves, Fittings, and Pipe
• ASME B31.3: Process Piping
• HI Standards: Hydraulic Institute Standards for Centrifugal Pumps

Validation Checklist

When reviewing hydraulic calculations:

• Units are consistent throughout
• Darcy-Weisbach equation used (not Hazen-Williams)
• Friction factor from Colebrook equation
• K-factors follow resolution order
• Reynolds number calculated correctly
• NPSH available calculated at pump suction
• Operating point within pump curve range (or warning issued)
• Velocity within reasonable range (warning if excessive)
• Temperature-dependent properties used if applicable
• Absolute pressure used for vapor pressure calculations