🚰 Darby 2K & 3K Pipe Fittings Minor Head Loss

Calculate accurate minor head losses in pipe fittings using Darby 3-K method (2001): loss coefficient K, total head loss (m), pressure drop (kPa), and equivalent length (Leq) across laminar, transitional, and turbulent regimes.

⚡ Fortran 90 Engine Double Precision (IEEE 754) ✓ ISO / ASME Validated

Darby 2K & 3K Pipe Fittings Minor Head Loss

Fluid Mechanics

📊 Solver Telemetry ● ACTIVE

👁️ Views 21

⚡ Solves 20

💾 Downloads 424 📦 Fortran Code 4.5 KB

📅 Released Jun 2026

⏱️ Latency < 1 ms

💡 Hardware & Sizing Partner: Need to size a control valve or check ASME flange bolt torque for this line?

FLOWKS IEC 60534 Sizer ↗ • API 6D Valve Catalog →

🚰 Pipe Fitting Flow Separation & Minor Head Loss

Real-time visual simulation: Elbow streamline curvature, secondary eddy vortices, and pressure dissipation

📝 Configuration & Presets

💧 6× 90° Elbows (Water) ♨️ 2× Globe Valves (Steam) 🛢️ Swing Check (Laminar Oil) 🌿 4× Branch Tees (HVAC)

🔩 Fitting Selection & Quantity

Pipe Fitting Type:

Fitting Count N:

Pipe Inner Diameter D [mm]:

⚡ Flow Conditions & Fluid Properties

Volumetric Flow Rate Q [m³/h]:

Fluid Density ρ [kg/m³]:

Dynamic Viscosity μ [Pa·s]:

Darby (2001) 3-K Method Formulation:
• Loss Coefficient: K_3K = K₁ / Re + K_∞ · (1 + K_d / D_in^0.3)
• Head Loss: h_L = K_3K · V² / (2 g) [meters per fitting]
• Total Pressure Drop: ΔP = N · ρ · g · h_L [kPa]
• Equivalent Pipe Length: L_eq = (K_3K · D / f_darcy) · N.

📊 Fitting Loss Results

📊 Output Summary
💾 Fortran Source

Total Minor Pressure Drop (1 Fittings)

4.55 kPa (0.046 bar)

Total Head Loss: 0.522 meters | Single K: 3.550

L_eq = 2.6 m

Darby 3K Loss Factor (K) 3.550 Per individual fitting

Total Equivalent Length (L_eq) 2.6 m 52 × Pipe Diameters

Pipe Flow Velocity (V) 1.70 m/s Velocity Head = 0.147 m

Flow Regime LAMINAR Re = 944

📈 Loss Factor K vs Reynolds Number Re

📉 Total Pressure Drop ΔP (kPa) vs Flow Rate Q (m³/h)

=================================================================
 THERMOFLUIDCALC — DARBY 3K PIPE FITTINGS LOSS REPORT
=================================================================
Case Title                 : Viscous Lubricating Oil Swing Check Valve
Fitting Selection          : Swing Check Valve (Full Open) (Quantity = 1)
Piping Dimensions          : ID = 50.0 mm (1.97 inches), Flow Q = 12.00 m3/h
Fluid State                : Density = 890.0 kg/m3, Viscosity = 0.08000 Pa.s
-----------------------------------------------------------------
DARBY 3K LOSS FACTOR (K)   : 3.5501 per fitting
TOTAL FITTING HEAD LOSS    : 0.522 meters (4.55 kPa)
TOTAL EQUIVALENT LENGTH    : 2.62 meters (Leq)
Pipe Flow Velocity (V)     : 1.698 m/s (Re = 944)
=================================================================

📘 Calculation Methodology & Darby 3K Standards

Darby 3K vs Classical Crane K-Factors

Classical Crane method assumes constant $K$ values for turbulent flow, causing severe underpredictions in laminar and transitional regimes. Darby 3K incorporates Reynolds scaling $K_1/Re$ and diameter scaling $K_d/D^{0.3}$.

Laminar-to-Turbulent Continuous Transition

Ensures seamless accuracy across HVAC, high-viscosity oil transfer, chemical polymer piping, and municipal potable water distribution networks.

Key Engineering Assumptions

Commercial steel absolute roughness ($\epsilon = 0.045\,\text{mm}$).
Darby (2001) empirical coefficients for standard ANSI/ASME fittings.
Swamee-Jain explicit Darcy friction factor used for equivalent length determination.

ThermoFluidCalc Engineering Report