When is Darby 3-K better than Crane L/D?

When Re < 2000 (laminar / viscous fluids) or when you need size-dependent turbulent K. Crane TP-410 L/D is a turbulent-flow screening shortcut.

How is L_eq related to K?

FEK converts with L_eq = K·D_i/f_T using Crane’s fully turbulent friction factor so lengths compare with TP-410 tables.

What do K₁, Kᵢ, and K_d mean?

K₁ scales the laminar term K₁/Re; Kᵢ is the turbulent asymptote; K_d scales the diameter correction (1 + K_d/D_in^0.3).

Darby 3-K Fitting Loss Calculator (Laminar & Turbulent K-Factor)

K = K_{1} / R e + K_{i} (1 + K_{d} / D_{in}^{0.3}), L_{e q} = K \cdot D_{i} / f_{T}

Darby 3-K / Crane TP-410

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1. Formula & conversion factors

Ron Darby — Chemical Engineering Fluid Mechanics (3-K method) · Crane Technical Paper No. 410 — Flow of Fluids Through Valves, Fittings, and Pipe · ASME B36.10M / B36.19M — Pipe inside diameter

K = K₁Re + K_i · (1 + K_dD_in^0.3)

L_eq = K · D_if_T

Darby 3-K · Crane TP-410 f_T for L_eq · ASME B36 D_i

Hero K · L_eqK₁/Re Laminar termKᵢ Turbulent asymptoteL_eq K·D_i/f_T

Resistance coefficient from Darby 3-K constants (K₁, Kᵢ, K_d) with pipe Reynolds number and internal diameter in inches. Equivalent length uses Crane fully turbulent f_T so L_eq compares with TP-410 L/D screening. Prefer Darby 3-K when Re < 2000 (laminar / high viscosity).

K (Resistance coefficient) — Darby 3-K loss coefficient for the fitting (total = per-fitting × quantity).

K₁ (Laminar constant) — Low-Reynolds fitting constant in the K₁/Re term.

Kᵢ (Turbulent constant) — High-Reynolds asymptotic constant (K_∞).

K_d (Diameter scale factor) — Pipe-size scale constant in the (1 + K_d/D_in^0.3) term.

Re (Reynolds number) — Pipe Reynolds number Re = ρ v D_i / μ.

L_eq (Equivalent length) — Straight-pipe length with the same loss at Crane f_T: L_eq = K·D_i/f_T.

2. Quick reference lookup table

Default screening duty (NPS 2 Sch 40 · 90° std elbow · Re 50,000)
Quantity	Value	Unit	Notes
D_i	52.51	mm	B36 Sch 40
K₁ · Kᵢ · K_d	800 · 0.09 · 4.0	—	Darby 3-K
K	≈ 0.396	—	Re = 50,000
L_eq	≈ 1.09	m	via Crane f_T
Regime	Turbulent	—	Re > 4000

Hero K follows Darby 3-K physics. L_eq uses Crane f_T so lengths compare with TP-410 L/D tables.

3. How to use this calculator

Select NPS and schedule

Fixes ASME B36 inside diameter D_i and Crane f_T for L_eq.

Choose fitting type

Loads Darby constants K₁, Kᵢ, and K_d for the fitting or valve.

Enter Reynolds number and quantity

Re sets laminar vs turbulent weighting; quantity scales total K and L_eq.

Read K, L_eq, and Crane comparison

Hero shows K and L_eq; rows split laminar/turbulent parts and Crane K = f_T·(L/D).

4. Engineering FAQ

A tool that estimates fitting resistance coefficient K and equivalent length L_eq using Darby’s 3-K constants across laminar, transition, and turbulent Reynolds numbers.