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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2 Inch Schedule 40 specification summary

Pre-seeded geometry for this programmatic URL. Adjust inputs in the calculator to recalculate; primary selections update the clean path for sharing and indexing.

Parameter	Value
Nominal pipe size (NPS)	2"
Schedule	Sch 40
Outside diameter (OD)	60.33 mm (2.375 in)
Wall thickness (t)	3.91 mm
Inside diameter (ID)	52.51 mm

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.