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Minor Loss Coefficients (K) — Reference

Localized losses from fittings, valves, bends, entrances and exits, by the velocity-head method: hL = K·V²/(2g), with V the mean pipe velocity. Values are typical for fully-turbulent flow; K varies with size, Reynolds number, and manufacturer — use Crane TP-410 or vendor data for final design.

Entrances & Exits

ComponentK
Re-entrant / projecting pipe entrance0.8–1.0
Sharp-edged (flush) entrance0.5
Slightly rounded entrance (r/D ≈ 0.1)0.2–0.25
Well-rounded entrance (r/D ≥ 0.15)0.04–0.05
Exit (pipe → reservoir), any shape1.0

Bends & Elbows

ComponentThreadedFlanged
90° elbow, regular (standard)0.90.3
90° elbow, long radius0.60.2
45° elbow, regular0.40.2
180° return bend1.50.2
90° bend, smooth (r/D = 4–6)0.15–0.30
Mitered bend, 90° (no vanes)1.1–1.3

Tees

ComponentThreadedFlanged
Tee, line (run-through) flow0.90.2
Tee, branch flow2.01.0

Valves (Fully Open)

Valve typeK
Ball valve, full bore0.05
Gate valve0.15–0.2
Butterfly valve0.3–1.2
Swing check valve2.0–2.5
Angle valve2–5
Globe valve6–10
Foot valve with strainer (hinged)0.8–1.5

Gate valves throttle steeply: ¾ open ≈ K 1.0–1.2, ½ open ≈ 5.6, ¼ open ≈ 17+. Always design for the fully-open value unless throttling is intended.

Sudden Expansion & Contraction

ComponentK (based on smaller-pipe velocity)
Sudden expansionK = (1 − A1/A2)²   = (1 − (d1/d2)²)²
Sudden contractionK ≈ 0.5(1 − A2/A1)   (0 for no change, 0.5 for exit into pipe)
Combine with friction loss. Total head loss over a run is h = (ΣK + f·L/D)·V²/(2g). For long pipelines, minor losses are often negligible; for short runs with many fittings they can dominate. Equivalent-length alternative: Leq = K·D/f added to the pipe length.

Sources: Crane Co. Flow of Fluids Through Valves, Fittings, and Pipe (Technical Paper 410). Munson et al., Fundamentals of Fluid Mechanics, Table 8.2. Values are representative; manufacturer/size variation is significant for valves.

Computing pipe head loss? Open the Darcy-Weisbach calculator → · Water main? Use Hazen-Williams.

Related cheat sheets and tools

Pair these K values with pipe friction from the absolute roughness (ε) card and the Darcy-Weisbach tool, or with Hazen-Williams C for water distribution. For full pressurized-network or storm-system modeling with junction and structure losses, see HydroComplete.

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