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
| Component | K |
| Re-entrant / projecting pipe entrance | 0.8–1.0 |
| Sharp-edged (flush) entrance | 0.5 |
| 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 shape | 1.0 |
Bends & Elbows
| Component | Threaded | Flanged |
| 90° elbow, regular (standard) | 0.9 | 0.3 |
| 90° elbow, long radius | 0.6 | 0.2 |
| 45° elbow, regular | 0.4 | 0.2 |
| 180° return bend | 1.5 | 0.2 |
| 90° bend, smooth (r/D = 4–6) | 0.15–0.30 |
| Mitered bend, 90° (no vanes) | 1.1–1.3 |
Tees
| Component | Threaded | Flanged |
| Tee, line (run-through) flow | 0.9 | 0.2 |
| Tee, branch flow | 2.0 | 1.0 |
Valves (Fully Open)
| Valve type | K |
| Ball valve, full bore | 0.05 |
| Gate valve | 0.15–0.2 |
| Butterfly valve | 0.3–1.2 |
| Swing check valve | 2.0–2.5 |
| Angle valve | 2–5 |
| Globe valve | 6–10 |
| 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
| Component | K (based on smaller-pipe velocity) |
| Sudden expansion | K = (1 − A1/A2)² = (1 − (d1/d2)²)² |
| Sudden contraction | K ≈ 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.