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) |
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.
Worked example: pump discharge header
8-in flanged discharge, 700 gpm (1.56 cfs), tank entrance to reservoir exit
In station piping, check valves and branch tees usually dominate, and elbows contribute much less than you might expect. If a header loses too much head, look first at the valve choice and the tee orientation. Minor loss scales with velocity squared, so upsizing the header from 8 to 10 inches cuts every term by more than half.
Common mistakes
- Counting the exit loss twice, or leaving it out. The exit to a reservoir loses the full velocity head (K = 1.0). If the energy equation already ends at the reservoir surface with zero velocity, that 1.0 is where the velocity head goes, so include it once.
- Using the wrong velocity for a size change. Expansion and contraction K values are based on the smaller pipe’s velocity in the table above. Some references base them on the larger pipe. Check which one the source uses.
- Using fully open values for a throttled valve. A gate valve at half open has a K about 30 times its fully open value.
- Mixing threaded and flanged values. Threaded fittings in small pipe have K values several times higher than flanged fittings of the same type.
When this card doesn’t apply
These K values assume fully turbulent flow and fittings spaced far enough apart to act independently. Fittings close together, such as two elbows in different planes, interact and can lose more than their sum. Laminar flow raises K substantially. Control valves, meters and strainers have manufacturer flow coefficients (Cv), which should be converted and used instead of a generic K.
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 the Hazen-Williams equation and its C coefficients for water distribution. For full pressurized-network or storm-system modeling with junction and structure losses, see Culvert inlet vs outlet control (48-inch CMP).