Fittings, Valves and Minor Losses
Loss coefficients for bends, tees, entrances and valves, equivalent length, Cv and Kv, and control-valve sizing.
The loss coefficient K
Every bend, tee, valve and change of section disturbs the flow and costs pressure. These are called minor losses (they are not always minor), and are written in terms of the velocity head:
ΔP = K × ρ v² ÷ 2 hL = K v² ÷ (2 g)
The total head loss of a line is therefore hL = (f L ÷ D + ΣK) v² ÷ 2g: the pipe friction and the fittings share the same factor.
Typical K values
The values depend on the size, the radius of bends, and the maker; the tables in Crane Technical Paper 410 and Idelchik are the standard sources. For a rounded entrance (radius above about 0.15 D) K falls to 0.05 to 0.1, so a rounded inlet on a suction pipe is cheap insurance against cavitation.
Adding up the fittings
Worked example: the DN80 line with its fittings
The 100 m DN80 line carries 10 L/s at 2.10 m/s (velocity head v² ÷ 2g = 0.224 m). It has these fittings:
| Fitting | Number | K each | K total | Head loss |
|---|---|---|---|---|
| Pipe entrance, sharp-edged | 1 | 0.50 | 0.50 | 0.112 m |
| 90° elbow, standard (threaded or welded) | 4 | 0.90 | 3.60 | 0.807 m |
| Gate valve, fully open | 1 | 0.15 | 0.15 | 0.034 m |
| Swing check valve | 1 | 2.00 | 2.00 | 0.448 m |
| Tee, flow through the run | 2 | 0.60 | 1.20 | 0.269 m |
| Pipe exit into a tank | 1 | 1.00 | 1.00 | 0.224 m |
| Total | 8.45 | 1.895 m |
- ΔP for the fittings = ΣK × ρ v² ÷ 2 = 8.45 × 2 195 = 18.55 kPa.
- The 100 m of pipe lost 55.1 kPa (see Pipe Friction and the Moody Diagram), so the fittings add 33.7 percent: small here because the line is long. In a short pipe, a pump skid or a plant room, fittings often dominate.
Equivalent length
Older references give a fitting as an equivalent length of straight pipe, Le = K D ÷ f, that has the same loss. It is convenient but only holds for one pipe size and one f.
For a standard 90° elbow (K = 0.9) in the example pipe with f = 0.0196: Le ÷ D = 46 (the textbook figure for fully turbulent flow is about 30 to 40), so Le = 3.6 m of the DN80 pipe. Use K for new work, and use equivalent lengths only to read old tables.
Expansions and contractions
- Sudden expansion (Borda–Carnot): K = (1 − A₁ ÷ A₂)² based on the velocity in the smaller pipe. A pipe discharging into a tank is the limit A₂ → ∞, K = 1: all the kinetic energy is lost.
- Sudden contraction: K ≈ 0.5 (1 − A₂ ÷ A₁), on the velocity in the small pipe. A gradual cone (included angle under about 15°) cuts the loss to a few percent of v² ÷ 2g.
- Gradual expansion (a diffuser) recovers some of the kinetic energy as pressure: much better than a sudden step, but a cone wider than about 7° per side separates.
Worked example: a sudden expansion
- 20 L/s flows from a 50 mm pipe into a 100 mm pipe: v₁ = 10.19 m/s. K = (1 − (50 ÷ 100)²)² = 0.563.
- The head lost is 0.563 × 5.29 = 2.98 m. Bernoulli alone would predict the pressure to rise by 4.96 m; the real rise is only 1.98 m because of the mixing loss.
Valves: Cv and Kv
Valve makers rate a valve by a flow coefficient rather than K. Kv is the flow of water at 5 to 30 °C (m³/h) that gives a 1 bar drop through the fully open valve; Cv is the same in US gallons per minute for a 1 psi drop, and Cv = 1.156 Kv.
Q = Kv √(ΔP ÷ SG) Kv = Q ÷ √(ΔP ÷ SG)
Worked example: sizing a control valve for water
- The valve must pass 20 m³/h with about 0.5 bar across it: Kv = 20 ÷ √0.5 = 28.3 m³/h (Cv = 32.7).
- Choose a valve with a rated Kv of about 32: at 20 m³/h it drops ΔP = (Q ÷ Kv)² = 0.39 bar. Pick it so that the valve is 20 to 80 percent open at the working flow, not fully open.
- In terms of K, a 50 mm valve with that drop at 2.83 m/s has K = ΔP ÷ (ρ v² ÷ 2) = 9.8.
- A control valve needs to take a good share of the system pressure drop (valve authority above about 0.3) or it cannot control the flow: an oversize valve does nothing until it is nearly shut.
Related
- Previous: Pipe Friction and the Moody Diagram. Next: Pipe Systems: Series, Parallel and Networks.
- Pipe Flow and Pressure Drop Calculator (fittings are entered as a total K).
- Pneumatic and Hydraulic Actuators for valve types in fluid power.
- Fluid Mechanics and Pipe Flow: the whole guide.
FAQ
Are minor losses really minor?
Only in a long pipe. A line with 10 000 diameters of straight pipe has friction of f L ÷ D = 250 or more, so a few fittings with ΣK = 10 are 4 percent. In a short line, ΣK can dominate.
Which diameter do I use for K?
The one in the pipe the fitting sits in, and its velocity. For a reducer or an expansion the K value is given against the stated pipe, usually the smaller one.
What is the difference between Cv and Kv?
They are the same idea in different units: Kv in m³/h at 1 bar, Cv in US gpm at 1 psi. Cv = 1.156 Kv. Make sure you are using the right one in a catalog.
Why do check valves cost so much pressure?
The disc has to be held open by the flow against a spring or its weight, so there is a minimum pressure drop at low flow and a high K for swing types. Nozzle or silent check valves are lower in loss but cost more.
References
- Crane Co., Flow of Fluids Through Valves, Fittings and Pipe, Technical Paper No. 410.
- Idelchik, I. E., Handbook of Hydraulic Resistance, 3rd edition.
- IEC 60534-2-1 and ISA-75.01.01 (control valve sizing equations); Hydraulic Institute, Pipe Friction Manual.
Last reviewed: October 2026. K values are typical for turbulent flow: use the maker’s data for valves.