Minor losses through elbows, tees, and valves by the ΣK excess-head method — the companion to straight-pipe friction.
ΔP = ΣK · ρv²/2; h = ΣK · v²/2g
How it works
Every elbow, tee, and valve dissipates a multiple K of the flowing velocity head. Count the fittings, sum their K values, and multiply by the dynamic pressure ρv²/2 — that's the minor-loss share of the line's pressure drop, added to the straight-pipe friction.
Worked example
50 m³/h of water in a 100 mm line through 4 elbows, 2 gate valves, and a globe valve. ΣK ≈ 9.3 costs ≈ 14.6 kPa — and the single globe valve contributes almost two-thirds of it.
Why is a globe valve so much worse than a gate valve?
A gate valve opens to nearly a full bore (K ≈ 0.17), while a globe valve forces the flow through two right-angle turns even when fully open (K ≈ 6). That's why globe valves throttle well and gate valves isolate well.
When is the K-factor method not good enough?
At low Reynolds numbers (viscous liquids, small pipe) K rises well above the turbulent value, and small fittings differ from large ones. The 2-K (Hooper) and 3-K (Darby) correlations capture both effects.
How do I combine this with straight-pipe friction?
Compute the straight-pipe ΔP with the Pipe Pressure Drop tool and add this fittings ΔP. Equivalently, some designers convert ΣK to an equivalent length L_eq = ΣK·D/f and add it to the pipe length.
Assumptions
Fully turbulent flow — K taken constant. At low Reynolds numbers K rises and the 2-K/3-K methods should be used.
Typical screwed/welded fitting values; actual valves vary by pattern and manufacturer — use vendor Cv/K data where it matters.
Add this ΔP to the straight-pipe friction from the Pipe Pressure Drop tool for the total line loss.
References
Hooper, W.B. (1981), 'The two-K method predicts head losses in pipe fittings', Chemical Engineering, 88(17).
Darby, R., Chemical Engineering Fluid Mechanics — 3-K method and typical loss coefficients.
Related Fluid Mechanics tools
Pipe Pressure Drop — Frictional ΔP and head loss for single-phase flow in a circular pipe (Darcy–Weisbach, Swamee–Jain friction factor).
Pipe Velocity & Reynolds — Line velocity, Reynolds number, and flow regime from flow rate and pipe inside diameter.
Friction Factor (Moody) — Darcy (and Fanning) friction factor from Reynolds number and relative roughness — Colebrook–White solved exactly, with the Swamee–Jain explicit fit for comparison.
Pipe Line Sizing (velocity) — Required pipe bore for a target line velocity, with the resulting velocity and typical service velocity guidance.