Duct Elbow Loss Coefficient

Idelchik Diagram 6.1 — Co values and how they're calculated.

Skip ahead: estimate elbow losses with the free duct static pressure calculator — it computes round and rectangular elbow losses using its implemented coefficient model. Check geometry and source limits before using the result.

What the loss coefficient means

The pressure drop through a duct elbow is the product of a dimensionless loss coefficient Co and the velocity pressure Pv at the elbow inlet:

ΔP = Co × Pv

For a smooth-radius elbow, DuctStatic computes Co = A1 × B1 × C1 (round) or Co = A1 × B1 × C1 × kRe (rectangular), following Idelchik Handbook of Hydraulic Resistance.

Curvature correction B1 — round & rectangular (Idelchik 6.1)

B1 scales Co with the centerline radius to diameter ratio R/D. Tighter elbows cost far more:

R/D	0.5	0.75	1.0	1.25	1.5	2.0	4.0
B1	1.18	0.51	0.21	0.19	0.17	0.15	0.11

R/D = 1.0 is the HVAC default. Going from R/D 0.5 → 1.0 cuts the coefficient roughly 80%.

Angle correction A1 (Kθ)

Co is calibrated for a 90° bend; other angles scale it:

Bend angle	45°	70°	90°	135°	180°
A1	0.64	0.85	1.00	1.22	1.40

Aspect ratio correction C1 — rectangular only

Square/round ducts take C1 = 1.0. Rectangular elbows use the ratio of height to width in the bend plane:

a₀/b₀	0.25	0.5	1.0	2.0	4.0	6.0
C1	1.30	1.17	1.00	0.85	0.90	0.98

Rectangular Reynolds correction kRe

Idelchik applies a Reynolds-number correction for rectangular duct. At typical HVAC flows (Re 30k–80k), kRe ≈ 1.4–1.6 — significant. This is why the same R/D costs more in rectangular than round duct.

Worked example — 90° round elbow

Shown in the default English view; the header toggle switches the display to SI (m/s, Pa).

A 90° round elbow, R/D = 1.0, at 1,500 FPM. Velocity pressure Pv ≈ 0.14 in w.g. Co = 1.0 × 0.21 × 1.0 = 0.21. Pressure drop ≈ 0.21 × 0.14 = 0.03 in w.g.

Try it: build a fan-and-elbow system in the calculator and watch the per-segment elbow loss update live as you change R/D and velocity.