🔨 Minor Losses in Bends & Fittings
A virtual F1-22 rig: six fittings in series — mitre, elbow, short bend, long bend, enlargement, contraction — each straddled by a manometer pair, plus a gate valve on a differential gauge. Run a range of flows, read the head drops, and extract each fitting's loss coefficient K — then see why "minor" losses are anything but minor.
Objective
To determine the loss coefficient K for a range of pipe fittings, including several bends, a contraction, an enlargement and a gate valve.
Theory
hL = K·v²/2g • same-bore fitting: hL = Δh (manometer difference) • area change: hL = Δh + (vup² − vdown²)/2g
Each fitting destroys energy in the swirl and separation its geometry provokes; the loss scales with the velocity head, and K is the constant of proportionality. Where the bore changes, part of the manometric difference is velocity-head exchange, not loss — across the enlargement the piezometric head actually rises — so the kinetic correction must be applied before computing K.
Equipment
F1-10 hydraulics bench; F1-22 energy-losses-in-bends apparatus (twelve manometers, differential gauge, air-bleed valve, flow control valve); stopwatch; clamps; thermometer.
Pipe bore d = 18.3 mm Enlargement outlet / contraction inlet d = 24.0 mm Collect ≥ 60 s per flow
Procedure — perform it here
Observations & Computations
One row per fitting per run. v refers to the 18.3 mm pipe (the reference for K). For the enlargement and contraction the kinetic correction (v₁²−v₂²)/2g is applied to the raw manometric difference before computing K; the gate valve uses the differential gauge.
| Run | Q (L/s) | Fitting | Δh raw (mm) | hL (mm) | v²/2g (mm) | K = hL/(v²/2g) | K typical |
|---|---|---|---|---|---|---|---|
| No runs yet — set a flow, collect, then Record. | |||||||
hL vs velocity head — slope = K
Discussion & Precautions
Why are “minor” losses often not minor?
In compact pipe networks — pump stations, plant rooms, building services — fittings can outnumber metres of straight pipe, and a single half-open gate valve (K ≈ 2) wastes as much head as many metres of pipe friction. The name refers to the analysis category, not the magnitude.
Why does the mitre lose more than the long bend?
The sharper the turn, the stronger the flow separation and the secondary (twin-vortex) swirl it sets up: mitre (K ≈ 1.1) > elbow (≈ 0.9) > short bend (≈ 0.75) > long-radius bend (≈ 0.45). Gradual geometry lets the flow turn with attached boundary layers.
Why does the piezometric head rise across the enlargement?
The flow decelerates into the larger bore, converting kinetic energy back to pressure (a diffuser). The rise is less than the ideal (v₁²−v₂²)/2g because Borda–Carnot separation loss eats part of it — that shortfall is exactly the hL the experiment extracts.
How does the gate valve's K change with opening?
Dramatically and non-linearly: roughly K ≈ 0.2 fully open, ≈ 0.9 at three-quarters, ≈ 2 at half, and ≈ 17 at one-quarter open — which is why throttling with a gate valve is so dissipative, and control valves exist.
Precautions: purge all air from the manometers and gauge before readings; take readings only at steady flow; apply the kinetic correction where the bore changes; collect for at least 60 s; note the water temperature.