Fluid Mechanics, HVAC & Refrigeration · Minor losses
What the fittings cost
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What the fittings cost

An elbow is barely 150 mm of pipe, and it can cost more head than twenty metres of straight run. The loss is not friction along a wall; it is the swirl and separation left behind when a stream is made to change direction. Two bookkeeping systems price it, and a working engineer converts between them without thinking.

By K factor: hL=Kv22gh_L = K\,\dfrac{v^{2}}{2g}h-L equals K, v squared over two g. hLh_L is the head the fitting takes, in metres; vv is the velocity through it in m/s; gg is 9.81 m/s²; and KK is the resistance coefficient, a bare number from a table. Read it as plain English: K is how many velocity heads this fitting eats. A gate valve wide open is 0.2 of one. A standard 90° elbow is about 0.9 — near enough one whole velocity head, per elbow. A globe valve is 10, which is why nobody balances a system with one.

Fittings in series share the same velocity, so their K factors simply add: total up ΣK\Sigma K first, apply the velocity head once. Adding never averages.

By equivalent length: Leq=KDfL_{eq} = \dfrac{K D}{f}, where LeqL_{eq} is the metres of straight pipe that would lose exactly as much, DD is the bore and ff the pipe's friction factor. The conversion falls out in one line — set Kv22gK\dfrac{v^2}{2g} equal to fLDv22gf\dfrac{L}{D}\dfrac{v^2}{2g}, and the velocity head cancels off both sides. Note what survives: an equivalent length is meaningless without the bore and the f it was quoted for. The same globe valve is worth 50 m in DN100 and 25 m in DN50.

The name is a historical insult that stuck. On a short branch stiff with fittings, the minor losses routinely beat the major ones — and a pump sized on straight pipe alone will arrive, get installed, and quietly under-deliver.