Pipe fitting K factors (minor loss coefficients)

Every row above is read from src/lib/fittings.ts, the same array the Studio's fitting dropdown and the solver's minor-loss element read. The K stays editable in the app: selecting a fitting fills the coefficient, it does not lock it.

How to read the source column

The source string is carried on each entry as data, not written here as commentary, so it moves with the value.

• Crane TP-410. Crane Co., Technical Paper No. 410: Flow of Fluids Through Valves, Fittings and Pipe, the standard industrial reference for fitting resistance. The bulk of the library.
• Crane TP-410, and GFSSP opt.13. The same Crane value, which NASA's GFSSP also carries in its common-fittings option (documented in NASA/TP-2016-218218). Worth saying plainly: GFSSP's fitting table shares Crane's lineage, so seeing a value in both is corroboration by a validated code rather than an independent second measurement. We have not treated it as independence.
• ASHRAE. Loss data for ductwork components, from the ASHRAE Handbook, Fundamentals volume.
• Manufacturer typical. No standard tabulates these. They are representative of published manufacturer data for a clean component and are the least certain rows in the library. Treat them as a starting point and use the vendor's own figure for the item you are actually buying.

Where a value is a wide range across sources rather than a firm handbook number, the entry name says so. The strainer rows are the clearest case: a clean Y-strainer sits near the value listed, and a partly blinded one is several times worse, so the tabulated number describes the day it was commissioned and not the day it starts giving trouble.

Why one fitting does not have one K

Three things move a real coefficient away from a tabulated one, and it is worth knowing which is biting before you argue about the second decimal place.

Size. Crane expresses many valve and fitting coefficients as a multiple of the fully turbulent friction factor of the attached line size, and that friction factor falls as the pipe gets larger, so the same valve type has a lower K in a big line than a small one. You can see the effect directly in the table above: the library carries three separate butterfly-valve rows, for DN50 to DN150, DN200 to DN350, and DN400 and above, and the coefficient falls by more than half across that span. Where a fitting has only one row, that row is the value for a representative size.

Reynolds number. Tabulated coefficients are fully turbulent values. Below roughly a Reynolds number of a few thousand through the fitting, the true coefficient climbs steeply, so a single turbulent K understates the loss for viscous oils, cold glycol and small-bore laminar lines. The published refinements for this are the two-K method of Hooper and the three-K method of Darby, which add a Reynolds-dependent and a size-dependent term. Fluid Network Studio uses a fixed K, so on a laminar fitting-heavy circuit treat the fitting losses as optimistic and check whether they matter to your answer at all.

Geometry. Contraction, enlargement and orifice coefficients depend on the bore ratio, and the single number in the table is only representative of one arrangement. Do not size an orifice plate from the tabulated value. The Studio has parameterised contraction, expansion and orifice elements that compute the coefficient from the actual bore ratio, and those are the ones to use once the geometry is known.

Turning a manufacturer's figure into K

A datasheet almost never gives you K. It gives a flow coefficient or a pressure drop at a rated flow. Both convert exactly, and the library carries both conversions as functions so the arithmetic is done once and tested.

From a metric flow coefficient Kv, in cubic metres per hour of water at one bar of drop, with the attached bore D in metres:

K = 1.6e9 * D^4 / Kv^2

The US flow coefficient Cv, in gpm at one psi, converts as Cv = 1.156 Kv, so a Cv goes through the same relation once divided by 1.156.

From a rated pressure drop dp at a rated volumetric flow Q, with A = pi D^2 / 4 the attached bore area and rho the density at which the rating was taken:

K = 2 * dp * A^2 / (rho * Q^2)

That second form is the honest way to model a heat exchanger, a filter, a package skid or any other lump of equipment the vendor has characterised by a single duty point. Note the strong dependence on D in the first relation: a fourth power means that using the valve's own bore where the line is one size larger, or the reverse, is a factor of two error rather than a rounding error.

Equivalent length, and why we do not publish it

Many older references give minor losses as an equivalent length of straight pipe rather than as K. The two are related by

L_e = K D / f

where f is the Darcy friction factor of the pipe the fitting is fitted to. The friction factor is in that relation, which is the problem: an equivalent length is only valid for the roughness, diameter and flow regime it was worked out for, and it silently changes when any of those change. K does not, so K is what the library holds and what the solver uses. If you need an equivalent length for a hand check, take K from the table and divide by the friction factor you are actually working at rather than borrowing a length from another table.

Frequently asked questions

What is the K value for a 90 degree elbow?

A standard-radius threaded or welded 90 degree elbow is usually taken as 0.9, a long-radius bend as 0.6, and a threaded elbow in small bore as high as 1.5. Those are the values in the table above, from Crane TP-410. The spread between them is larger than most people expect, so the elbow type is worth getting right on a circuit with many bends.

Do I add fitting losses to the pipe friction, or are they already included?

You add them. Pipe friction covers the straight run only. The usual practice is to sum the K values on a run and apply them to the velocity head of that run, which is exactly what Fluid Network Studio does when you attach fittings to a pipe. Adding a nominal percentage to the friction loss instead is a rule of thumb that fails badly on short, fitting-dense runs such as pump suction and pump discharge manifolds.

Which velocity does K use?

The velocity in the pipe the coefficient is referred to, which for a constant-bore fitting is simply the line velocity. For contractions and enlargements, Crane refers the coefficient to the smaller bore. Getting this wrong is the single most common error with minor losses, because the velocity is squared.

Can I use these K values for air and other gases?

Yes, with one caveat. K is defined on a velocity head, so it is fluid-agnostic and the same coefficients serve liquids, gases and homogeneous non-Newtonian fluids, including circular ducts. The caveat is compressibility: in a gas line the density and therefore the velocity change along the run, so the velocity head at the fitting is not the one at the compressor. Fluid Network Studio evaluates it at the local condition in the compressible solve.

How accurate are tabulated K values?

It depends on the row. For firm handbook items such as elbows, tees, gate valves and globe valves, published sources agree closely and the tabulated value is a sound working number for a well-installed fitting at fully turbulent flow. For strainers, wafer checks, laterals and anything marked as a manufacturer typical, published values disagree by a factor of two or more, and the entry is a starting point rather than a design value. In most systems the fitting losses are a modest share of the total, so this uncertainty rarely decides a pipe size, but on a short pump-suction line it can decide whether the pump cavitates.

References

• Crane Co., Technical Paper No. 410: Flow of Fluids Through Valves, Fittings and Pipe. The source of most of the coefficients above. tp410.com
• Majumdar, A. et al., NASA/TP-2016-218218, documenting GFSSP and its common-fittings resistance option, which corroborates the Crane values marked above. ntrs.nasa.gov
• ASHRAE Handbook, Fundamentals, for the duct fitting and damper coefficients.

Related

• Absolute pipe roughness values by material, for the other half of a pressure-drop calculation.
• Pipe schedule dimensions, for the bore the velocity head is referred to.
• Orifice plate loss coefficient calculator, which computes K from the bore ratio rather than reading it from a table.
• Pipe flow and pressure drop calculator and the supply line with a fitting worked example.
• Open the Studio to attach fittings to a real network and see what they cost you.