loss coefficients 5

1 - Determining the resistance of fittings is not an exact art. The Crane tables have been based on empirical research. But when, and how, it was done very few will know. Did they test the full range of fittings? Or did they take a few samples, and fudge the neat looking table?

The Crane "Flow of Fluids though Valves, Fittings, and Pipe" is a convenient means of approximating the equivalent resistance of the indicated fittings. The discrepancies involved probably are of a lesser order than variations due to indeterminate factors such as a degree of roughness of the pipe interior, or exact similitude of shape.

2 - A pipe bend can mean a standard 90 deg fitting, or a bend of any radius and angle made specially to suit. A 90 deg bend is very specific and excludes 45 deg, or 30 deg etc.

3 - A misconception has been more or less prevalent to the effect that all short-radius bends and fittings necessarily cause greater pressure drop than long-radius bends. Published results show that the least overall resistance is produced by bends having a radius of 1.5 to 2d do not compare unfavourably with those having a radius of 4 to 6d or greater. The agreement of nearly all observers that a curviture between 2 and 4d gives a minimum overall pressure drop is explained by the supposition that too short turns on the one extreme give excessive pressure drops, whereas on the other extreme of easy curviture the disturbance persists over a great length of travel.

4 - The Moody or Fanning Diagram relates f to the Reynolds number. So an equivalent length will automatically take into account the Reynolds number effect.

5 - Here we get into the "fiddle factor" again. The table values are an approximation. No one has tested the values for back to back fittings, or the difference between a fitting hard on the pump, compared with one further away.

The loss through all fittings can be expressed as a function of the velocity head (V^2 / 2g). The Moody or Fanning f expresses pressure loss as a function of velocity head. In some cases it is more convenient to express the values in terms of straight length of pipe - it simplifies the calculation. But either K of f will do the job. Pick the one that suits you best.

Thank you!


(1) Are the Crane tables available to the public free of charge?

(2) I realized that the first website has the same L_equiv/D as for 90 degree bends in the second website, so I'll assume that the first is for 90 deg bends only and not pipe bends in general. According to Thrusterman's reference, K increases with increasing angle from 0 to 180 deg.

(3) I see now that there is an optimum bend radius (2-4 D) for a minimal pressure drop. I am confused, though, by the arguments at the "short" and "long" extremes. Isn't the bend radius different from the bend angle? A large angle (e.g., 150 deg) pipe could have a small radius (i.e., sharp corner).

(4) The second website has a table of standard friction factors depending on only pipe diameter. I guess the actual length of each fitting and the fluid kinematic viscosity are standard so that the diameter determines the velocity.

The Crane TP-410 has for many years been available for purchase, and my guess is that it remains so. (So many people have been willing to purchase it; why should they give it away?).

Mine is pre-internet, so you might check to see if some data is published somewhere.

Technical Paper No. 410 "FLOW OF FLUIDS through Valves, Fittings and Pipe", Crane Co. 757 Third Ave. NY, NY 10017

As usual the question you have to ask is "how accurate do you need to be?" In my experience, and this is backed up by most references that I've seen, the so-called "minor losses", the subject of our discussion here, are a small percentage of the loss across the straight pipe on MOST practical systems. Of course there are exceptions, and I've been up against them too.

I have usually found (the hard way) that, as a practicing grunt engineer and not a lab researcher, my time and effort expended to try and account for these differences between, say, a SR ell and a LR ell, or a 5d field bend, did not pay out in the big picture of the project as far as making the difference in cost savings by going to a smaller pump or a different line size. Same for NPSHa calculations for a pump. Note this is NOT the same issue as accounting for the difference between a full-port and a reduced port ball valve, for example.

Most of the time your delta P, velocity, and rate calcs are likely only good to ±80% anyway because you have no way to address the unknowns, your fluid properties are not that exact, etc.

I used to lose a lot of sleep over this very issue in the past, but not anymore. It just has not proven to be that necessary. Yet. Now, having said that, the obsessive-compulsive in me wants to see that all-inclusive, divinely-inspired, omnipotent pipe-fitting-and-valve K-factor chart so I can fix my spreadsheet once and for all... ;-) Thanks!
Pete