Crane vs ISA; K velocity head coefficient eqn for contraction

[frogcurry]

ISA S75.01-1985 quotes for an inlet reducer (Eq 6, pg 15):
K1 = 0.5 * (1 - (d^2/D^2))^2

Crane 410M page 2-11, eqn 2-10 quotes

K1 = 0.5 * (1 - (d^2)/(D^2))

These would appear to be equivalent concepts but there is a difference - ISA quotes an additional squared at the end of the eqn.

So, am I confusing two different "K" factors here or is one wrong?

 

[JLSeagull]

In ANSI/ISA–75.01.01–2002 (60534-2-1 Mod) the factor includes the additional squared term.

 

[EGT01]

All the valve manufacturer's handbooks I've seen also show the inlet reducer resistance coefficient as

K = 0.5 * ( 1 - d^2/D^2)^2

but I suspose they would since they reference ISA S75.01.

I've questioned that too since it doesn't match what is presented in general fluid flow texts...
K = 0.5 * ( 1 - d^2/D^2)
and I've never seen an explanation for the discrepancy.

What you see for the outlet reducer (or rather enlargement) does match general fluid flow texts...

K = 1.0 * ( 1 - d^2/D^2)^2

So it makes one wonder if there's a typo in the ISA standard or if there is some other explanation.

I see that ISA S75.01 references
Baumann, H.D., "Effect of Pipe Reducers on Control Valve Capacity," Instruments and Control Systems, December 1968.

Maybe that's got an explanation.

 

[katmar]

One thing to take note of is that Crane Eq 2-10 is for a sudden contraction and not for a reducer.

I do not have access to the ISA document. Is there any chance that their equation is for the combined effect of the inlet and outlet reducers, or do they give separate equations for each of them? The data I have on the effect of reducers on valve sizing all take the angle of the reducer into account. Strangely this seems to be ignored by ISA.

Looking through some of the references I have here it certainly does appear that there are discrepancies in other sources as well. I will try to dig into this a bit deeper tomorrow.

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[frogcurry]

The ISA eqn quoted above is just for the inlet reducer.

 

[katmar]

I have now had a chance to look at a few more sources, and I am certain that the difference is that the Crane equation is for a sudden contraction, and the ISA equation is for tapered reducers.

There is some experimental data published in Perry (6th Ed, Table 5-13) for sudden contractions, and this agrees quite well with the Crane equation. The ISA equation gives numbers quite a bit lower than this experimental data, and of course lower than Crane. The ISA numbers correlate fairly well with my estimates for a conical reducer with a 30 degree included angle.

In a typical valve installation the pressure drop through the valve itself will be much greater than that through the attached reducers. So I would say that the ISA formula is fine for valve sizing in all but the most critical cases. The Crane formula should not be used, unless you are actually using a sudden contraction, but I have never seen a control valve installed this way.

Harvey

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[frogcurry]

After reading your last post I did some quick analysis in Excel of this using Cranes method for gradual reducers as well as sudden reduction:

const beta factor result
Crane 0.5 0.75 1 0.375
ISA 0.5 0.5625 1 0.2812
2-13 0.8 0.75 0.258 0.1552

2-13 refers to the eqn of that number in crane, assuming 30 degree slope on a reducer.

based on this, ISA seems to be using an intermediate value between the two. Varying theta I got the same value as ISA uses with the Crane eqn for gradual reductions with a theta of just under 60 degrees.

Hence the ISA method seems to be valid given this, and not too unconservative, at least when used in the specific application it was intended for. And it looks as though both are correct (and I got my equations mixed up).

 

[frogcurry]

Ahem... that theta is of course an angle of convergence in Crane, so the 60 degree theta is for a 30 degree slope on the wall.