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# Darby 3-K Method - K Factor for Reducers and Expanders

## Darby 3-K Method - K Factor for Reducers and Expanders

(OP)
Hi All,

I am writing this post to seek clarification on the methodology for calculating the K factor for reducers and expanders per Darby 3-K Method. Per page 194 Darby's book " Chemical Engineering Fluid Mechanics" says for fittings that involve area changes Kf value is based on the pipe size that results in larger velocity. This means that Kf is based on the smaller pipe. The statement from Page 194 is copied below.

"For sections that undergo area changes (e.g., pipe entrance, exit, expansions, or contractions), the entering and leaving velocities will be different. Because the value of the velocity used with the definition of Kf is arbitrary, it is very important to know which velocity is the reference value for a given loss coefficient. Values
of Kf are usually based on the larger velocity entering or leaving the fitting (through the smaller
cross section), but this should be verified if any doubt exists."

But on page 195 at the top of the in the Table 7.4 it says "Kf to be used with upstream velocity head,
V1^2/2. β = d/D"

Also the note at the bottom of the Table says

"Note: NRe,1 is the upstream Reynolds number, and f1 is the pipe friction factor at this Reynolds number."

Does Darby mean the smaller pipe when he says upstream velocity and that Reynolds number and pipe friction factor are based on the smaller pipe diameter?. This is my question. The Pages 191 - 196 for reference.

Thanks and Regards,
Pavan Kumar

### RE: Darby 3-K Method - K Factor for Reducers and Expanders

The highlighted note on page 194 says the larger velocity is usually used. While the header note on page 195 table 7.4 specifically refers the velocity upstream.
So there is no doubt that for a expander it is the higher upstream v to be used.
Since the wording on page 194 only says "usually", I would interpret this as being not applicable to the reducer losses on page 195

### RE: Darby 3-K Method - K Factor for Reducers and Expanders

(OP)
Hi All,

I am looking for the "Calculate Head Loss Caused by Change in Pipe Size" by Hooper W. B, Chemical Engg., 95, Pages 89-92, 1988. Darby's method of calculating the K factor for contraction and expansion is taken from this paper. If some one has access to it, it would be of great help if he/she can post it in reply to my post.

Thanks and Regards,
Pavan Kumar

### RE: Darby 3-K Method - K Factor for Reducers and Expanders

(OP)
Thank you very much pierreick. That was great help to me.

Thanks and Regards,
Pavan Kumar

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