Flow Coefficient for 2 different valves installed in parallel flow paths

[MaintEngnr]

The flow coefficient can be used to calculate the predicted pressure drop across a valve. How do you predict the pressure drop if you have two valves in parallel that are both open but the valves have different flow coefficients?

 

[zdas04]

Start the flow and put in a gauge.

There is no theoretically rigorous way to calculate this simple-looking arrangement. We have to fall back to empirical equations. I've tried (several times) to iterate on the flow until the two dP's were identical to 6 decimal places and the dP I calculated was far different from reality. The empirical control valve equations (which include Cv) are a tiny step better than simply making up a number. The revisions that try to account for exit losses are a couple of little steps less robust.

The equations we use are good enough to size a valve ±20% with some windage built in. They aren't bad at predicting cavitation. Third decimal place calcs are way beyond them.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. —Galileo Galilei, Italian Physicist

 

[btrueblood]

Or use a pressure independent control valve.

 

[gerhardl]

What is the actual purpose of your excercise?

If you look at the definition of flow Q and Cv (see for instance

http://www.fnwvalve.com/FNWValve/assets/images/PDFs/FNW/tech_AboutCv.pdf

) you will remember that Cv is a measured unit, measured under a given set of conditions. Imagine now an open vessel with a filling keeping the water at a constant level = constant pressure, and this pressure equal to the required pressure for the cv measurement. With free outlet, and not connected, your two valves will then run full flow with different innards and give two different cvs'. This is your starting point.

If you now instead run theese valves in a parallell, connected to a common outlet, and over a number of other devices, restrictions and regulators, you put in a vast number of possible variations. The main variations are related to the rest of the pipeline and what happens after your two original valves. Influences are for instance the pipelines' total cpacity, resistance at different flows, outlet capacity and variations. In addition comes possible throtteling after the valves, layout where the one valve with higest afterpressure will influence flow of the other, the ratio of the one cv to the other, etc. etc.

See the mathematical difficulties?! I would go for Zdas04s' measurement solution, or at least a part test mimicking the actual connection and further throtteling, and test at a number of flow-points to get a grphic curve.

Accuracy by theoretical solution? No experience, but Zdas04 is usually correct!

 

[ione]

I think David (zdas04) has touched an important key in his previous post: the formulae which are used to express the flow coefficient of a valve (Cv for those of us who are familiar with US customary units, or Kv for those who work with SI units) are empirical and don't give exact values, but rather a guide of the “capacity” of a valve. Likewise, when you have to deal with parallel flows, you have to use an iterative calculation procedure, which can converge more or less rapidly to a value which is acceptable from an engineering point of view and for the degree of accuracy required by the specific application.

Now the OP should say whether he/she knows how to apply the iterative method in order to solve his/her configuration. Frankly this is the only way I'd go in order to make a prediction of the flows and pressure drops, without starting the flow and putting in a gauge to use David's words.

 

[curtis2004]

MaintEngnr,

I would joint GerhardL with the question: What is accrual purpose of your exercise? What is the problem and what is your trying to achieve? Can you give use a bit more information (without confidential data)?

The reason I would like more info is there are different ways to answer to your question, to solve your issue. Most likely there other people who might face your problem already, some might have even a solution.

Kurt

 

[BigInch]

The flow through each valve will be whatever it must be to result in equal pressure drops across each valve. Depending on the Cv settings of each valve (depend on open<->closed position), it might be very little flow in one valve and a lot in the other, or vice versa, however if both valves are flowing, the pressure drop across each valve will always be the same. There are nearly an infinite number of combinations of Cv values that you can make, but the only ones that really matter are full open. You automatically know you can do somewhere between 0 and the flowrate at max Cv.

Pick one Cv value for one valve, find the pressure drop for a given flow. Using the same pressure drop, find the flow possible in the other valve. Add the flows.

you must get smarter than the software you're using.

 

[katmar]

A valve's Cv may not be the most accurate parameter around, but it is the best we have got and countless installations around the world have been successfully designed using this technique. It is probably a bit unusual to have to apply it to parallel valves, but it is not difficult. Provided that the attached piping in the two parallel paths has negligible resistance then the calculation of the combined Cv is simply the sum of the individual Cvs since

Q = Cv / [&radic;](SG/[&Delta;]P) (by definition)

[&Delta;]P is the same for valves in parallel, so
Q_TOTAL = Q₁ + Q₂ = Cv₁ / [&radic;](SG/[&Delta;]P) + Cv₂ / [&radic;](SG/[&Delta;]P)

= (Cv₁ + Cv₂) / [&radic;](SG/[&Delta;]P)

and therefore Cv_COMBINED = Cv₁ + Cv₂

There was a similar discussion over Cvs in series in the thread thread378-326544 that gave a link to the formulas for series and parallel valves on the Engineering Toolbox web site. Note that the symbols used on that web site may not be familiar to some engineers, but the differences are highlighted in the referenced thread.


Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[MaintEngnr]

The reason for this exercise is that I know the pressure downstream of the valves in parallel and I was trying to estimate the pressure upstream of the valves in parallel using the dP formula. We are looking to install a check valve upstream of these valves in parallel and I was needing a pressure to help with my sizing calculations. One of the valves in parallel is a 3-inch 90 deg globe valve with a Cv = 68 and the other is a 2-inch 45 deg globe valve with a Cv = 60.

 

[BigInch]

You have the same flow in each valve, within 10%. So figure your upstream pressure using one valve, 1/2 the flowrate in the system and the average Cv and you'll be very close.

you must get smarter than the software you're using.