Flowrate through proportional control valve. 1

[456LachTray]

Hi everyone,

At our laboratory we are using two proportional valves of type 2836 to control a level control system. I would like to know the formula computing flow rate through those valves. Is the formula Q = K*u*sqrt(deltaP) correct? (where K is a constant, u is valve opening and delta P is pressure drop across valve) .

I just want to verify the correctness of this formula. In order to identify the constant K, I conducted some simple experiments by fixing the inlet flowrate to a tank . Water is drained out of this tank through one valve and voltage applied to the valve coil is varied. Afterwards, corresponding equilibrium tank levels were measured and converted to corresponding delta_P values. If the formula mentioned above is correct, the product u*sqrt(delta_P) should be constant. However, experimental results showed that this was not the case and I suspect I am using a wrong formula.
Can anyone give me the correct formula? Or, if the formula is correct, what could be a reasonable reason for what I observed?

Thanks in advance,

 

[mbt22]

K is the total resistance of the system. If you are varying the valve position, you are varying K. Your experiment is effectively determining the valve curve.

Matt

 

[456LachTray]

Hi Matt,
So, am I using right formula and only correction should be K as a function of u?
Do you mean inherent characteristic or installed characteristic curve by 'valve curve'?

Thanks,

Viet

 

[Latexman]

Control valves are usually characterized with a C_V value at full open. Vendors usually have data on C_V vs. % open or degrees open (0 to 90 degrees for a quarter turn valve). The classic equation in U.S. units is:

[Δ]P = (Q/C_V)²[ρ]/62.4

A C_V of 1 means the valve will flow 1 gpm of water at 1 psi differential.

Many references contain this information. I prefer Crane Technical Paper No. 410

To convert C_V to k use:

k = 891d⁴/(C_V)²

Q (gpm), [ρ] (lb/ft³), d (inches), [Δ]P (psi)


Good luck,
Latexman

 

[456LachTray]

Hi Latexman,

Following your suggestion, I found from my vendor data on Cv vs. %open as you can see here (page 2/4):

http://www.buerkert.de/products_data/datasheets/DS2836-Standard-EU-EN.pdf.

Actually the characteristics curve of valves are shown. And it in fact shows relationship between Kv/Kvs and %open.

But I can't really interpret it. Does it show the relation between Kv/Kvs and %open for a constant ΔP and slope of the curve may be different for different ΔP?

Thanks,

Viet

 

[Latexman]

They are using the same equation; just different units and different symbology (Kv vs. Cv)

I do not know how they ran their experiment and collected the data. For each % open data point, they would need the flow, pressure drop, and density to calculate the corresponding Kv.

Good luck,
Latexman