Flow vs Kv for a Pressure Regulating Ball Valve

Are you interested in calculating flow because your professor told you to?

No, I want to understand about sizing for a control valve based on the data available from valve data sheet.

In theory, it would be fully-open Kv/95*1415. The pressure drop is the same for both cases and Kv is directly proportional to flow. You didn't give fully-open Kv.

But in practice it's more complicated. Published Kv figures are for valve in a pipe of the same size. Control valves are usually a size or 2 less than the pipe, and the Kv is multiplied by a swaging factor, typically 0.8, to account for the additional losses caused by the tapers. But 0.8 is somewhat arbitrary, and varies with valve opening, approaching 1 for small openings. When sizing a control valve I use swaging factor 0.8 for the max flow/min ΔP condition, 1 for the min flow/max ΔP condition (for safety, as that gives greatest range max Kv/min Kv, important for valve selection).

To complicate things further, if the ball valve is in a same-size pipe, when fully open the resistance is only about the same as in a pipe of same length. So depending on the system details there's likely to be more pressure drop in the rest of the system than in the valve itself.

Also there's the question of critical flow. It doesn't affect answer above as you only asked about flow at 17 bar ΔP, but if ΔP is more than about 0.5 x upstream absolute pressure, flow is sonic. You didn't give upstream pressure, but there's a good chance at 17 bar ΔP its sonic, at 1 bar ΔP its subsonic.

Thanks Codemaster for a detailed answer, GA.

I could not get term "In theory, it would be fully-open Kv/95*1415". Can you please clarify? Here, I want to give some more information.

It's a caged ball valve and fully open Kv is 1330. Pressure drop in both cases are not same, it is 17 bar and 1 bar, but weight flow rate is the same. Upstream pressure in first case is 35 barg and in second case 19 barg, so it looks the flow is not sonic. Pipe size on both side are same as valve, 6".

Your post says flow = 1415 cu.m/hr flow rate with 17 bar pressure drop, with valve Kv 95, and you want to calculate flow with fully open valve at 17 bar pressure drop.

Same pressure drop, so flow is proportional to Kv. For fully open Kv 1330, flow = 1330/95*1415 = 19800 cu.m/h. Perhaps you didn't mean that, but it's what it said.

Some more queries. Gas flow is usually stated at normal (0°C, 1 bara) or standard conditions (10, 15. 20 or 21°C depending on your taste, and 1 bara). They don't differ that much. But assuming any of them, Kv 95 for 1415 cu.m/h and 17 bar pressure drop is a long way out. I get somewhere near 95 by assuming it's actual flow at 36 bara. And you also mention weight flow.

To calculate Kv I take upstream pressure p1, downstream p2. Pressure ratio = p2/p1. Critical pressure ratio r_c = 0.528 for air. Effective pressure ratio r for formula below = r_c if p2/p1 < r_c, and = p2/p1 if p2/p1 > r_c.

Kv = Q/(p1*457)*√(T1/r/(1-r))

Q in Nm³/h, T1 upstream temperature K. This is for air, to avoid further complication.

I notice that for p1 = 36 bara, p2 = 19 bara, p2/p1 is spot on 0.528 = r_c. This is probably not a coincidence, it looks like somebody has calculated p2 at critical pressure drop.

You can work it out from that, but come back if you need more (and clarify flow basis etc). You still need to take account of my #3.

Many thanks Codemaster and GA.

I mean it (the value 19800 cu.m/hr), but it looks very high. At 43 deg valve travel it is 1415 cu.m/hr. Will the flow rate in ball valve after about half a travel can increase 14 times. I had calculated the actual flow at 35 barg pressure and 35 deg C. Nm3/hr is same in both the cases, that's why I mentioned same weight flow.

Now with your valuable comments I'm doubting whether full open Kv (1330) is right figure or not (it was taken from valve data sheet).