Overflow box pipe sizing

[Magos]

Hello,
I was hoping I could get some feedback on the design of an overflow box. In particular, I want to make sure that I'm sizing the pipe correctly. I have attached a diagram with the relevant dimensions.
In short, there is a water flow of Q=36 m[sup]3[/sup]/h incoming over a weir and I must size the pipe so that the water doesn't accumulate in the box. Additionally, splashing outside the box should be kept to a minimum. The bottom end of the pipe is expected to connect to a much larger pipe that isn't expected to fill up.
After reading threads on this and other forums, the correct approach seems to be the one described in "Designing Piping for Gravity Flow" by P.D. Hills. In particular, the case I'm looking for would be "Self-Venting Flow in vertical Pipes".
Based on this, using a pipe with an inner diameter D=180 mm would result J[sub]L[/sub]*=0.296 which satisfies J[sub]L[/sub]*<0.3 (Equation 6). With this, would it be correct to assume that all incoming liquid will be drained properly, without surging? Does the length of the pipe (H2 in the diagram) matter at all for this scenario?

Another approach to this problem would be to apply the Bernoulli equation covering the height of the box plus the height of the pipe (H1+H2). This would of course include the losses due to friction and the box to pipe transition. If we assume that the bottom of the vertical pipe is exposed to atmospheric pressure (Since the much larger pipe it connects to is never full) then a pipe diameter can be calculated so that the water exits the box at the same rate that it enters it. Would it then be correct to assume that any pipe larger than that would ensure that the box doesn't fill up to H1?

I would greatly appreciate any insight you may have on how to approach this case. It's been a while since I last did fluid mechanics in college and one thing they really drilled into us is to be careful with the assumptions we make.

Also forgive me if the phrasing is awkward. I'm not a native English speaker.

 

[LittleInch]

Try reading this post which also has some good links.

https://www.eng-tips.com/viewthread.cfm?qid=409750

But don't undersize this. There is a lot of info about sizing of gravity drain pipes.

Forget Bernoulli.

Basic sizing is to use a CSA of 7/24 at about 3m/sec to get max capacity of a vertical pipe with no choking or slugging.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[pierreick]

Hi Magos,
Your calculation is correct, you may consider some safety margin.
Cheers
Pierre

 

[katmar]

It is important to note that the criterion of Fr<0.3 is applicable to vertical downflow pipes where the base of the pipe is sealed or flooded. If you have a meter or 2 of flooded piping at the base it will enable any entrained vapor to disengage and be vented upwards against the liquid flowing downwards.

If the vertical downflow pipe is discharging directly into the vapor space of a partially filled larger pipe then the vapor that is entrained by the falling liquid will be carried with the liquid and be discharged into the larger pipe. This is similar to the functioning of a downpipe from a rain gutter from a roof. Basing the drain size on the Fr<0.3 criterion will still result in a working design but you should be aware that some vapor will be carried with the draining liquid. If you want to prevent any vapor from being carried with the liquid you can install a U-seal in the drain before it enters the larger pipe - See Hills figure 1.

Your dimension H2 is not critical, but as stated above you need some flooded length if you want the vapor to disengage from the liquid.

A velocity of 3 m/s is far too high for a drain pipe. Bernoulli and even Darcy-Weisbach are not of much help when the pipe is not running full.

I agree that you should include a bit of a safety factor to cope with process variations. Usually using the next standard pipe size above the calculated diameter is enough.

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[LittleInch]

The 3m/ sec bit was for very long vertical pipes down mine shafts... So h2 does matter a bit.

Too big and you will end up with laminar flow on the inside of the pipe.

It also might work if you step the pipe down so you start bigger then reduce it in stages. This would reduce splashing or any occasional back flow of air.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[Magos]

Thank you all very much for your replies!

Little Inch - Thank you for the link. The thread was illuminating. I thought I had exhausted all keywords when googling this topic but I guess I didn't.

Katmar - I understand now that what I'm doing here doesn't really fit with what's described in Hill's article.

Both of you mention a speed of 3 m/s. Where does that value come from?

Thank you

 

[LittleInch]

I think it's in that post I linked to which is one of my archived posts and is terminal velocity inside a vertical pipe when it's not full of liquid. I think.

The 7/24 th full is only useful if you know the velocity.

See this one as well

https://www.eng-tips.com/viewthread.cfm?qid=439424

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[katmar]

Here is a completely theoretical solution that might work, but which I would not implement myself or recommend to others.

If you were to size a vertical drain such that the friction exactly matched the static head available, for a flow of 36 m3/h you would need a diameter of only 45 mm with a velocity of 6.5 m/s. According to Hills equation (2) you would need a level in the overflow box of about 110 mm to keep the pipe flooded. This would work provided that the flow remained constant at 36 m3/h but if it increased above this level the box would quickly get to an overflowing situation.

One might then be tempted to install a 100 mm drain pipe to give a bit of a safety factor. I have seen drains (with a sealed base) accidentally designed to operate in this regime. What happens is that the drain is initially able to cope with the flow but the high liquid velocity entrains air and this chokes the pipe and the flow decreases significantly. This causes the overflow box level to increase and this extra head gets the flow going again and the box will drain and then start entraining air again. You can see this gets into a cyclical operation and is sort of what Hills illustrates in Figure 1 - but without the side pipe introducing air. Provided the depth of the box is sufficient to prevent overflowing during the low-flow portion of the cycle this can be a safe way to operate, but it is very difficult to predict what the maximum level will be in the box. Although some drains have worked successfully for years in this cyclical manner, I have also seen a very expensive accident caused by this behavior.

In my own work I have always stuck to the Fr < 0.3 rule and the drains have worked, although I have had people comment that they seemed larger than required. The fact that you spent a few extra bucks on the larger pipe will soon be forgotten, but if you go with the smaller pipe that overflows and showers the people from time to time you will be remembered forever.

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[georgeverghese]

You've got the additional liquid height above the weir as it spills over, if this matters to you. The narrower the weir, the greater this height will be - see expression 6-58 in the 7th edn of Perry Chem Engg Handbook for total developed liquid height H.
Slope the drain line downward continuously. You will be pulling in some air also through this drain nozzle nevertheless since it is not adequately submerged in liquid, even if you operate at a superficial Nfr < 0.3.