7 replies to this topic

[robbiejustice]

Hi there,

 

I am looking at gravity flow for the attached system for the drain line from the upstream vessel (~atm pressure) to the downstream vessel (~atm pressure). For a given inlet liquid flow (say water at 15m3/h) to the upstream vessel I wish to calculate if the drain line to the downstream vessel has the capacity to prevent filling the upstream vessel above its high alarm set point. I understand this system will result in unstable flow, as described in the PD Hills article, whereby the liquid level in the upstream vessel will rise and fall as gas is entrained and then driven out by the higher liquid level.

 

My approach has been to:

 

1. Calculate the liquid height in the upstream vessel required to avoid gas entrainment based on the upstream vessel inflow (based on the equation in the PD Hills article)
2. Based on this calculate the single phase liquid flow of the drain line based on the frictional losses equal to the static head.
3. Compare flow rate calculated in part 2 to the liquid flow rate into the upstream vessel  and if the drain rate is higher then I assume that the level in the upstream vessel should not rise significantly above that calculated in part 1.

 

Does this approach seem reasonable? Perhaps there is a simpler way?

Attached Files

•  Gravity flow.pdf   10.49KB   126 downloads

[katmar]

In principle the approach seems reasonable, but I suspect that when you start applying it to some real numbers it will turn out to be a bit more complicated than that. Hills' Eq 2 will tell you that you need only 70 mm of liquid depth above the 2" outlet to ensure that no air is entrained. To drive 15 m3/h through 24 m equivalent length of 2" pipe will require around 1.9 m of head. But this head cannot be compared with the 70 mm of coverage that Hills requires because the 1.9 m could be supplied by the difference in elevation between the 2 tanks if the line runs full.

If we start off imagining the situation where tank 1 and its outlet line are empty, and the 15 m3/h starts flowing into tank 1 we can try to predict what will happen. The level in tank 1 will rise and water will start flowing into the outlet line. The outlet line was initially full of air and the first flow of water will be along the bottom of the pipe and it will run part-full. At some stage the flow of water will reach the point where it is sufficient to flush the air out of the pipe. This happens when the Froude No gets to about 0.64, or a flow rate of 3.6 m3/h in a 2" pipe.

But the head you need to drive 3.6 m3/h into the line is less than 20 mm - note that this neglects the friction along the length of the pipe because it is intially only part full and there is no friction pressure gradient. As the pipe fills with water and flushes the air out it will develop its own head which will siphon the water out of the tank. This is where it gets difficult to predict what will happen because air will be entrained and we need to be able to calculate the 2-phase friction loss in the pipe. But to do this we need to know how much air is entrained and that is close to impossible.

Depending on the geometry of the pipe between the tanks it may be that you never reach the 70 mm coverage and the pipe keeps running and entraining air, or the flow may stall at some point and require the level in tank 1 to back up a bit before the flow starts again - I have certainly witnessed this situation.

If your sketch is even vaguely to scale and you have at least 300 mm of potential level in tank 1 above the outlet, the difference in elevation between the bottom of tank 1 and the top of tank 2 is around 5 m, and you ensure that there are no high points in the line between the tanks, I would think that you would be safe at 15 m3/h in a 2" pipe.

Your 10" vapour return line looks like a bit of overkill to me, but I suppose there could be other details that you have not described because they are irrelevant to the current problem.

[robbiejustice]

Hi Katmar,

 

Thanks for having a look and apologies for the glacially slow response.

 

Based on this quote:

 

"But the head you need to drive 3.6 m3/h into the line is less than 20 mm - note that this neglects the friction along the length of the pipe because it is intially only part full and there is no friction pressure gradient."

 

Can I ask how you calculate this flow rate if you neglect friction? Could you expand on this point a little bit?

 

Yes, the 10" vapour line is sized for other reasons as there are other infrequent feeds into the vessel. 

[katmar]

The 20 mm of head is what is required to overcome the entrance losses (K = 0.5) and to accelerate the water to the flowing velocity (the kinetic energy term in the Bernoulli Equation).  This is an idealized calculation because some of this head could be supplied by the liquid in the drain pipe, so it does not necessarily mean that the level in the tank has to reach 20 mm.  It defines an edge case where we can say that once the level in the tank reaches (at most) 20 mm the flow rate out of the pipe will be enough to flush the air out of the pipe.  The difficulty is that because this 20 mm is less than the 70 mm calculated from the Hills reference, there will probably be more air being entrained into the pipe and we cannot conclude that the pipe will run full.

 

This is one of those situations that you would probably accept if it is an existing installation and you just want to know if it has a good chance of working - but if it is a new installation then you would probably not design it this way.

[samayaraj]

If your sketch is even vaguely to scale and you have at least 300 mm of potential level in tank 1 above the outlet, the difference in elevation between the bottom of tank 1 and the top of tank 2 is around 5 m, and you ensure that there are no high points in the line between the tanks, I would think that you would be safe at 15 m3/h in a 2" pipe.

 

Dear Mr. Katmar,

 

As per the attached excel I made, 2" line is sufficient for the above said query. But I have a doubt in my excel. I just applied Bernoulli equation to calculate the hydraulics (Assuming line is full of water). Is this a correct way to approach gravity flow line sizing for completely filled line? The excel I made is correct for this situation? I want you to validate this excel. I already posted this excel in this forum for validation. As you mentioned in one of the post "Understanding gravity flow is a bit like learning to ride a bike. Once you have "got" it you wonder how you ever didn't get it. But when you are starting out to learn, it seems impossible to master", I'm still trying to understand gravity flow line sizing.

 

#Samayaraj

Attached Files

•  12. New Gravity flow calculation-050315.xlsm   78.47KB   47 downloads

Edited by samayaraj, 05 March 2015 - 12:37 AM.

[samayaraj]

Dear Mr. Katmar,

 

Find attached the above said Gravity flow line sizing calculation excel without password.

 

#Samayaraj

Attached Files

•  12. New Gravity flow calculation-Sam(Unprotected).xlsm   76.05KB   66 downloads

[katmar]

Samayaraj, if you are describing a different problem from that originally presented by robbiejustice then it would be better to start a new thread.  Anyway, for now I will answer you here but remember to start a new thread in future.

I agree with your Excel calculation.  But the problem you have is not really a gravity flow problem.  You are transferring liquid from one tank to another where the available pressure difference is larger than that taken up by the pipe (when you use the 3" pipe) and the difference is taken up by a control valve which ensures that the top tank always has its outlet flooded.  This is no different from a pumping problem.  So although most of your driving force comes from gravity, it is not what is usually called a gravity flow situation.

In a typical gravity flow problem the flow rate and/or levels find their own equilibrium.  If you were to use the 2" line with no control valve that would be a gravity flow problem and in my opinion the available head and the required head are too close to each other to be able to confidently propose the 2" pipe as the solution. Particularly as you have a vacuum in the second tank you must ensure that the outlet from Tank 1 is always flooded (unless you include U-bend seal in the line between the tanks)

Edited by katmar, 06 March 2015 - 12:50 AM.

[samayaraj]

Dear Mr. Katmar,

 

You gave me a crisp & clear explanation about this topic and you didn't give me an opportunity to start a new thread in this topic! Thanks for this!!

 

Ya, sure I suppose to start a new thread, but I started here. Sorry for that!

 

 

#Samayaraj

Edited by samayaraj, 08 March 2015 - 11:09 AM.