8 replies to this topic

[sang]

Hello all

I have searched the forums for this and while there are lots of postings (especially by Art), I couldn’t find any that would directly help me solve my problem. Hence, the post.

We have a vessel (open to atmosphere) which is used to throw seawater (at 25°C) overboard to the sea via a pipe from vessel bottom. The only driving force available is the static head which is about 10 m (ignoring the change in the level in the vessel which is relatively smaller). The equivalent length of the pipe is 100 m. I need to size the pipe so that the pipe runs full of water. I understand that for the pipe to run water full, or for 'self-venting' flow, the Froude number, v/(gD)^0.5 < 0.3, where

v = velocity, m/s;
g = 9.81 m/s² and
D = pipe ID , m

The way I am trying to do this, is as follows:

• Assume a pipe size
• Calculate the maximum flow possible with static head as the only available driving force (corresponding to 0.1 bar approx.)
• Use the velocity in the pipe obtained in Step 2 and the assumed size to calculate the Froude number. If it is less than 0.3 then the line size is adequate, else increase the line size and repeat the above steps.

• 
  The problem with the above is that as I increase the assumed line size, the calculated Froude number also goes up. Hence, there is no solution to the problem.
  
  For example: for a 4” Schedule 40 pipe (102.3 mm ID), maximum flow possible is 99.6 m³/hr. The velocity is 3.37 m/s and the Froude number is 3.36.
  
  For a 8” Schedule 40 pipe (202.7 mm ID) maximum possible flow is 600 m3/hr. The velocity is 5.16 m/s and the Froude number is 3.65.
  
  I have assumed a density of 1,000 kg/m3 and viscosity of 1 cP for the above calculations. Moody friction factor of 0.015 has been used.
  
  So it can be seen that the Froude number is increasing with size and there is no solution using this method.
  
  My questions thus are:
  
  a) Is my method correct? If yes then where is the mistake I am making?
  
  b) If the method is incorrect how can the line be sized?
  
  As a corollary, had this been a vertical pipe, the equivalent length being 10 m (assuming no fittings), the maximum possible flow in an 8" pipe is calculated to be 1,933 m3/hr !! Does this make sense? What would happen in a real life situation?
  
  Thanks and Regards
  Sanjay

[katmar]

The criterion of F_r < 0.3 is applicable to vertical pipes and I guess if you have an equivalent length of 100 m and a static height of 10 m then your pipe is not vertical. Designing for a self venting requirement in a pipe with horizontal sections is a serious challenge. It can be done, but it is better avoided.

If a vertical pipe is sized for self venting flow then the pipe will definitely not run full, so you cannot use the Darcy-Weisbach formula to calculate the pressure drop. In self venting flow the pressure drop is irrelevant because it is less than the change in height.

If you control your flow rates to the values you calculated then the pipe will run full. But in real life you would have a conflict with the other process parameters such as the flow rate into the vessel and any requirement for level control in the vessel - so you could not control the flow rate at that rate continuously.

The most frequent scenario is that you calculate the maximum rate of draining that you will require (probably based on the inflow rate) and then size a drain pipe to cope with that flow rate with the head available. This could be designed as a self venting pipe, and it would probably be best to do it that way because you will most likely get water hammer if the tank outlet valve closes with a non-self venting drain.

[sang]

Hi Katmar

Thanks for the detailed response. Obviously my understanding of self venting flow and sizing such lines is quite limited.

You say:


"If a vertical pipe is sized for self venting flow then the pipe will definitely not run full, so you cannot use the Darcy-Weisbach formula to calculate the pressure drop. In self venting flow the pressure drop is irrelevant because it is less than the change in height."

Could you please explain this further? Why will the pipe not run full? If the pressure drop is irrelevant then how do you calculate flow in a vertical pipe?

Further, you say:

"The most frequent scenario is that you calculate the maximum rate of draining that you will require (probably based on the inflow rate) and then size a drain pipe to cope with that flow rate with the head available. This could be designed as a self venting pipe, and it would probably be best to do it that way because you will most likely get water hammer if the tank outlet valve closes with a non-self venting drain."


This is where my confusion is. The inflow rate is relatively small and maximum flow possible through even a 2" pipe exceeds that due to the large available head (Please note that now I'm talking about my non-vertical line) In this case how do you size the line? Wouldn't the pipe 'tend' to flow more than the inflow rate leading to vapour 'sucking' - hope I'm expressing myself clearly?

Could you also please explain why "you will most likely get water hammer if the tank outlet valve closes with a non-self venting drain." ?

Thanks for your help.

Regards
Sanjay

[Art Montemayor]

Sanjay:

Congratulations. You have succeeded in drawing the attention of Mr. Harvey Wilson. Harvey's background in Fluid Mechanics is broad and well-respected.

I only interject myself into this thread to offer a workbook I put together to explain gravity flow and the term “self-venting” – as well as a classic article on gravity flow by P. D. Hills. Perhaps some of the sketches can help you out.

I will now sit back and hopefully await Harvey’s return to this thread – if he is available at the present – anticipating his valued responses to your queries.

Attached Files

•  Art's Gravity Flow.xls   1.25MB   4650 downloads

[katmar]

I'm glad that Art has put up the link to his excellent summary of gravity flow. Read through that and the article by Hills which, as Art has pointed out, has some sketches with descriptions that will help you get a feel for gravity flow and the associated problems. 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.

Rather than try to answer all your queries I will leave you to study Art's spreadsheet and come back with any remaining problems - but I will make one brief comment that will hopefully get you thinking along the correct lines.

Taking your example of the 4" line and assuming water as the liquid - if the flow is at a Froude Number of 0.31 then the velocity is 0.3 m/s, the flow rate is 8.9 m³/hour and the friction pressure drop in a horizontal pipe would be 1.1 mmH₂O per meter.

Now, if you turn that pipe to be vertical the driving force becomes 1000 mmH₂O per meter and the resistance is 1.1 mmH₂O per meter. This is clearly not stable and the water will accelerate and empty the pipe. This shows that it cannot run full. For Fr < 0.3 no bubbles will be entrained and the water will flow out exactly as fast as you pour it into the pipe - so there is no problem (or need) to calculate the flow rate or the pressure drop.

Please do come back with any remaining problems you might have after reading Art's material and we will help you out. I would guess that more than 50% of the piping problems I have come across over the years have been due to people misunderstanding gravity flow, so it is a subject that is well worth putting some effort into understanding.

[sang]

Harvey, Art

Thanks for your responses. I had gone through Art's excel file and Hill's article before posting. Some things were not clear then and that's why I made the original post. Having gone through that again, I'm still unsure on a few things. Please bear with me and help understand the following:

1. In Hill's article, Figures 1a-1e show a separate gas line. The process described depends on the gas inlet being filled with water (Figure 1d) to have the cyclic nature. However in my case there is no separate gas line - the source is just a horizontal vessel with a bottom outlet. Is the explanation given still valid?

2. In your description of vertical pipes, you say

"For Fr < 0.3 no bubbles will be entrained and the water will flow out exactly as fast as you pour it into the pipe - so there is no problem (or need) to calculate the flow rate or the pressure drop"

That implies that flow rate has to be controlled to get Fr< 0.3. Thus, I can choose any size for the drain pipe and as long as I control the flow such that Fr<0.3, I'm fine. Is that correct?

3. Quote:

"Taking your example of the 4" line and assuming water as the liquid - if the flow is at a Froude Number of 0.31 then the velocity is 0.3 m/s, the flow rate is 8.9 m³/hour and the friction pressure drop in a horizontal pipe would be 1.1 mmH₂O per meter."

Here you are coming at it backwards, already assuming that velocity is 0.3 m/s. This again would need the flow to be controlled. In my case, no control is proposed (as the water is just being dumped overboard - though one can argue if water is "just" being dumped, then why worry about self-venting flow, but let's just ignore it for the moment) so flow would be determined by the static head available which is quite high (10m). So what line size should I select?

My system is as described in Hill's article as 'complex' system-offshore pipe with several vertical/horizontal segments. That's why the equivalent length is 100m. Even if I had a smooth 1:40 slope, how I solve equation 5 in Hill's article for line size without knowing the flowrate is not clear. Or is a controlled flow rate still assumed?

I must admit that I am still struggling to fully understand Hill's article (specially Figure 3 and its application). Sorry for such a long mail. Hope you have the patience to answer them. I repeat my basic question: How do I size this line flowing just by static head such that there is no/minimum air entrainment without any flow control?

4. A little more light on "water hammer if the tank outlet valve closes with a non-self venting drain" would be appreciated.

Thanks & regards
Sanjay

[katmar]

Sanjay, I'm glad to hear that you have read through that material and it is clear to me that you are making a concerted effort to understand this phenomenon, so I am happy to help if I can.

Using your numbering system:

1. Hills' sketches are valid, and important, in developing an understanding of this type of flow - even if they are not exactly the same as your situation.

2. Yes - this is exactly the right understanding. If you want self venting flow. I will come back to that.

3. I am coming at it backwards, in the same way you started from some assumptions in your first post and then showed that the assumptions didn't hold. My aim was only to show that you cannot have Fr < 0.3 and have a full pipe in vertical flow.

We need to go right back to the beginning and ask why you want self venting flow. If the tank outlet is flooded (Hills Eq (2) and (3) ) then no air can enter the pipe and it is no problem. You simply decide what flow rate you want and knowing your head available you can size a pipe for running full of liquid. Because you have a relatively high head available for the length of pipe the velocities could be quite high and this is why I said you need to be cautious of water hammer. In any liquid-only situation where you have high velocities and valves which close fast you could have water hammer. The problem here is if the valve is at the bottom of the tank then when you close it there is a lot of water in the downstream pipe that wants to keep on flowing. It may be a better alternative to put the valve at the discharge end of the pipe rather than at the tank. But still don't let it slam closed.

If you do want self venting flow then you could take a short line from your tank outlet and tee it into a larger vertical section of pipe - with a Hills style vent pipe - that is designed for self venting flow. In this case if your outlet valve slams shut there is only a small amount of water in the full pipe, and the water in the self venting section can continue flowing and draining as it sucks air down the vent without hammering against anything. This gets back to your point 2. If the outlet valve and the short pipe to the self venting section are sized to ensure that the flow remains below the self venting limit of the larger section then you have a safe design.

In many instances the self venting design is the safer design, but also the more expensive (because of the larger pipe diameter required). If you can ensure safe operation without self venting flow there is no obligation to use the more expensive option.

Perhaps you should give us a bit more detail on the tank's level control system (or requirements) and the maximum rate of outflow required and we can work with some concrete examples.

[sang]

Hi Harvey

Your responses answer most of my questions. I'll get back to you if some doubts arise later. Many thanks for your guidance.

Regards
Sanjay

[BouncingRadical]

Hello,

 

I stumbled across this topic in a google search. I am in the process of redesigning a poorly designed gravity drain system and was basing all of my work on the 1970's paper “Process Piping: Functional Design”. The link to Art's information was extremely informative and was assurances that I was making the correct modifications and a few further tweaks to ensure the system works well as it has some twists and turns.

 

Thanks