Basic question: Full pipe vs Partially filled pipe flow 9

[SilverRule]

Hi Guys,

I've been studying regular fluid flow in pipes (full pipe) fundamentals i.e., pressure drop, flow calcs etc.

I stumbled upon the concept of fluid flow when the pipe is only partially full like perhaps when the pipe is oversized for example. I'm trying to grasp the fundamentals of this flow better but every source online is talking about open channel/conduit situations only with gravity being the primary driver. This is not relevant for me as I'm simply trying to understand it for a horizontal, closed, circular pipe.

1) Are the fundamentals different for this kind of flow? Is pressure differential not the primary motive force in this case? If not, what causes the flow here?

2) Is this considered two phase flow even if the material flowing is just water? I've seen someone call this two phase flow elsewhere. If it IS two phase flow, how so?

3) Does this kind of flow cause any fundamental problems and is to be avoided as a rule of thumb/best practice or is it OK?

4) I'm going through Crane TP-410 and I haven't seen it mention how to do calculations and what formulas to use for this flow unless I missed it. Can you please point me to a source which has this information without confusing it with gravity flow in open channels?

Thank you so much!!!

SR

 

[SilverRule]

katmar/LittleInch,

Thanks for your inputs again. In order to understand the exact problem I'm dealing with, please look at the attached screenshot of the model I'm working with in FluidFlow3. I made it an extremely basic/simple model in order to understand the fundamentals and each section of pipe is labeled clearly with the length, size, flow and velocity. To simply everything as much as possible, all the takeoff flows in the branches are the same and they all also have the same length and size. You can also see that every section of pipe in the header is also the same length, again to simplify. (Take a couple minutes to absorb the model, my questions will make a lot more sense.)

The big difference is in the sizes of the sections of pipe in the header. They start off big and progressively decrease. The reason it is like this is because I initially had all those sections of pipe in the header at the same size of 2 inches and when the program calculated the results, it recommended different sizes for each section of pipe in the header with what it calls "Exact Economic Size"... this is supposed to be the optimal size taking into consideration both capital costs AND operating costs per year. So then I changed the sizes from 2 inches to what its recommendations were and then ran the calculation again.

NOTE: It seemed you guys were referring to slopes, angles, inclined piping and gravity a lot. I want to highlight that this is purely all on the same horizontal plane -- no elevation difference --> so no slopes or angles, so no influence of gravity.

1) Now here's the question: the program didn't flag any issues. But if you calculate Q/d^2.5 (Flow/diameter^2.5), that value comes out to be < 10.2 for EVERY SECTION OF PIPE in the header and EVERY BRANCH. That means, according to Branan, all these sections of pipe and branches are flowing less than full. Note that my intention is NOT to design a system with partially filled flow. But rather, that just seems to be result of specifying the pipe sizes the program is calling optimal. Now I know katmar was saying that Branan's rule is probably only referring to the discharge point of the horizontal pipe and not the entire pipe. I'm not sure if this is true, I haven't found the original article Branan is referencing. But if this is true, how does one actually calculate if an entire section of pipe (not just the discharge point) is partially full or completely full? Seems like it ought to be a basic calculation.

2) If we assume Branan's rule applies to the entire section of pipe, then the entire pipe network in this model is only partially full. Would this work in reality? An entire pipe network that is flowing partially full with no elevation changes. Is that possible? If so, I'm still trying to understand what would be the driving force? Wouldn't the static pressure at every point be the same? How would there be any pressure drop with flow?

Again, I really appreciate your guys' responses!!

 

[SilverRule]

I'm attaching here the relevant page from Branan's book on his rule for convenience.

 

[razookm]

To answer your specific query, the following is required.
1. How flow to each destination will be controlled. I will expect a valve or a restriction orifice to be present at each branch. How far away is this restriction device from the branch take off.
2. You have mentioned that header is horizontal. What about branch line? Is it also horizontal.
3. send a typical routing sketch of branch line. Make sure that sketch indicates the high or low points, location of flow restriction and whether the line is connected to vessel at above liquid level or below.
4. What is the pump discharge pressure?
5. What it's the elevation of horizontal header with respect to destination vessels.

 

[SilverRule]

To answer your specific query, the following is required.
1. How flow to each destination will be controlled. I will expect a valve or a restriction orifice to be present at each branch. How far away is this restriction device from the branch take off.
2. You have mentioned that header is horizontal. What about branch line? Is it also horizontal.
3. send a typical routing sketch of branch line. Make sure that sketch indicates the high or low points, location of flow restriction and whether the line is connected to vessel at above liquid level or below.
4. What is the pump discharge pressure?
5. What it's the elevation of horizontal header with respect to destination vessels.

1. Yes, a valve. Let's say location is at half way through the branch.
2. Branch is also horizontal.
3. What do you mean routing sketch of branch line? The diagram in the model is essentially the routing sketch. It is all horizontal - no high or low points. Restriction would be half way. Let's say the discharge is above liquid level.
4. Pump discharge pressure = 8 psig.
5. Horizontal header at same elevation as the branch pipes discharging into the destination vessels.

 

[razookm]

Your case is a very simple case. The pipe until the valve at each branch will be full of liquid. Any air present during startup will eventually flow through because there is no high point. For the part of the line after the valve will be partially filled and behave as open channel flow which was already well explained in detail by @LittleInch and @Katmar. Please note that pressure at upstream of the valve will be 8 psi - the pressure drop in the line and pressure at downstream of the valve will near to the tank pressure. Being partially filled will not be of any concern and there should be no issue with your piping design.

 

[katmar]

As much as it is interesting to work out exactly what is happening in each of the pipes, in this case I believe it would be better to take bimr's advice and avoid the situation. Hydraulics are only part of the design. Safety, operability, maintainability etc must be considered as well. It might be a good idea to have the whole manifold self draining and make everything slope down towards the discharge points.

Even if this is only a hypothetical design for learning purposes, it must be workable. Your drawing and calculations do not include the valves or other means to control the distribution. Until that is resolved all other questions are meaningless.

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

 

[LittleInch]

"But if this is true, how does one actually calculate if an entire section of pipe (not just the discharge point) is partially full or completely full? Seems like it ought to be a basic calculation."

Well try looking through the book I posted that gives you that length in the figure 9.9 above.

I'm with Katmar here - it appears as if this equation only really relates to the end section when discharging to the open air / above a liquid level.

It doesn't seem to try and calculate the length from the end to where the pipe is actually full and for other parts of the system seems to result in quite a high velocity which would normally be seen as being able to blow out any air int he system and result in a full pipe.
This is the length referred to in diagram 9.9 above.

For truly horizontal pipes you are correct in thinking that for any reasonable flow rate the length back from the open end cannot be infinite as partially filled pipe because otherwise there is no driving force ( head / pressure). As soon as the required head to flow your flow in an semi open pipe exceeds the ID of the pipe then that implies that the pipe is full at that point. It is complicate dby the fact that as the pipe fills up the velocity changes. If you look at diagram 9.9 you can see that the slope of the liquid level changes and becomes flatter in the middle.

The full pipe velocity in the example page listed that you posted turns out to be about 0.8m/sec (for a full pipe). I find it difficult to believe that a long pipe could flow that fast without being full.

So your second point - can this be for an entire network - yes if the flow is low enough. The driving force is simply the head of water in the pipe at the entry point is higher than it is at the exit point. So for say a 6 inch pipe, if the depth of water at the entry point is say 5 inches above invert level, but at the exit point say 25m away, it's 2 inches above invert level, hence flow in a partially full pipe, but must be really quite low.

I think though you are extending this < or > 10.2 equation away from where it is valid ( the end of the pipe where it exits to free air) to the entire network where it isn't valid.



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

 

[pierreick]

Hi ,
You may be interested with the document attached "determining sealing flowrates in horizontal run pipes" chem eng 1998 .
Enjoy the reading
note : an application could be an estimation of the flowrate in a drainage system where the pipes are partially filled .
Pierre

 

[LittleInch]

The key section to me is the phrase "...at the end of the horizontal run...", so is focused primarily, as far as I can see, on whether as the fluid exits the pipe, is it a full pipe or a partial pipe.

Doesn't seem to go into how far back you get any transition from full pipe to partially full pipe.


Also " At the flowrate represented by this value [the 10.2 number ] a horizontal pipe will be sealed at its end by the flow of liquid in the pipe" - my emphasis.

So for flow in the rest of the system I can't see the value of this number, but is useful to note that the last section of pipe pressure drop would be different to the fully filled pipe.

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

 

[SilverRule]

pierrick,

Thank you SO MUCH! This conclusively clears it up!

 

[SilverRule]

The key section to me is the phrase "...at the end of the horizontal run...", so is focused primarily, as far as I can see, on whether as the fluid exits the pipe, is it a full pipe or a partial pipe.

Doesn't seem to go into how far back you get any transition from full pipe to partially full pipe.


Also " At the flowrate represented by this value [the 10.2 number ] a horizontal pipe will be sealed at its end by the flow of liquid in the pipe" - my emphasis.

So for flow in the rest of the system I can't see the value of this number, but is useful to note that the last section of pipe pressure drop would be different to the fully filled pipe.

LittleInch,

Yep, looks like katmar and you were right all along. I just wanted confirmation. Thank you for sticking with it! This makes a lot more sense now.

And yeah those were my thoughts too exactly... only thing it's missing is saying how to calculate how far back it's not sealed for. This does seem to be only valuable for that last section of pipe. But weirdly enough, without knowing where that transition is, how would you practically use this anyway?

By the way, does this mean that the pressure at the destination is the same as the pressure THROUGHOUT the non-sealed section of the pipe?

 

[Compositepro]

Yes, an air pocket with no air flow has uniform pressure throughout.

 

[jari001]

@SilverRule
To me, the usefulness is as a method to check that the piping discharge runs full at steady state. If you find that your discharges aren't sealed then you have to re-evaluate the design - be either full flow or partial flow always, as bimr pointed out.

 

[LittleInch]

Well to estimate the length based on that diagram 9.9 I would calculate the pipe full head loss for your flow rate, figure out or estimate what the depth of the liquid is at the end and then extrapolate back until you hit the top of the pipe. Or just ignore the depth and use the pipe invert. The real point will be somewhere between the two.

At the least it will be a start point for any calculations and you can see if that amount of partial flow pipe is significant it he grand scheme of things. So if you calculate that and it's 5m, but your pipe is 50m long then I would just ignore it. if is 15m and your pipe is 20m long different story.

Anyway it's been quite interesting thinking about this so a good discussion all round.

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