adjusting pressure drops to ensure equal flows 1

[keekooceeaou]

Hi,

I have a pipe system as in this picture:

The water flows in with flow rate of V1 [m3/s].
I have to adjust diameter of openings in flanges (d1 and d2) so water flows with the same speed through each small hole (diameter d3).
There are n1 holes in section I and n2 holes in section 2.

How to calculate d1 and d2?
All dimensions of, fluid properties, pressure etc. are known.

Thanks for any help,
Paul

PS.

My idea is to calculate flow rates in section I and II:
(V.I=n1/(n1+n2)*V1, V.II=n2/(n1+n2)*V1), and then then:
1. adjust d1 and d2
2. calculate pressure drops (for example from inlet to section I and from inlet to section II)
3. repeat 1 & 2 until I get the same delta P for section I and II.
Is it worth trying or am I totally wrong?

 

[epoisses]

Sorry for cheating, but if you can modify d1 and d2, can't you make V1 tie in between d1 and d2 and have symmetrical piping toward I and II? You'd spend a bit more on pipe but much less on engineering hours.

 

[sshep]

It isn't clear if V1 must be some specific value, but I suspect you have a design total flow. If V1 has a target value then you can calculate the flow through each chamber (as you suggest). You can also calculate the pressure of the chambers directly from the d3 discharge pressure boundary condition via orifice calc (calc Pin from F, bore, and Pout). The size of each orifice d1 and d2 also then becomes a simple orifice calc (calc bore from F and dP). In otherwords, if the flow of each branch is known, no itteration is required by working backwards from the discharge pressure.

If V1 does not need to be any specific value then there are infinite solutions. You may specify d1 at any value, and calculate d2. In fact if your objective is only to have the same velocity through each d3 hole, then why have a restriction at d1 and d2 at all? If the pressure in I and II are line pressure, then the flowrate through all the d3 holes will be the same. This will be possible without restriction d1 and d2, if the cross-section of (n1+n2)*d3^2*(pi/4) is << cross-section at V1.

If you must control the total flow at some value why not just put a single restriction in the common line, or resize the d3 holes so as to give that design flow without additional restrictions (if either option is possible).

best wishes,
sshep

 

[gerhardl]

sshep have in my opinion pinpointed the case :

...<< If the pressure in I and II are line pressure, then the flowrate through all the d3 holes will be the same .... If you must control the total flow at some value why not just put a single restriction in the common line....>>
...
What is your actual target? Within 'normal' viscosity range and full pipeline all d3's will give the same output, as sshep says.

Sizing of d3's (with good approximation) by outlet from one d3 at given size and pressure, multiplied by total number of d3s.

Regulating: either regulating valve in main pipeline if excess pressure or variable pump for boosting and regulating if too low.

If open to atmosphere and natural fall, you could even regulate the flow somewhat by having a higher placed common feeding vessel and maintaining a certain level (or levels) in this.

If closed to atmosphere you have the possibility to regulate pressure by topping the vessel with regulated air or gas pressure (open or bag enclosed gas in the vessel).

 

[dcasto]

If it has be exact, then you are going to have to model the curved portion of the left most nozzel, know the hieght of each chamber where the holes are. Way to much going on.

 

[BigInch]

If precision is required for exit flows from the flange at the bottom, good luck. The eddies coming off the Tee, Ell and flow patterns set up from the curved segment, not to mention the square edge opening into the chamber and the variable distance from the edges of the chamber to the holes will all complicate the situation. First of all, with the eddy formation, I sincerely doubt you will ever reach a steady state pressure drop across either one of the orifice plates.

I'm afraid Bernoulli won't do you a very good job and you'll have to get out the Flower manual before you'll even be able to start looking at that seriously.

BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[keekooceeaou]

Hi,
Thanks for replies

Sorry if something was unclear.

First, so called "section I and II" are not chambers, but pipes, each with many holes (more than 20).
V1 and inlet pressure are known and constant, as well as all pipe system dimensions and arrangement.

What I have to do is to, by adjusting orifices (without changing anything else), ensure that flow rate into each "section" is about the same (for simplification I can omit in calculations pipes "I" and "II").

I just want to know if I can solve this by calculating pressure drops (friction factors for pipes, K-factor for bends, tees and orifices, etc.) and adjusting orifices, so that pressure drops (from inlet to "I" and from inlet to "II") are the same.

 

[keekooceeaou]

Oops!

Of course the flowrates into pipe "I" and "II" shouldn't be the same, but proportional to number of d3 holes in each pipe.

Sorry for confusion.

 

[gerhardl]

Biginch... I agree. My thoughts were based on laminar conditions, ideal Bernoulli.

 

[RJB32482]

What program was used to post a picture in the forum? I have been trying to do that on some questions with no luck.

Thanks.

 

[BigInch]

RJB,
I've written exact instructions for posting diagrams in this thread,
thread378-184348: "Parallel" Pump Head Calculation

BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[RJB32482]

Thanks BigInch. Now the sketch that I made is in the word format. How do I convert to one of the other formats so I can post the sketch? Or do I need another program to make the sketch?

Thanks

 

[BigInch]

I don't use word format so I don't know if this will work, but try selecting the sketch, copying it, open MS Paint (comes with Windows) and paste it into MS Paint. Then when you save it, you'll get options to save it as a 24 bit bitmap picture(*.bmp) file or as a JPEG picture(*.jpg) picture file. I think it should work.

OK, I just opened Word and made a few stick figures with the drawing tools. I selected the result, copied it, then opened up MS Paint and pasted it there. I saved it as a JPG, so now I'm sure that it (should) work like I told you above.

BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[ScottyUK]

BigInch,

There's a FAQ which addresses image posting. Might be easier to just point to it than having to re-write the information each time.

faq559-1100


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Sometimes I only open my mouth to swap feet...

 

[djack77494]

To get to a desired split of flow to your two destinations, you must match the desired flowrates to the hydraulic losses. Let's call the destination (downstream side fo the holes) of your chamber or pipe I A. Similarly, let's call the second destination B. Starting at the area where your label V1 is, the pressure drop from V1 to A must result in the desired flowrate. I assume you know what flowrate is desired (n1 * d3), so your only unknown is the orifice delta P. Calculate it, and then you can calculate the orifice size. Circuit A done! Do the same for the second circuit and you're finished. (I have assumed that the orifices are small relative to the pipe diameter, which would normally be true in the case of a restriction orifice. If that's not true, then you may need to address some piping concerns.)
Doug