12 replies to this topic

[chemeng2016]

Hello,

 

I have a system in which I have a pressure indicator on a water header, which then splits into 3 (unequal) streams of water for distribution. I have a pressure indicator for each of the 3 streams, and I want to verify through calculation whether the pressure read on each of the stream's indicators makes sense. 

 

Essentially, I want to know how pressure behaves once it is split into 3 pipelines. I understand that the pressure will depend on velocities. Lets say each of the 3 pipeline's diameter is different. Say, P1 is the main header pressure and it splits into P2, P3 and P4. 

 

How can I calculate P2, P3 and P4, assuming that I know P1. What variables do I need (i.e. diameters, velocities, etc.)

 

Thank you in advance,

 

Gina

 

Imagine: P1 splitting into 3 streams P2, P3 and P4. 

                _______P2

P1---------|_______P3

               |_______P4

[breizh]

Hi Gina,

 

Consider the resource attached , it should help you .

 

Good luck.

 

Breizh

[christopherchoa]

Diameter, flowrate, pipe roughness, 

[shantanuk100]

Hello Gina,

 

In general,

1. First step is to conserve the mass flow, assuming your fluid is incompressible. For this use the equation of continuity.

2. Second step is to conserve energy flow, using the Bernoulli equation for the entire system containing P1, P2, P3, P4, since there is no other external energy source.

3. Once you finish both these steps, the pressure will be nothing but a consequence of these equations, and additionally, you can also consider downstream flow losses due to friction etc if you want to be exact to the point.

4. But in general, unless there is any obstruction, the exit pressure will be almost equal to the inlet pressure for similar diameter pipelines, though we also include friction losses.

5. But please note, all these pressures and losses depend on your pipeline diameters though.

 

Regards,

Shantanu

Edited by shantanuk100, 19 April 2016 - 06:12 AM.

[Mahdi1980]

Dear Gina

It seems that you have made a misunderstanding concerning the relationship between pressure and velocity( flow rate).

Pipelines are similar to electrical circuits. Delta P is like Voltage and flowrate is like electrical current.

In parallel circuits like parallel pipeline ( your case), although electrical current ( flow rate) are divided regarding the resistance, the voltage ( delta P) is constant.

In other words, in your case P2, P3, P4 are nearly equal to P1 and from main stream ( P1) to each stream, the bit differential pressure could be calculated by Darcy's equation. You can find this famous equation in every fluid mechanics and hydraulics books.

But the pressures do not have a dramatic difference.

 

Mahdi

[samayaraj]

Hi Gina,

 

The scheme you have provided is "Flow in parallel pipes". Here the pressure drop across each branch is same as other branches.

Look at the attached sketch for better understanding. Also look at the attached link for more information.

 

http://nptel.ac.in/c...rallel_pipe.htm

Attached Files

•  parallel flow in pipes.png   12.4KB   6 downloads

[fallah]

samayaraj,

 

As Op mentioned that three pipelines have different diameters, then there is no reason based on which the three points in a plane cutting three parallel pipelines have the same pressure.

[samayaraj]

samayaraj,

 

As Op mentioned that three pipelines have different diameters, then there is no reason based on which the three points in a plane cutting three parallel pipelines have the same pressure.

 

Dear Mr. Fallah,

 

I could not understand. Can you elaborate?

 

In parallel flow, whether its same or different dia pipe, the pressure drop in each branch (in same elevation) is same as other branches.

[fallah]

 

I could not understand. Can you elaborate?

 

In parallel flow, whether its same or different dia pipe, the pressure drop in each branch (in same elevation) is same as other branches.

 

 

Dear samayaraj,

 

Yes, of course, for flowing fluid the pressure drops are equal in all parallel branches from starting point of splitting to termination point; but as you shown in your sketch in different dia parallel pipes for the points along the branches even with the same elevation the friction loss are different hence the pressures can be different...
 

[samayaraj]

 

 

I could not understand. Can you elaborate?

 

In parallel flow, whether its same or different dia pipe, the pressure drop in each branch (in same elevation) is same as other branches.

 

 

Dear samayaraj,

 

Yes, of course, for flowing fluid the pressure drops are equal in all parallel branches from starting point of splitting to termination point; but as you shown in your sketch in different dia parallel pipes for the points along the branches even with the same elevation the friction loss are different hence the pressures can be different...
 

 

 

I Agree Mr. Fallah. I have shown the picture for same dia. pipes. Yes, from the splitting point to terminal point, pressure drop across each branch is same as other branches.

[Mahdi1980]

Dear Samayaraj,

 

Confirming Mr. Fallah view point, I should say that according to Darcy equation:

dp= f (L/D) . V²/2g

in addition to friction loss which is proportional to the diameter of branch, the diameter itself has a role in pressure drop. So, in the same length of each branch, pressures would be different.

For instance, if a header is 10 inches and there are two branches of 1" and 8" it is obvious that delta P is much more higher than that in 8" pipe branch.

Before, I have checked it practically several times.

 

Mahdi

[Araboni]

chemeng2016

As you may know , in such piping network , according to the energy (Bernoulli) equation, we have below pressure drop terms :

- Pressure drop (Delta P)

- Pressure drop due to elevation change(Delta Z)

- Pressure drop due to acceleration of fluid

Now , you should note that what your Press Indicator/Gauge shows is the Hydraulic or Static Pressure (i.e. P+Z) which is sum of  the Pressure term and gravity term.

Moreover , in compliance with any Fluid Mechanic book, total head loss or hf equals to this Hydraulic Pressure drop (Z+P).

Now the question is whether or not, you have a parallel pipeline network. I mean, whether your three lines will be eventually connected together again (to the same header , for instance in a cooling water network , wherein there are many parallel piping system). If so ,for each pipe junction or ‘‘node’’ in the parallel pipelines, continuity tells us that the sum of all the flow rates into the node must equal the sum of all the flow rates out of the node. So ,

 Q=Q1+Q2+Q3

Also, the total head loss (pressure drop plus Elevation head loss or P+Z) between the two nodes ,  equals to the total head loss of either individual pipe in parallel lines.

 

I think that your case might not be a parallel piping network and so for this case , if I were you , I would do the following:

-first measure in practice the static pressure drop for either pipe (P2-Pjunction)  and then calculate the hf. Next , you can calculate hf , theoretically by Darcy equation as said by Mahdi1980 , for either pipe but remember that if there is any fitting head losses , you have to incorporate them into Darcy equation (hf=(fl/d+SIGMA K) *v2/2/g). Then the calculated hf is expected to be equal to the measured hf.

Edited by Araboni, 19 April 2016 - 05:35 AM.

[S.AHMAD]

Chemeng2016

 

Youare asking a very simple queation that is you want to verify the pressure P₂, P₃, P4 by calculation. Let say to calculate use following equation:

 

_H2 = H₁ - f(L/D)V²/2g

 

Where H1, H2 are pressure expressed in m of fluid. If you are using SI unit the above correlation shall give you in m of fluid. You can convert to Pa if you know the density of the fluid.

 

Hoping this simple explanation helps you.

 

S.Ahmad

Edited by S.AHMAD, 23 April 2016 - 06:56 PM.