How to calculate a pressure drop in a branch of a loop ring pipe

[Amaelle]

Good day I'm trying to calculate the pressure drop in each branch of the following loop ring system

I used the following formula to find the pressure drop

but i seems that it worked only for the ring, and the branch #2 ( the branch in the middle), the solution given by the professor show different results for the other branch!( in each branch there is one valve and one reducer)
any help would be highly appreciated!
best regards

 

[jrmichler]

What? Only one compressor? You lucky person.

On these type of problems add the estimated/calculated flows to each pipe, and to the points of usage to the diagram. Then add the calculated pressure drop for each segment. It makes the problem much easier to understand, easier to communicate to others, and easier for somebody else to check your work. Also include pipe sizes, lengths, and units for all dimensions.

Some simplification is necessary in large complex systems. I once designed a heated water system with over 750 points of use, so have some experience at this.

 

[Amaelle]

Thank you jrmichler so let me write everything in detail
The candiate has to size the loop ring pipe and primary air receiver AS1 in a compressed air system given that

• Standard conditions
• Compression ratio 7
• P1= 1bar we consider the temperature constant over the pipeline
• so P1V1=P2V2 so P2=7 bar

AC= required compressed air
so the the volume of the AS1=12,28m3
my problem comes in the calculation of the pressure drop in the the first and last branch ( those values displayed in the image are those of my professor)

for the calcuculated diameter=sqrt((FR/AV)*4/pi)

the nominal and internal diameters have been taken from this table

I used this formula

to calculate the pressure drop in all branches but seem to work only for the main loop!
thanks!

 

[jrmichler]

Your chart does not clearly tell me what the pressure and flow are, and where. Each segment of pipe has a flow, so add the flows to the diagram. Each segment of pipe has a flow, a length, a diameter, and a pressure drop. Add the lengths and diameters to the diagram. Calculate the pressure at each junction, starting with the compressor, and add those numbers to the diagram. Show each point of use with a short arrow pointing away from the pipe, and add the flow at each of those arrows.

Then go through and check. Make sure that total usage flow equals compressor flow. Look at the pressure drops and see if anything does not make sense. This is called a sanity check, and is done without calculations. If you cannot find anything wrong, then it's time to recalculate the pressure drops using a Moody Diagram (search the term if you are not familiar with it).

Make sure that the finished diagram is clear and easy to read.

 

[Amaelle]

Thanks a lot for your long reply
I would be very grateful if you could show me some ressources where i can study the pressure drop in the pnemumatic conveying more in depth!
thanks a million!

 

[jrmichler]

An excellent book on compressed air systems is Compressed Air and Gas Data, edited by Charles W. Gibbs, and published by Ingersoll-Rand Company. I see that it is available used from Amazon. Highly recommended.

It's more than you need if you only need to size pipes and calculate pressure drops. For that, the Moody Diagram is enough. But for understanding complete systems, it is possibly the best source available.

 

[Amaelle]

thanks!