Selecting pumps for two pump stations discharging into a header 4

[AmbroseChappel]

Hello,
I would like to design two pump stations of similar but not equal elevation and capacity which discharge to a common header. I can calculate the head losses up to the point of the header, which is where my confusion begins. How can I calculate the head loss through the header when both pumps are operating so that I can choose the pumps? Can you recommend a reference that might point me in the right direction? Everything I have found on the subject refers to the method of intersecting the composite pump curve with the system curve (from the header on) after subtracting head losses up to the junction from each curve, but I haven't gotten as far as selecting a pump yet!

The attached figure shows the system
Qa = 25 L/min, Da = 100mm, La = 500m
Qb = 20 L/min, Db = 100mm, Lb = 200m
Dab = 150mm, Lab = 500m

Any advice would be greatly appreciated. Thank you.

 

[TenPenny]

When both pumps are operating, you have 45 l/min through AB. So calculate the friction through that section.
Pump A has to overcome the elevation, plus the friction in A (based on flow of 25 l/min) and the friction in AB (based on 45 l/min), so you now know the required head of pump A at 25 l/min.
Similarly, Pump B has to overcome the elevation, plus the friction in B (based on 20 l/min) and the friction in AB (based on 45 l/min), so now you know the required head of pump B at 20 l/min.

 

[Artisi]

Good response and a star, I started down the same track but got a bit tongue tired so put it aside - you have now saved me any further problem.

It is a capital mistake to theorise before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts. (Sherlock Holmes - A Scandal in Bohemia.)

 

[AmbroseChappel]

Thank you for your reply, TenPenny. This seems so intuitive to me now I cannot believe it didn't occur to me in the first place. Cheers.

 

[LittleInch]

First rule of any network analysis is start at the end and work backwards to common pressure junctions e.g. the join between A and B.

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