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Affinity laws for multistage pumps

I am wondering how to solve a problem with a two-stage centrifugal pump, I would like to revamp the pump to increase its performance by increasing impeller diameters and of course considering maximum available motor horsepower, and applying affinity laws get the size of impellers to the target flow and pressure. The issue is that I have the pump performance curve but not individual impeller´s performance, how I should apply the affinity laws for multi-stage pumps? Some pump data are 250 gpm @ 280 psig, 90 Amp, 3600 rpm, 9-11/16" both impeller diameters, I like to increase pump performance up to 350 psig at discharge or as much as possible regarding 115 Amp max motor current. Pump casing let to increase impeller diameter up to 11-1/2".

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Permalink Reply by Jack Condon on February 9, 2010 at 12:29pm: the performance curve you have with 9-11/16" trims can be used to directly figure flow, head, and hp at a new speed using the affinity laws. the additive nature of the two stage is already taken care of in the performance curve. if you want to install larger trims, up to possibly the 11-1/2" you mention, you will require a new performance curve at those trims unless your existing curve is multi-trim already. if it has various trims the same laws apply. cannot coment on your 115A max current without knowing what voltage this is at or the motor hp this relates to. would advise to increase the trims equally or face some possible issues with bearings - check with the manufacturer on any changes you plan to make - they may not be as keen on doing it as you.; ▶ Reply to This

Permalink Reply by Carlos Alberto Llinas Jessup on February 10, 2010 at 6:23pm: Jack, thanks for your answer. Yes, I do have the performance curve for the hole pump, but not for individual impellers, and the curve is a single-trim. May I use affinity laws in some other manner not needing to have individual impellers´performance? let´s say, supposing pressure rise and power is equally distribuited on impellers, then first impeller handles first half of differential pressure (140 psig), and second stage impeller handles the balance (140 psig), for a 280 psig total differential pressure across the pump?, so, applying affinity laws individually and then adding results I can get an approximated result, Does it make sense for you?

Jack Condon said:
the performance curve you have with 9-11/16" trims can be used to directly figure flow, head, and hp at a new speed using the affinity laws. the additive nature of the two stage is already taken care of in the performance curve. if you want to install larger trims, up to possibly the 11-1/2" you mention, you will require a new performance curve at those trims unless your existing curve is multi-trim already. if it has various trims the same laws apply. cannot coment on your 115A max current without knowing what voltage this is at or the motor hp this relates to. would advise to increase the trims equally or face some possible issues with bearings - check with the manufacturer on any changes you plan to make - they may not be as keen on doing it as you.; ▶ Reply to This

Permalink Reply by Ian Simpson on February 14, 2010 at 12:28am: Yes treat each impeller as an individual unit, ie calculate for 1 impeller using the affinity laws and if the second impeller is the same diameter just double the first number to give you the total head. At the end of the day if the head achieved is slightly over your requirements and causing problems it is allowable to reduce the second impeller diameter to bring it back to suit your head/ flow requirements..
Remember power increases at the cube of the diameter change..; ▶ Reply to This

Permalink Reply by Carlos Alberto Llinas Jessup on February 16, 2010 at 4:26am: Ian, thanks for your answer, I will do it in that way!!

Regards,

Carlos Llinas; ▶ Reply to This