What's my pump displacement?

I have a centrifugal pump connected to a motor that has an rpm of 1725 rpm, its water inlet is 2 in. and the outlet is 1 1/2 in.

what formula will help me to calculate it's output in gallons per minute when pumping water ?

Answer:
Output is inverslly proportional to head. ( Head is sum of line friction and delivery hight )
We nned to know what is the impeller diameter, motor rating and at what level you want to measure output ?
In general if your outlet is 11/2 in, take 6 fps velocity hence flow rate will be around 5000 LPH at 5 - 10 mt head
you can't because you don't know the efficiency,psi,hp ect of the pump.
Can't even know the max without knowing the psi.

Best thing for you to do is try to search around for a replacment pump of the same type and go by it's gpm.
You would need to know the motor HP, the impeller size, and the inlet and outlet design pressures to get a specific flow rate for that particular pump.

However, since it has a 1 1/2" outlet , and assuming the outlet piping is designed for a maximum liquid velocity of 5 ft. per second which is a reasonable design velocity for water, then the piping system would be limited to about 32 GPM, assuming 1 1/2" std. steel pipe is connected to it, so you could assume the pump capacity was about = 32 GPM.
try Bernoulli's Law:
You can't calculate it. First, you have to know if it is a dynamic (centrifugal) pump or a positive displacement pump. If it is a centrifugal pump, you have to know anything about the shape and size of the impeller. Then you have to know about the discharge pressure. The same pump will vary flow depending on the discharge pressure.

A positive displacement pump could be longer or have different dimensions other than the inlet and outlet.

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