How can you differ using pumps in series from using pumps in parallel?

We use pumps in series in applications where we required to increase static head while keeping the same discharge whereas in parallel application discharge can be increased keeping head constant.
standby option can be applied in parallel arrangement.

To increase discharge head at a given floerate pums are intalled in series while pump are install in paraiiel to increase flow rate at a given head.

You know your flow rate and discharge head, Stop one of the two pumps and then measure both Q & H If Q decreased to half its value, then your connection was parallel.
If H decreased to half its value, Then your connection was series.

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Everyone will find answers here!  But, to answer the question.  Series pump = higher head / same flow-rate.  Parallel pump = same head / higher flow-rate.  Multistage pumps can achieve a combination of this.  Large split-case pumps are used for more flow, but less head.  Single stage centrifugal pumps are used for a higher head, but a lower flow-rate.  This also applies to vertical pumps. It is a trade off of one for the other. 

It is all depend on application . if the application required  a high pressure ( such as pressure used in R.O. plants) then you need to use a booster pump which is connected in series to a high pressure pump. In case of applications that require a flow rate that can't be achieve by single pump, you need to use pumps connected in parallel.

Shutdown one pump primover if flow decrease then parallel connection if not series connection(parrallel connetion suction from one source pipe and series suctionof one pump from delivery of2nd pump)

It dependes up on the application you need 

you need pressure or flow rate  if you need to raise pressure then you have to connect them in series as the delivered pressure from the first one will be the suction pressure to the second 

 

if you want to more flow rate then you have to connect them in parallel then the sum flow rate will be the sum of each pump flow rate