Can you advise if its best to start a pump against a closed valve then gradually open to the fully open postion, or start the pump when the discharge is full open to the system?

The quality of the response is directly proportional to the quality of the question.

what type of pump is it...positive displacement or centrifugal?

Max pressure that pump will generate when the system is blocked?

Power of motor running the pump?

what is the application?

Above and beyond these points, starting any pump against a closed valve is a bad idea.

Some pumps should absolutely be started up against a blocked or pinched discharge valve.  Examples include systems with potential for water hammer, vertical turbine pumps with a large number of stages that can up-thrust and buckle the shaft, control schemes where flow must be introduced gradually and highly unstable processes where a runaway reaction can occur.  But, for many other pumps, starting up against a blocked discharge could be disastrous.  Examples could include some PD pumps, multi-stage centrifugals, high speed Sundynes, and chemicals with thermal stability problems.  Without more details, it is really pointless to even speculate.

If centrifugal pumps:

As others have mentioned, it depends on your system.  For example, very large pump (say discharge pipe dia 6 feet or larger) pumping into a surge tank on a hill above the pump half a mile away.  You would probably want to start against a closed valve and open the discharge valve at an appropriate speed to avoid significant referse flows and keep the discharge line full.  For very large pumps, check valves, if available, may be bad news due to water hammer.

For smaller pumps, you may want to start at reduced horsepower to avoid excessive motor inrush currents.  If this is the case, check the pump curve to see the horsepower vs. flow curve.  For low specific speed pumps, power may be lower at shutoff.  For high specific speed pumps, power requirements may be highest at shutoff.

If the pump is small enough, you may just want to put a check valve in to prevent reverse flows and just start it.  If the system curve is all friction, forget the check valve and just start it.

You have three things you must optimize

The pump
The motor and switchgear
The system

Pumps generally hate low flows.  The higher the horsepower, the more they hate them.  Minimize time at minimum flow.

Motors and switchgears hate high inrush currents.  They hate high horsepower starts.  Minimize starting torque.

Systems hate large momentum changes.  The larger the system, the greater the opportunity for surge problems.  For these systems, large flow changes cause problems.  Systems often like closed valve, open slowly.

You must optimize between these concerns.  In very large units, system requirements dominate.  In very small units, pump requirements dominate.  In between, motors and switchgear can dominate.  You can optimize by modifying valve states and closure rates.

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