Increase the head on the pump, this will reduce power required or reduce the impeller diameter to suit the motor.
Replace the motor.

Supply the curves etc so we can have a better look.

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.)

Apologies for not being clear. I don’t want to replace the motor nor the pump. I just need to know the flow rate it can provide. The pump curve is the typical curve of a centrifugal pump.

The pump curve for the pump shows the head/flow/speed/horsepower relationship.

It seems you're missing a detail. The motor will spin at its specific speed PERIOD. At that speed with the given plumbing (head) the pump will demand a specific hp. If it is more than the motor's rating the motor will be overloaded. If you have appropriately installed motor protection it will trip to prevent a fire. That's a fact.

So, do not think that X horsepower will only pump Y flow thru your system. It will either pump all of the demanded flow or burn up/trip off.

The correct solution in an applied situation like yours is to hook a clamp-on ammeter on one of the motor's leads and run the system. If the current is less than the motor name plate "FLA" value you're good. If it's barely over the FLA it's bad. By restricting the outlet any number of ways you will reduce the horsepower demands. You can close a valve in the outlet until the current seen drops to the FLA. You would then need to placard the valve explaining it cannot be opened further and possibly put a lock box over it as a set throttling valve.

Keith Cress
kcress - http://www.flaminsystems.com

If you only want to know the required flow rate, beyond which the limiting motor may trip, then the flow may be estimated as follows

Flow gpm = Motor Power (HP) x 0.95 x 3960 x Pump Efficiency (decimal)/(specific gravity x heat in feet)

Use another factor of safety of 0.95 for motor overload protection. The right solution could be one of the following

1) Install a smaller impeller if the system head and flow requirements permit

2) Install a bigger size motor

It is very strange for any pump and motor combination to act like this unless one part or the other has been modified. Motors are supposed to be able to supply the power the pump takes at all point on the curve.

As stated above, if for some reason you want this to work, just follow the power curve on your pump data sheet and when it gets close ( say 95% of rated motor output) stop and draw a vertical line. That will be your flow rate which you will need to control to.

If the intersection between pump curve and system curve is to the right of this line then without restricting the flow, the motor will simply trip on excess amps or eventually start smoking and catch fire if there are no motor protection devices...

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

Thanks for the helpful answers. I think I know which direction to go next.
Probably I should have said that the system works fine for a certain fluid but there are circumstances where a heavier, more viscous fluid needs to be pumped (at a lower flow rate if needed) and the company doesn't want to spend the money to upgrade just for those rare events.

Yes you should have said that as it explains why this is happening.

You will definitely need a lower flow rate.

I hope your motor has an over load protection on it so it trips when someone forgets the "special procedure" needed for these occasional events.

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

Sounds like you need solid overload protection and then two ball valves or solenoid valves. The one in the high viscosity path needs an additional throttling valve set correctly as I described above. When the high-viscosity stuff is pumped you fully close the straight-thru valve and fully open the valve on the restricted side.

If, as Little points out, someone forgets the motor trips off and they get-a-clue.

Keith Cress
kcress - http://www.flaminsystems.com