To perform an analysis of a pump and know what it's capabilities and limitations you need your pump curve. You will be given the rpm and impeller size. You probably know this but your x axis is your flow rate with your y axis you TDH or total dynamic head. For your impeller at zero flow you will have your maximum TDH. If you take this number and divide it by 2.3 you will have the psig the pump will register when it is dead headed. If you are able to share with me the need for the minimal flow that would help.
Once your minimal flow is established you are able to verify the flow using the pump curve and a pressure gauge on the discharge of the pump. Read the pressure gauge, multiply it by 2.3 and that is the TDH you are imposing on your pump. Find that TDH on the y axis and run horizontally until you intersect the impeller curve. From here move vertically down to the x axis and that is the flow you have.
Of course if you have a positive displacement pump it is a different case. You cannot, cannot, cannot deadhead the pump. Positive displacement pumps almost always have either an integral or installed separately a pressure relief valve. The rating of the pressure relief valve will give you the maximum pressure or minimum flow the pump is designed for. This pressure rating multiplied by 2.3 will give you the TDH. As mentioned above find the TDH on the y axis and run horizontally to the impeller curve you have, run down to the x axis and that is the bare minimum flow you will ever have. Soooo, run a higher flow (less pressure) than that other wise the pressure relief will be going off.
I hope this helps.