A given pump can operate at a range of horsepowers depending on the flowrate and differential pressure and operating point on the pump curve. Therefore when it is stated that the pump is 5 hp it means it has a 5 hp motor and operates at a differential pressure and flowrate that requires no more than 5 brake horsepower at design operating points.
For pump P601A, we then installed a 3HP motor, will this not cause a problem since the plant flow diagram requirea a 5HP. See attachment for the pump installed.
Maybe and maybe not. The actual required pump motor horsepower may be under 3 hp although the flow diagram shows 5 hp. If the pump works ok with a 3 hp motor then the 5 hp motor was oversized. A pipe pressure drop calculation is performed initially to size a pump and determine the estimated required horsepower. Perhaps the original sizing of the pump was in error or considered future changes in process that did not occur so 3 hp is really all that is required. If the motor don't burn out/overheat or keep burning out the fuse circuit protectors and provides the flow you need then 3 hp is ok.