How can we guess Motor KW rating without seeing Name Plate?
This is related to small and large size Induction Motors.We can easily see motor KW rating from Nameplate of motor. If nameplate is not available then how can we guess motor KW rating from running data of motor. Motor running data includes running KW, running KVA, running KVAR, applied Voltage, running current, running power factor and frequency.
Can we relate motor curves showing power factor and KW load?? If yes then which curves do you recommend??? Your suggestions and recommendation are needed!!!!!!!

you can know the power from frame size with speed , hz . Or you can calculate through P=U*I, get it from voltage and current .

you can know the kw of induction motor by the size of the frame and sfaft diameter and applied voltage and motor running currents

Unless the application is one which requires a very high starting torque condition (well above 100 percent), most machines are designed to have some "margin" between rated shaft output power and the power required for the process. This occurs since a machine is often seen as a significant capital investment - one that only is undertaken at fairly lengthy intervals. Therefore, the "buffer" between rated power and required power AT THE TIME THE MACHINE IS PURCHASED. Everyone in industry "knows" that over time, the process demands will increase without corresponding capital outlay .. which in turn means the equipment will be run harder and hotter (and of course eating into that initial buffer).

Most machines are purchased under the assumption that the load will only require 80-100 percent of the nameplate rating; the longer the cycle between capital expenditures, the more likely the load will be less than 100 percent.

The available running data for any machine that is viewed by an end user as essential to a process (regardless of actual machine rating) should also include the measured temperature rise. Each machine is also required to meet some maximum allowable temperature rise - typically, this is around 80 C above ambient for a machine operating at full nameplate rating. In general, the observed temperature rise is proportional to the square of the current. Understanding the speed vs power relationship for each process being reviewed will help to determine the machine's per-unit loading for each instance, and - in conjunction with observed rise - help determine maximum nameplate capability.

The difficulty with using a PF vs KW curve is that these can vary greatly in terms of slope. If the curve is relatively steep (more than 10 percent change in PF for 25 percent load swing in the region of interest), there is a reasonable chance of determining nameplate power from the curve. If, however, the slope is shallow the chance of error is extremely high. Note that the curve MUST be generated from as-tested results for the individual machine being examined, and NOT a "composite average" or "calculated" version that applies across multiple units and/or ratings.

In your initial question, you mentioned that you have "running" data for the equipment - KW, KVAR, KVA, V, A, PF, and HZ. Are the measurements for volt and ampere true RMS values? And are they actual phase measurements taken at the same time stamp, or an average of all phases? I ask because a small difference (less than 1 percent) in phase voltage can significantly affect phase currents, which will in turn affect both power factor and kilowatt/kilovar measurements. Trying to project these conditions to find a "nameplate" value only compounds the probability of error.