If you are looking for an estimate based on some correlations, this is highly empirical. For a given stirred speed, the power required depends on the resistance of the fluid to rotation induced by the impeller. This of course depends on the geometric details of your specific impeller (size of blades, blade angle, proximity to outer tank walls, etc.). Note that a simulation could include all of this information. If you are merely looking for a ballpark estimate, then do some research and find the range of power consumption for mixing tanks that are used for applications similar to yours. For example, average power consumption per unit volume for industrial bioreactors ranges from 10 kW/m^3 for small vessels to 1~2 kW/m^3 for large vessels. Friction in the stirrer motor gearbox and seals reduces the energy transmitted to the fluid; therefore, the electrical power consumed by stirrer motors is always greater than the mixing power by an amount that depends on the efficiency of the drive. So taking that range of numbers for bioreactors, the power in kW can be obtained for a mixing tank of a specific volume.