Calculating AC Motor's Running Power

I've been asked to calculate the power consumed by a motor knowing only its HP rating and rotational speed. Most of the motors are driving centrifugal pumps.

I am finding conflicting information. I see one expression that is constant: P = τ · ω. Tables show that as ω drops, τ increases, linearly. I don't understand that, P should be proportional to the work done, the mass moved per unit time.

I read mechanical power of a centrifugal device is proportional to the SQRT of ω.

So I am lost. I am most likely not going to have I and V values available and need to understand how to calculate this.

Thanks for the help.