Arraitch,
The nice thing about what Cran has posted is that it is not Bernouilli, but rather that staid Englishman, Newton. Simply put, who gives a damn about pressure, the rotor tosses air down, and in the process, picks the aircraft up. If the rotor were a machine gun shooting large pellets of lead downward, we could calculate how much lead, how fast, to create the lift we need. That is all the momentum equation Cran posted does.
The great confusion created by Bernouilli, pressures and curved airfoils gives me a headache, and I have several thousand hours of experimental test flying!
Remember this: The rotor lifts the aircraft up because it throws air down. Small rotor throws less air, so the air has to be going faster. Big rotor throws more air, so the air can go downward slower. Downwash is the name we give that air stream that lifts us. If you are doing 100 knots, or at a steady hover, you have to transfer the momentum to that air to stay up. Same downwash, at any speed.
Tip vortexes and other losses cost energy, and they add velocity that is in outward directions, so they don't help lift you, they are a measure of the extra (lost) energy that the engine must produce.