In your hypothetical hand, I 3bet the Flop and bet out on the Turn regardless of what hits. If I get to the River against only one opponent, I bet that too regardles of whether I hit a draw or not.

The 3bet may drive out the original Bettor and puts a lot of pressure on the Button, who may have been Raising with either the Flush or Straight draws.

That 3bet just screams "I have a Set" and may win you the hand even without hitting a draw.