yes you are correct, no taper. you still need an exit at the bottom and a reservoir for what collects. I believe on my 1 1/2 inch in and out it was 2 inch at the bottom.
typically on a 1 d 3 d the length is 3 x the tube ID. having it shorter will give you a higher pressure drop across the cyclone than having it longer. At least that is what Stephen has found in testing.