A fan needs at least the same area in the circumference of fan. Simple as can be. You can't move all a 153cm square area (140mm fan) can if the area feeding it is only 88cm square. 88cm square is the area of a 20mm space (feet on you case) around a 140mm circle.
Hope you understand.
Try this and see if it helps you understand. Take your 140mm fan and with it running move it from flat on top of you desk (or whatever flat surface you want to use) and put your face so fan is blowing at it. now lift the fan up to 10cm, back down to 5c, then 3cm, then 2cm. You will feel the difference. The closer you get to surface the less air the fan will blow up at your face... and the louder the fan will sound.
At the end of the day you will do want want to do. And that's fine with me.
Very often case design is for looks and appeal, not real function.