I don't have more than a high-school physics education (and even then, that was like 3+ years ago), so pardon my noob-ness.

What is the formula/how do you figure out how much bigger the pipe needs to be in a bend so that it acts like it's the same size as the pipe before it? Like say you have a 1.5" ID straight tube, then you have a smooth bend. What size ID does the bend need to it to 'act' like the 1.5" straight pipe?

Like Bisi's header, it's a bunch of curved bends that are a 'large' diameter, but because the laws of physics (and shit that I have no clue about...), the curves 'act' like a straight pipe of a smaller diameter.

Attached image is a picture of some Lotus with a engine making around 280hp, NA.