Heh, sorry, but this is not up for debate. God has decided that viscosity of air will be increase with temperature, who's RRE to argue? Seriously though, just look up a viscosity/temperature table for air and you'll see what I mean. By the way, a 2.5" front section is typically used on 3" DPs because otherwise there would be oil filter clearance issues. Coinkidink? You tell me.
Okay, equation for head loss i.e. pressure drop, assuming incompressible flow, is as follows :
For a circular pipe,
head-loss = f * L/D * V^2/2g
f is a dimensionless friction factor which is a function of the Reynolds number,
L is the pipe length
D is the pipe diameter
V is the flow velocity
g is gravitational acceleration
I won't get into how to find f, but it can be calculated if you know the Reynolds number of the flow, which is in turn dependent on the velocity and viscosity. Look up some fluid dynamics texts and it'll be in there.
Now, any bends, contractions, expansions will have their own associated pressure losses, so as you can imagine, this gets pretty convoluted very quickly. All I can say is that the ideal IC pipe really depends primarily on the flow volume you are putting in.
If we were to assume that mitsubishi's engineers did the requisite flow modeling in specifying the engine, let's assume that the 2" IC pipe gives the minimum headloss for a stock engine's airflow. If we double the air flow through the pipe, making huge assumptions that all else are equal (e.g. air temperature/pressure etc), you end up with a pipe diameter of 1.32 larger than stock. To derive it, assume that you keep the same headloss, thus the above equation reduces to V1^2/D1 = V2^2/D2. Then using the relation that velocity = flow volume / x -sectional area, you end up with V2/V1 = (Q2*D1^2)/(Q1*D2^2). Combining the two equations will give you the result of D2/D1 = 1.32.
Now just add temperature and pressure influences to make it reflect reality a little closer.
