Please, Nathan, NEVER fall into the trap of specifying a pressure of "100 psi". This lazy terminology will always beg the question "is that 100 psia or 100 psig? If it is psig what is the local atmospheric pressure?" Avoid that predictable dialog by being careful to say "psia" or "psig and local atmospheric pressure is 12.3 psia".
There are a lot of ways to approach this, and all of them are (to varying degrees) wrong. It is basically an HVAC branch problem. The difficulty is accounting for exit losses into each of the branches.
My approach (that works, but doesn't give you the absolute minimum) is to size the trunk as though the entire flow was making it to the end with adequate pressure (you didn't say what the expected pressure at the branches had to be, more information leads to better help). Let's say that you can only tolerate 0.25 psid in the trunk. I'd go to the isothermal gas flow equation and find the standard pipe diameter (rated for 2200 psig) that gives me less than 0.25 psid. At 100 psig it is unlikely that the process would benefit from a tapered header like you often see in HVAC systems (which run at very low pressure).
I know that in most engineering programs empirical fluid mechanics problems are frowned upon (and mostly absent). In real life engineering we use empirical equations almost exclusively. If you want to end up as an effective engineer, you should temper the (mostly useless) theoretical engineering stuff that you're learning in school with a strong dose of how stuff really works. Buy a copy of Crane Technical Publication 510, Cameron Hydraulics, and the GPSA Field Engineering Data book. Buy them now, with your own money. Don't loan them out. I recently sat down and thought "what do I wish I had known when I was starting out?" Things like the fact that there are almost no closed form fluid mechanics equations and how do I pick one empirical equation over another? So I wrote a book
Practical Onshore Gas Field Engineering that addresses as many of these issues as I could get into 600 pages. Take a look at it, it could be useful temporizing the ivory tower stuff that you get buried in during your college years and then never use again.
[bold]David Simpson, PE[/bold]
MuleShoe Engineering
In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist
