In my opinion a hydraulically calculated system is the only way you have any chance of making the 2 1/2" underground work.
The size of the building and the fact that the domestic water comes off the same 2 1/2" line is irrelevant. If your ceiling is 12' high the area of application with quick response sprinklers will be 945 sq ft.
The theoretical minimum amount of water the system will need is 95.5 gpm for Light Hazard and that doesn't change if the building is 1,000 sq ft or 50,000 sq ft the theoretical minimum amount of water you will need remains at 95.5 gpm.
Just the way it normally works we all know the actual amount of water you will need is around 110 to 125 gpm but we will work on that in a bit.
For above ground pipe we will use Sch. 40 and for the underground let's use Type M copper with an ID of 2.495"
Experience tells me you will need a double detector check so let's use an Ames Colt
[URL unfurl="true"]https://www.vikinggroupinc.com/sites/default/files/documents/ES-A-C200-C200N.pdf[/url]
Use Group B I am assuming it is an office or what? If it is an office the density will be .10 gpm but if a small mercantile shop it would be Ord Haz II with will be a density of .20 gpm over the 945 sq ft.
If Light Hazard space your K5.6 heads as close to 148 sq ft as possible so we achieve the 7.0 psi end head pressure. If Ord Haz use K8.0 heads spacing them as close to 106 sq ft as possible again to achieve the 7.0 psi end head pressure.
If spaced right for Light Hazard we will calculate 7 pendent sprinklers on 1" drops but now is not the time to scrimp on pipe size.. my branch lines will all be 2" with a 2 1/2" feed main. At 120 gpm I would estimate the total friction loss of the overhead system to be less than 6.0 psi but let's call it 8.0 psi to be on the safe side.
At the base of the riser we can expect to need 7.0 psi end head pressure plus 8.0 psi friction loss plus 12*.433=5.2 psi elevation for a total head requirement of 20.2 psi flowing 120 gpm.
At the backflow we can expect another head loss of 5.8 psi bringing us to a total of 26.0 psi at the base of the riser with the backflow assembly.
For the underground we have 340' of Type M copper and to this I added 40 equivalent feet of fittings just to be on the safe side for a total of 380 equivalent feet. Flowing 120 gpm our head loss through the underground is 0.035 psi/ft and we end up with an underground loss of 13.24 psi. At the street you will need 20.2+13.3=33.5 psi @ 220 gpm (I added the 100 gpm hose stream at the city connection). For Light Hazard this is easily doable with most city water supplies that I have seen.
In my opinion the only way to do this is by installing a hydraulically designed system... forget the pipe schedule.
If a shop we would be Ordinary Hazard Group II and we could run into difficulty.
Most likely you will have heads spaced as close to 106 sq ft as possible and we are going to calculate 10 heads. Overhead pipe will be 2" branch lines with 2 1/2" cross mains with cross mains looped if need be. The cost of the overhead system is negligible when compared to having to replace the underground with a 4" main so we will do whatever we have to design a system with the lowest possible pressure requirement.
With 10 heads flowing 21.2 gpm we will need around 220 gpm if we do it right.
At the base of the riser we can expect to need 7.0 psi end head pressure plus 10.0 psi friction loss plus 12*.433=5.2 psi elevation for a total head requirement of 22.2 psi flowing 220 gpm.
Head loss through the backflow will be about 6.0 psi bringing us to 220 gpm @ 28.2 psi at the base of the riser.
Our head loss through the 380 equivalent feet of 2 1/2" underground is 40.6 psi bringing us to a required supply of 470 gpm @ 68.8 psi which would be a problem in more than half the country (guess on my part) so I hope your building is an office and not a mercantile store.
I assumed a ceiling height of 12'-0" but if it is lower it would be to our advantage by maybe one pound. I assumed Type M copper but if Type K or Type L it would be to our advantage and, with that said, my guess is that it is Type L.