Question 134522
First and formost we should know that that the size of a given hose is always referring to the INSIDE DIAMATER.
Therefore given 2-1/2 inches rad. hose, outside diameter where the clamp is will be around 3 inches, depending still on the thicknes of the hose.
Now, since you have  a clamp with a length of 7 inches, the maximum hose diameter this can go is 1-1/2 inches inside diameter only (approx. 2" out.dia)
Why I know? Because I currently work for hoses & fittings for many years now.
There's no direct formula with a given length clamp to cover a hose. The sizes of clamps are generated because of "actual" measurement, not by formula.
Then they just put a tolerance to a minimum-maximum diameter of the clamps to cover because thickness of hose varies because of different manufacturer. There's no standard size for thickness anyway. 
Any feedback please you're most welcome.
Thank you.