/diy/ - Do It Yourself

I'm building a fence. I want to use 2 by 4's for the rails but the short side (1.5") facing the boards. My posts are 6.5ft max apart. About 15 pickets between posts. 3.5 inch width pickets with 1 inch air gap, pickets only on one side. 5ft fence height, 2 rails between posts.

Should I be worried about it sagging or will it be strong enough? Brown Pressure treated pine is the wood. I'm doing this because I think it looks nicer and the screws I bought are too long if I orientate the 2 by 4's the other way. I think it would be OK, but I can't find the numbers to do the math.