you first need to determine your criteria for blockage.  For the safety factor, you might assume that half the rack is blocked.  You will then want to look at the other half and determine the area obstructed by the bars.  The remaining area should be equal to or greater than the cross sectional area of the 36" pipe.  In order to get a large enough capacity, you might want to consider the sides of your "box" are also open.

I’m thinking that sum of the individual areas of the openings of the racking would have to be significantly larger than that of the pipe. the pipe's Hydraulic Radius is approximately 9" where an individual opening on the  racking is 0.5" approx. because the Hydraulic radius  of the rack does not change the larger it gets (The area of the racking is just multiplies of little area/ little perimeters)I am looking for some sort of relationship between the racks Rh and Pipes Rh.

I am basically trying to reduce the K value of the trash rack to zero.

what do you peoples think?

Like cvg said, the blockage criteria is important.  What is allowed to pass through the pipe?

This product does not go up to 36":

http://www.agridrain.com/surfaceproduct.asp?prodtype=304

but the design does try to divert larger objects off of the inlet.

to make the k value of the rack zero, it will have to be sufficiently large enough so that headloss is negligble.  Not normally possible - so headloss through the rack should be estimated and included in your analysis

I would suggest taking a look at the Federal Highway Agency's manuals

HDS 5 (culvert check the safety section for how to clculate flow loss through safety (or debris) grates

HEC 9 on debris protection for bridges and culverts.  The FHA has some very nice trash racks.  Also debris deflectors which I like in more urban areas.

You always have head loss, though say a post and cable system that is about 10 times the culvert width tends to have a minimal loss, but as cvg suggests the biggest loss is typically the debris stuck to the rack.

I look at a lot of trash racks.  One item I would suggest is to look at nearby dams or highway culverts.  Every area has different trash (construction material to cornstalks with a lot of sediment in the middle).

A good design is another open length of larger diameter pipe surrounding the entry pipe with the top 3' above the entrance and the bottom 3' below. A six foot length of 72" diameter corrugated culvert with either solid walls or perforations installed vertical around the 36" diameter inlet.

this is the soulution I came up with..

I looked up the head loss as a percentage of 100' length of steel pipe at 36"dia at 120000gpm (approx 10%). Equated it to that of a pipe of a similar hydraulic Radius of the small grating openings( approx 1" x 4"), took that gpm and divided it into the 120000gpm, and got a resulting number of small openings.

Ended up with an intake of 8' x 12' taking in account of 25% blockage safety factor.

You can check it against this.

http://www.knoxcounty.org/stormwater/pdfs/vol2/3-3-5%20Trash%20Racks%20and%20Safety%20Grates.pdf