The first question is "Why". If you have at least 40" across and as tall as needed, put in the 36" pipe.

The crossing is under a secured fenceline (prison) where the maximum pipe size is 8" for obvious security reasons.

Okay.. interesting problem.. but we're engineers so we can solve anything given enough money to pay for the solution. Suggestions from our office are:

1) Set up a spreadsheet with the equations for culvert flow and then for your pipe bank work out a Stage-Discharge curve so you can see where your hydraulic gradeline will be for various numbers of "layers" of 8" pipe.

2) Set up a holding tank and a pump and put a forcemain between the 2 36" sections.

3) Talk to a few pipe manufacturers and see if you can get 8" square conduit or a large conduit with interior walls 8" apart. For example, have a steel fabricator put together a grate with 8" holes that is however thick that satisfies the security concerns and then have a concrete company cast it into a box section. You'd probably want to oversize the pipe a bit to account for the losses though the grate, but installation of the box on site would be comparatively cheap compared to have to connect a whole pile of individual 8" pipes.

No matter what you do, the end result won't be cheap. But like I always say "We can do anything you want... but it'll cost you."

David Dietrich
Thames Valley Engineering

I've done the same type thing before. Rather than area you need to get an equivalent KD or conveyance factor. This will account for the increased wetted perimeter to area ratio that you get with multiple pipes. A 36" RCP has a KD=666 (with an n=0.013). An 8" pvc has a KD=14.3 (with n=0.011). So divide 66 by 14.3 and you get 46.6 or 47-8" PVC's are needed. If you did it by area only you would get about 21 pipes needed. You can see that the increase in wetted perimeter has a very significant effect. Make sure you connect the smaller pipes to the 36" at a junction structure that has access for maintenance (inside the security fence), because you are going to have debris collection problems.  

why is the maximum pipe size only 8 inches?  It isn't obvious to me!  Typically, a man cannot crawl through a pipe any smaller than maybe 18 or 24 inches.  I would like to meet the contortionist that could fit through an 8 inch pipe.  If the concern is that other material such as tools or controlled substances might make it through the pipe, even 8 inches would be too large.  I would review these design assumptions / constraints before going any further.

Greetings…

In the last six years I have designed and/or managed the design of civil improvements for three federal prisons and one state prison here in CA. ScottBortz is dealing with a real requirement, as strange as it may seem.

The Federal Bureau of Prisons currently requires that ALL pipes crossing under the double perimeter security fences be 8" or smaller. It used to be that water and sewer could be 12", but that changed just before my last prison project. I was told that they made the change was because a prisoner tried to get out through a 12" sewer!!! So now, nothing bigger than 8".

FYI, when I was younger I got inside a 20' stick of 18" pipe to check on a problem with a joint, and the forman on that job was so skinny he said he had once entered a 14" pipe to do the same.

Anyway, Scott, mroberts approach is a good one. Each of my three federal prisons had 48" SD pipes (well…1220 mm since this is a federal job!) in and out of the "pipe matrix" and I conservatively used 51x8" pipes. At FCI Herlong (the most recent) the 48" pipes have a slope of about 0.0008 and change, but we used 0.0025 for the 8" pipes in the pipe matrix.

On my first federal prison, which is the one where I did these calcs myself, I remember looking at this as a multi-barreled culvert problem with submerged inlet and outlet (a common condition in our flat country). Here's my approach:

*  To compare the hydraulics of one large pipe to several small pipes, set up Mannings Equation for full flow in a culvert in terms of Q (i.e. Mannings Equation + entrance and exit losses)…I hope this is typed correctly…

   Q = A * sqrt(dH/(((Kin+Kout)/2g)+((L*n^2)/((1.486^2)*(R^(4/3))))))

   Q = flow (cfs)
   A = pipe flow area (sf) = 0.25*pi*d^2
   dH = head loss across the pipe matrix (feet)
   Kin = entrance loss coefficient = 0.4
   Kout = exit loss coefficient = 1.0
   g = gravitational constant = 32.2 ft/s^2
   L = pipe length (feet)
   n = Mannings n
   R = hydraulic radius (feet)

*  Pick a head loss across the pipe matrix (it doesn't make much of a difference, I checked it for dH = 0.1' to 0.25' just because that's about what the guy who ran the hydraulic model got when he used a 48" pipe in lieu of the pipe matrix…and the answers were all pretty close)

*  Calculate the flow through one large pipe based on the equation above.

*  Calculate the flow through one small pipe based on the equation above, using the same head loss.

*  Divide Q(big pipe) by Q(small pipe) to get the minimum number of pipes you should use, then add a few more.

One caveat though: if your big pipes are not flowing full, then this method cannot be applied as described herein. Open channel flow in the large pipe would then equate to full flow in the bottom pipes in the pipe matrix and possibly open channel flow in the top row of the pipe matrix. Even so, my method should be sound.

I determined the slope of the pipe martix (0.0025) by assuming the bottom row of pipes in the pipe matrix were half full and I wanted about 2 fps.

I hope this helps…or at least isn't too confusing.

Fred

That is similar to low water crossings that I have done in the past and each would require hand or spreadsheet calculations.  Unless you are using a modeling software that allows you to put in a table of areas and wetted perimeters.  the only thing I have found was that the losses at the pipe inlets should account for the expansion losses for the ASCE methods seemed to match the best.

Could you not use slotted drains everywhere you need inlets and that way the prisoner could not enter anywhere and still allow a big enough pipe system?

Nope. The Federal Bureau of Prisons holds fast to their requirement of no pipe larger than 8" passing under the perimeter security fence…even water.

Fred

Wow,

See, it pays to read these posts, I found this thread to be fascinating.  I think that fel3 and mroberts were on the right track.  Thanks folks, I copied and made a memo to my files if ever I am asked regarding a similar problem.

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