stage storage for underground pipe with slope

[dwitczak]

does anyone have an excel file that determines stage storage for an undergound pipe on a slope?

[vanderzwaagj]

If this is for a SWMM model application, I believe that SWMM will do this calculation for you. Just input the pipe at the desired slope with the downstream end at the node where you want to model the storage.

Otherwise, you could probably figure it out youself. The volume will be prismatic, so (I think) that Simpson's rule will yield an exact result, which reduces to the same equation as a cone because the far end is a point.

Vol = 1/3 * L * A

A = end area of a circular segment.
A = R^2*acos(1-d/R) - (R-d) *sqrt(2*R*d-d^2)
and of course L = d/S
S is slope, d is depth, R is pipe radius.

Someone correct me if I'm wrong, but I think this will at least give an excellent approximation.

[hatepoppy]

you can use a storage factor. basically, given pipe geometry, find the %full by flow area at each end of the pipe in question. average these %s and youll have a storage factor.

FULL PIPE VOL * STORAGE FACTOR = STORED VOLUME

it's an interpolation of %full in the pipe. with steep slopes and long pipes, it may be necessary to subdivide the pipe to make sure the bottom stays wet. if not, your storage factor will be off.

let me know if you need more detail.