Stage-Storage of Sloped Pipes
Stage-Storage of Sloped Pipes
(OP)
Does anyone have or know of a program to calculate the volume of a circular pipe on a slope in user definable increments. Our office is developing a spreadsheet to do this but it is turning into a lot of work. This would be used in calculating a stage-storage curve for routing an underground stormwater management system. We currently analyze pipe systems as if they are flat. Any help?





RE: Stage-Storage of Sloped Pipes
For a partially full circular pipe, with a depth at the end of D, slope of S, and radius of R
Where: y = D - R (can be negative)
[((PI*y*(R^2))/2) - (SQRT(((R^2) - (y^2))^3)) +
((R^2)*((yARCSIN(y/R)) + R*SQRT(1-((y/R)^2))))]/S
Nothin' to it! You can email me at parkscad@parks.state.nv.us if necessary
RE: Stage-Storage of Sloped Pipes
Assuming that the lower end of the pipe is full and the you know the slope and the elevation of the water surface: Calculate the length to the point where the top of the pipe is at the water/air interface. Then, calculate the length to the point where the bottom of the pipe is at the water/air interface. Add these lengths, divide by two, and multiply by the cross section area of the pipe.
RE: Stage-Storage of Sloped Pipes
PI*(R^2)*(R/S) or (1/2)*PI*(R^2)*(D/S)
where depth divided by slope is the length, which is the same as BillHolt's solution
The full formula should give a solution for situations where the pipe is not full at he lower end; i.e. Depth at the lower end of the pipe is less than the diameter of the pipe. Note that depth should be measured normal to the flowline of the circular pipe for the formula to work properly, if depth is measured on a plumb line then a slight error is introduced due to the slope of the pipe, but the error is going to be negligible for most practical purposes at slopes less than 10%.
RE: Stage-Storage of Sloped Pipes
RE: Stage-Storage of Sloped Pipes
Good luck!