Volume of trapezoidal channel

[stioffan]

I'm wondering if anyone has another method of determining the volume of water that is detained in a trapezoidal channel with check dams that measures 2.5'H x 8'BW x 18'TW (2H:1V sides). Check dams are the H (2.5') and are spaced 78' apart. Longitudinal slope of the swale is 0.032ft/ft.

I am just calculating the volume of a trapezoidal pyramid to get the volume of water. (1/3A*h - Where A is the area of trapezoid and h is length of swale) So behind one check dam I can get 845cf of storage before overtopping. It seems right to me. Anyone see a flaw with this?

 

[Ryb01]

I would approach the storage volume by calculating the channel area at the check dam first. From some quick math, based on the dimensions you've provided I get an area of approx 32.5ft sq. Since the storage area will decrease to zero at the upstream limits due to the longitudinal slope of the channel, you could take an average area of 16.25 ft sq(32.5 +0)/2 and multiply by the length of 78ft to get a total volume of 1,267.5 ft3.
Hope this helps.

 

[CarlB]

I agree that the 1/3 the area times the length versus 1/2 would be more accurate for a prism that tapers to a point, so I get the same value as you. Not sure i follow the dam being the same height as the channel, would this cause some flow around versus over the dam?

 

[gbam]

Rybo1 is correct on his approach using Average end area. The volume is 1268 CFT, not 845. You will be under estimating the volume. Assuming a flat Trap 2.5' deep you will get about 2535 CFT. Half of that is the Volume. Of course this does not account for slopes on the check dams. This approach assumes vertical ends.

 

[Drew08]

To be a bit more accurate:

V = L[BH/2 + zH^2/3]
Because it tapers to a line, not a point.

Solved by integrating the area B(xS)+z(xS)^2 from length x = 0 to L,
Where the water depth at any location = xS

L = length of channel
B = base width
H = maximum depth of water
z = channel side slope
S = channel longitudinal slope

 

[stioffan]

Thanks to all. I forgot I posted (being under the cosh), but I did end up realizing that the channel tapered to a line and did it the same way as described Ryb01. Thanks again guys.