An Ag Engineering problem

Cam solved an engineering problem last week. He did a great job. I’ll offer another. This is a diagram of a diversion, which is a very simple and common earth structure for diverting water. The question is to find the flow area (the area below the blue line). If the depth is less than 0.5 foot on the cross slope, the velocity is slow and not counted, thus the vertical blue line. The diversion height is 3 foot (-1.5 to +1.5), but there’s a 0.5 freeboard so the water depth is 2.5 foot. The cross slope (black line) is in percent, 100 foot horizontal to 1 foot vertical. The red slopes are 6:1 (6 foot horizontal to 1 foot vertical). For this section we want the cut/fill ratio to be 1.5. The amount of cut (blow black) is 1.5 times the fill area (above black line). The top width of the diversion is 4 feet and the bottom width of the diversion channel is 12 feet.

Note: The +1.5 and -1.5 was read from the graph, and are approximate. As you can see in the drawing the top is slightly above 1.5 and the bottom of the channel is slight above the -1.5
The exact difference is 3.000 however. Here's a hint. Lines pass through the origin to simplify the process. Moving the whole construction up or down is how the exact cut/fill ratio is obtained.

Question: What is the flow area? This is simple geometry, if you want to go further, then what is the amount of flow in cubic feet per second using Manning’s Equation, given other inputs?

Diversion


Inputs

Diversion Solution