There is a number out there for feet or meters per second for the speed of flowing water where below that number it does NOT cause erosion. Do you know what that number is? I used to know it but it has had so much other stuff piled on top of it that I can't seen to remember what it is.
That's how you determine how wide to make an earthen emergency spillway. Calculate the amount of water coming in, then run the numbers to make the emergency spillway wide enough so that volume of water is running less than "X" fps.
Below is the link for water flows thru channels. (I hope this is the data you remember, esshup.) I use this data since an emergency spillway is a form of a channel. The relevant chart is on page 6.
However, anyone utilizing this data also needs to read the technical discussion to use it correctly.
USDA - Erosion in Channel Flows PDF
