deter cut volume for a channel

[KenLucas1]

Can someone offer me a comment on how I could use arc pro [w/ both spatial & 3D analyst tools avail] to determine the amount of cut [in feet] from the existing ground surface down to a flow line that would allow water to drain to the south [instead of the north as present] along the red line?  I have accurate contour data for these horse corrals.