So say I have a dam, with a max capacity of 3,538,000 acres FT of water. It's currently storing 1,796,250 acre FT of water. Water is flowing IN at a rate of 1,050 cubic-FT per second, and out flowing at a rate of 2,630 cubic-FT per second.
I cannot for the life of my figure out how many DAYS it would take to empty the dam completely. So far the only part I get is that I need to first figure how much water is flowing OUT a second, which is simply 1580 cubic-FT per second, and then use that number and somehow convert to acres-ft and divide it by the stored amount..? Can anyone help me out with the process of this problem, for some reason I can't wrap my head around it.
Your problem is the different units. Remember that "acre" is a measure of area and we should convert to another measure of area such as square feet.
One acre is $43560\, \mbox{ft}^2$
Just multiply this by the given volume to get the volume in $\mbox{ft}^3$ and then divide by the net flow rate that you calculated.
This will give the time to empty in seconds. You will need to convert that to days by dividing by $24\times 60\times 60$.
I think you should be able to take it from here.