first time on this site. In my current work, I deal with mainly hydraulic related calculations, and the remainder of my math skills have become pretty lack luster. On looking through a spreadsheet in work, designed to calculate the size of a drainage basin (like an upside down pyramid, with the top chopped off) I spotted a volume error, but my math eludes me how to fix it. I have attached a crude sketch to help illustrate the problem.
We have a rectangular basin of a pyramidal frustum shape. Q represents the water flowing in, D (Depth) is the depth of water in the basin, and A (area) is the surface area of the surface of the water, both which increase over time. I ( Infiltration) is a constant of the water infiltrating (being removed from basin volume), and acts over the area A. so A*I*t= Volume removed, and Q*t = volume added. (Q*t)-(A*I*t) = Volume in basin; t=time.
I need to find a relationship that can compute the surface Area, A, at a step in time, with a varying flowrate. As (A*I*t) increase with depth, I realize some voodoo magic integration is required, but I haven't touched it since uni, and I'm unsure where to start.
I apologize if this is the wrong forum, mods please move if it is.
Anyway any help is very much appreciated.