Please let me explain this situation, I have a ditch which is being filled with rain, the ditch is emptied and can also act as storage if inflow>outflow.
Q_in-Q_uit=∂V/∂t
Q_in=A*I/1000=[m^3/h], with A area where rain falls, I intensity
Q_out = k_stricklerA_crossR^(2/3)*i^(1/2), With
R = hydraulic radius = A_cross/ Perimeter
A_cross = cross section of the ditch = (0.5B1H)+(B2H)+(0.5B3*H)
Perimeter = √(H^2+B1^2)+B2+√(H^2+B3^2)
See cross section here With B1 = 1.25 m, B2 = 0.1, B3=1.25 (but these can be tweaked and optimised)
i = height difference over the length of the ditch =around 0.2/180 =0.001 [-]
Now my question is the follwing: How do i have to solve this, I am doubtfull about the step ∂V/∂t = A_cross * dh/dt. can i do this?
Now how do i want to solve this, i want to know which dimensions i need to have an equilibrium so the ditch does not flow over, But the ditch needs to be as small as possible (Total width between 2-3m and depth 0.5-1 m)
Can I also deduce that if there is a rain intensity of f.e. 40 mm/h = 40 L/m2/h that after how many minutes the ditch is full and starts to flow over.
I hope my question are clear, I am able to use Pyhton (jupyter) to solve this.