On the first test we looked at a cooling tank for a radioisotope test facility. From Geometry and calculus we can determine that the relationship between the volume of the heavy water (m^3) and the height of the water (m) in the storage tank is given by the following equation:
V = pi . h^2 . ((3R - h) / 3) - equation 3
Additionally, the outflow of water Q (m^3/s) is given by
Q = CA (square root 2gh) - equation 4
where A is the exit area of the water outflow (use d = 0.05m to calculate A), h is the height of the water, g is the gravitational constant (9.81 m/s^2), and C is a coefficient = 0.63.
There is no need for a solver for h, since the differential equation is re-written in terms of h rather than volume:
dh2/dt = -2*C*A*sqrt(2*g*sqrt(h2))/(pi*(2*R-sqrt(h2))),
where h2 = h2, and other details are explained in the comments in the ...
This solution explains numerical methods differential equations.