Numerical Methods Differential Equations
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.
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Solution Preview
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 ...
Solution Summary
This solution explains numerical methods differential equations. The relationship between the volume of the heavy water and the height of the water is determined.