Apply the conservation of volume (see Prob. 1.9) to simulate the level of liquid in a conical storage tank (Fig. P1.11). The liquid flows in at a sinusoidal rate of Q_in = 3 sin²(t) and flows out according to

Q _out = 3(y – y_out)^1.5y  >  y_out

Q _out = 0 y ≤ y_out

where flow has units of m3/d and y 5 the elevation of the water surface above the bottom of the tank (m). Use Euler’s method to solve for the depth y from t 5 0 to 10 d with a step size of 0.5 d. The parameter values are r_top = 2.5 m, y_top = 4 m, and y_out = 1 m. Assume that the level is |initially below the outlet pipe with y(0) 5 0.8 m.

Cn top yam Cout