Apply the conservation of volume (see Prob. 1.9) to sim­ulate the level of liquid in a con...

Apply the conservation of volume (see Prob. 1.9) to sim­ulate the level of liquid in a conical storage tank (Fig. P1.11).

Figure P1.11

The liquid flows in at a sinusoidal rate of Qin = 3 sin2(t) and flows out according to

Qout = 3(y − yout)1.5   y > yout

Qout = 0   y ≤yout

where flow has units of m3/d and y = 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 = 0 to 10 d with a step size of 0.5 d. The parameter values are rtop = 2.5 m, ytop = 4 m, and yout = 1 m. Assume that the level is initially below the outlet pipe with y(0) = 0.8 m.