Chapter 1, Problem 11P

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 lows in at a sinusoidal rate of $Q_{\text{in}}=3{\text{ sin}}^{\text{2}}\left(t\right)$ and lows out according to

$\begin{array}{l}{Q}_{\text{out}}=3{\left(y-y_{\text{out}}\right)}^{1.5}y>y_{\text{out}}\\ Q_{\text{out}}=0y\le y_{\text{out}}\end{array}$

where low has units of ${\text{m}}^{\text{3}}\text{/d and }y=$ 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 $r_{\text{top}}=\text{2}\text{.5 m, }{y}_{\text{top}}=\text{4 m, and }{y}_{\text{out}}=\text{1 m}$. Assume that the level is initially below the outlet pipe with $y\left(0\right)=0.8$m.

FIGURE P1.11