$A^A$

$1\mathrm{.}9$ A storage tank $($Fig$.$ P$1\mathrm{.}9)$ contains a liquid at depth $y$ where $y=0$ when the tank is half full. Liquid is withdrawn at a constant flow rate $Q$ to meet demands. The contents are resupplied at a sinusoidal rate $3Qsi{n}^2(t).$ Equation $(1\mathrm{.}14)$ can be written for this system as

page $21$

FIGURE P$1\mathrm{.}9$

$\frac{d(Ay)}{dt}=3Qsi{n}^2(t)-Q$

$(\frac{\text{c}\text{h}\text{a}\text{n}\text{g}\text{e}in}{\text{v}\text{o}\text{l}\text{u}\text{m}\text{e}})=($ inflow $)-($ outflow $)$

or$,$ since the surface area $A$ is constant

$\frac{dy}{dt}=3\frac{Q}{A}si{n}^2(t)-\frac{Q}{A}$

Use Euler's method to solve for the depth $y$ from $t=0$ to $10$ d with a step size of $0\mathrm{.}5$ d $.$ The parameter values are $A=1250m^2$ and $Q=450\frac{m^3}{d}.$ Assume that the initial condition is $y=0.$