Chapter 1, Problem 10P

For the same storage tank described in Prob. 1.9, suppose that the outflow is not constant but rather depends on the depth. For this case, the differential equation for depth can be written as

$\frac{dy}{dt}=3\frac{Q}{A}{\sin }^2\left(t\right)-\frac{\alpha {\left(1+y\right)}^{1.5}}{A}$

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 $A=1250{\text{ m}}^{\text{2}},Q=450{\text{ m}}^{\text{3}}\text{/d, and }\alpha =150$. Assume that the initial condition is $y=0$.