A storage tank (Fig. P1.9) contains a liquid at depth y where y = 0 when the tank is half...

A storage tank (Fig. P1.9) 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 Liquid is withdrawn at a constant flow rate Q to meet demands.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 3Q sin²(t). Equation (1.14) can be written for this system as

or, since the surface area A is constant

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 m² and Q = 450 m³/d. Assume that the initial condition is y = 0.

Figure P1.9:

Equation 1.14: