Question $1.(25$ points$)$

The hydraulic system shown consists

of $4$ tanks. initially, tank $(1)$ is filled

with water, while all other tanks are

kept empty. Water flows into Tank

$(1)$ at a rate of $Q_i.$

At $t=0,$ all valves to all tanks

connecting to each other is opened and water flows from tank $1$ to subsequent

tanks as shown in the figure. Assuming that the valve resistance for all tanks are

the same and is equal to