A cylindrical tank with a height of $2m$ and a diameter of $1\mathrm{.}5m$ is initially filled with water until halfway. Water is sent at a speed of $10\frac{m}{s}$ with a pipe with diameter of $0\mathrm{.}03m.$

The flow rate at the outlet of the tank is directly proportional to the liquid level in the tank and given by $F_1=0\mathrm{.}01h.$

Under these conditions;

a$)$ Does the liquid level in the tank decrease or increase?

b$)$ What is the time required for $90\%$ of the tank to be filled?