A$7-4$ Water at $20C$ flows steadily through a tank, entering at a volumetric flow rate of $100\frac{m^3}{h}r$ through a $6$ cm diameter inlet, and exiting with an average velocity of $8\frac{m}{s}$ through a $5$ cm diameter outlet. A third opening on the tank, with $4$ cm diameter, may act as an inlet or outlet for water flow. Determine $($a$)$ the volumetric flow rate in $\frac{m^3}{h}r$ in or out of the tank at this third opening, and $($b$)$ the corresponding average velocity in $\frac{m}{s}.$