A pipe discharges wine into a $1\mathrm{.}5m$ diameter tank. Another pipe $(15cm$ diameter$),$ located near

the base of the tank, is used to discharge wine out of the tank. In order to maintain wine level in

the tank constant, what is the volumetric flow rate of wine in the inlet pipe?

Note: Calculation the flow rate under two scenarios:

$(1)(5$ points$).$ Assuming the velocity of the liquid at the tank surface is zero;

$(2)(10$ points$)$ the velocity of the liquid at the tank surface is NOT zero