$(35$ pts$)$ A $3-$m$-$diameter tank is initially filled with water of height $2$ m$.$ There is a of a sharpedged $10-$cm$-$diameter orifice at the bottom of the tank. The tank water surface is open to the atmosphere, and the orifice drains to the atmosphere through a $100-$m$-$long horizontal pipe. The friction coefficient of the pipe can be taken to be $0\mathrm{.}015$ and the effect of the kinetic energy correction factor can be neglected. Determine $($a$)$ the initial velocity from the tank and $($b$)$ the time required to empty the tank.