Problem $1.$ A swimming pool drains down to a storm sewer through a pipe. Water exits the pipe $18$ ft below the surface of the full swimming pool. The end of the pipe is open to the atmosphere.

$($a$)$ Neglecting the effects of viscosity, find the velocity of the water leaving the pipe $($in ft$/$s$)$ and determine the volumetric flowrate $($in gal$/$min$)$ for a $3$ inch diameter pipe.

$($b$)$ If the pool is $50$ ft long and $30$ ft wide, estimate the time for the level in the full pool to drop by $4$ ft$.$