$(30$ pts$.)$ Gasoline at $15\mathrm{.}6C$ flows from a large open tank through a variable diameter pipe and discharges into the atmosphere with a velocity of $3\mathrm{.}84\frac{m}{s}.$ The diameters of the pipe shown below are $d_1=2\mathrm{.}75cm,d_2=5cm,$ and $d_3=10cm.$ The distance between the gasoline free surface and the center of the pipe is $75cm.$ Atmospheric pressure is $98$kPa and the absolute vapor pressure of Gasoline is $51\mathrm{.}3$kPa. Assume the flow is steady, incompressible, and inviscid.

$($a$)$ Draw all streamlines required for analysis.

$($b$)$ Determine the velocity of the gasoline where the diameter of the pipe is the smallest.

$($c$)$ Determine the static pressure of the gasoline where the diameter of the pipe is the smallest.

$($d$)$ Does cavitation occur within the pipe? Why or why not?

$($e$)$ If cavitation does or does not occur, how would you change the diameters of the pipe to either stop or cause cavitation in the pipe?

$($f$)$ Sketch the Energy Line and Hydraulic Grade Line for a streamline from the free surface to the pipe exit.