Given a rocket with a propellant flow rate of $\backslash (5\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$s$\}\backslash ),$ featuring a nozzle with an exit diameter of $10$ cm $,$ the pressure at the nozzle exit is $1\mathrm{.}02$ bar, and the surrounding ambient pressure is $1\mathrm{.}013$ bar. The pressure within the thrust chamber is maintained at $20$ bar $,$ and the rocket produces a thrust of $71$ kN $.$ You are tasked to:

$1.$ Determine the specific impulse of the rocket.

$2.$ Calculate the specific propellant consumption rate.

$3.$ Compute the effective velocity of the jet expelled by the rocket's nozzle.