A rancis turbine develop; $800$ kW at efficiency of $90\%$ under a net head of $12$ m $.$ The draft tube used in this setup is a vertical cylindrical pipe of $2\mathrm{.}0$ m dia!neter. $($a$)$ What increase in power could be expected if a tapering vertical draft tube having an outlet diameter of $2\mathrm{.}5$ m replaces the existing cylindrical draft tube? $($b$)$ What would be the increase in the overall efficiency? Assume that the head, speed and discharge remain the same and there are no additional friction losses due to the new draft tube.