Q$\mathrm{.}2[$a$]$ The following data is from a test conducted in a laboratory on a turbine model:

Head at test: $8\mathrm{.}0$ m $,$ Unit power $\backslash (=9\mathrm{.}2\backslash )$

Unit speed $\backslash (=55\backslash ),$ Unit discharge $\backslash (=1\mathrm{.}25\backslash )$

$($a$)$ Calculate the efficiency at this operation point. $($b$)$ If a homologous prototype turbine works under a head of $24$ m $,$ for an operation point corresponding to the above data, calculate $($i$)$ its speed, $($iii$)$ discharge, and $($iii$)$ power developed.