$1-$ A twin$-$screw ship has two steam turbines each producing a shaft power of $11500$ kW at $3000$ rpm $.$ The turbines are connected to the two three$-$bladed propellers through reduction gearing of ratio $12$:$1.$ The shafting efficiency is $0\mathrm{.}940.$ The effective power of the ship is as follows:

$\backslash$table$[[$Speed$,$ knots,:,$30\mathrm{.}0,32\mathrm{.}0,34\mathrm{.}0,36\mathrm{.}0,38\mathrm{.}0],[$Effective Power, kW :$,9329,11693,14457,17658,21337,25533,]]$

The wake fraction, thrust deduction fraction and relative rotative efficiency based on thrust identity are $0\mathrm{.}000,0\mathrm{.}050$ and $0\mathrm{.}990$ respectively. The depth of immersion of the propeller axes is $3\mathrm{.}2$ m $.$ Design the propellers using the Gawn Series data given in Problem $1$ and the Burrill cavitation criterion for warship propellers.