SORU $28$

Wave$-$making drag $D_w$ of a ship hull can be expressed as $D_w=f(l,U,,g),$ where $l$ is the ship length, $U$ the ship speed, $$ the fluid density and $g$ the gravity. $($a$)$ Use dimensional analysis and find a suitable set of dimensionless pi parameters for this problem. Use $l,U,$ as repeating variables. $($b$)$ A towing tank experiment is planned for a $1/25-$scale model in fresh water $(=999k\frac{g}{m^3})$ for a $100-$m long prototype ship cruising at a design speed of $16\mathrm{.}3$knots in sea water $(=1,030k\frac{g}{m^3}).$ Determine the model towing speed to achieve Froude scaling $($or the Fr similarity$).($c$)$ Fig. $6$ shows the relationship between wave$-$drag coefficient $C_W$ and Froude number Fr$.$ Estimate the wave$-$making drag for each of the model and prototype ship. $($Note: $1$ knot $=0\mathrm{.}5144\frac{m}{s}$