Problem Model tests for ships are carried out under the condition that Froude number $Fr=\frac{v}{\sqrt[\phantom{2}]{g{L}_{WL}}}$ of ship and model are the same, i$.$e$.$

$Fr=\frac{v_S}{\sqrt[\phantom{2}]{g{L}_{W{L}_S}}}=\frac{v_M}{\sqrt[\phantom{2}]{g{L}_{W{L}_M}}}$

Subscript ${?}_S$ indicates full scale ship properties and subscript ${?}_M$ model properties.

$($a$)$ Compute the Froude number Fr for a ship of water line length $L_{W{L}_S}=183\mathrm{.}0m$ sailing at a speed of $v_S=22\mathrm{.}4kn.$ Use $g=9\mathrm{.}807\frac{m}{s^2}$ for the gravitational acceleration. Make sure you use consistent units! Remember that $1kn=1852\frac{m}{3600}s=\frac{0\mathrm{.}5144}{b}ar(4)\frac{m}{s}$

$(2$ of $50$ points$)$

$($b$)$ At which speed $v_M$ will the model be tested if you build a model at scale $=\frac{L_S}{L_M}=28?(2$ of $50$ points$)$

$($c$)$ Compute the Reynolds numbers $Re=\frac{v*L_{oS}}{v}$ for full scale ship and model under the conditions stated above. The length over wetted surface of the full scale vessel is $L_{O{S}_S}=189\mathrm{.}2m.$ Kinematic viscosity of sea water at $15$ degree Celsius is

$($