A $30,800-$tonne ship is $220$ m long with a required speed of $20$ knots. Its resistance test model is

$5$ m long. Based on the principles of geometrical and dynamical similitude, determine the following, assuming $15\backslash$deg C seawater for the ship, and $15\backslash$deg C fresh water for the model.

a$)$ The required displacement of the model in kilograms.

b$)$ The model speed $($m$/$sec$)$ to represent the ship at $20$ knots.

c$)$ The Froude numbers of the model and ship at their respective speeds.

d$)$ The Reynolds numbers of the model and ship at their respective speeds.