The drag force $F_D$ acting on a sonar sensor depends on its diameter $D$ and speed $V$ in a fluid

of density $$ and dynamic viscosity $.$ A prototype of $300$ mm diameter is towed at $1\frac{m}{s}$ in

sea water. A model has a diameter of $200$ mm is tested in a wind tunnel. Dynamic similitude

between the model and the prototype is enforced.

$($a$)$ Determine the speed at which the wind tunnel should be run.

$($b$)$ If the drag on the model is $25$ N $,$ estimate the drag on the prototype.

The densities of the sea$-$water and air are given as $1030k\frac{g}{m^3}$ and $1\mathrm{.}23k\frac{g}{m^3},$ respectively.

The dynamic viscosities of the sea$-$water and air are $1\mathrm{.}20{10}^{-3}N*\frac{s}{m^2}$ and $1\mathrm{.}79{10}^{-5}$

$N*\frac{s}{m^2},$ respectively.