QUESTION $9$

As shown in the figure, a sonar array is towed behind a towing boat. The drag force of the sonar array is to be studied in a water tunnel at a scale model $($model $\frac{1}{4}$ the size of the prototype$).$ The drag force $(D)$ is assumed to be a function of the speed of the ship $(V),$ the density and viscosity of the fluid $(,),$ and the diameter of the sonar array $(d).$

$(1)$ Give the dimensional analysis to the problems using the variables listed.

$(10)$

$(2)$ If the prototype towing speed is $3\frac{m}{s},$ determine the water velocity in the tunnel for the model tests.

$(3)$ If the model tests of part $($a$)$ produced a model drag of $900$ N $,$ determine the drag expected on the prototype.

$(5)$