Fluid Mechanic Dynamic Similarity Question

[Spoolx]

1. Hi All
I had a quiz in my fluid mechanics class with the question

A ship model scale 1/25 is towed through seawater at a speed of 1m/s. A force of 2N is required to tow the model.
Find the speed of the ship if the prototype is subjected to wave resistance only.



2. REm=REp
CD=F/.5ρV^2A
RE=ρVD/μ



3. My attempt was comparing the two Reynolds numbers and solving for the velocity
my professor marked me wrong and said "Cannot match the RE numbers"

Any guidance is appreciated

 

[SteamKing]

Wave resistance doesn't scale too well by Reynolds Number.

For ships, Re = ρ V L / μ

Since both the model and the full sized vessel are presumed to operate in seawater, ρ and μ cannot change. To use the same Re for the full size ship as the model implies that V*L remains the same. However, the scale factor requires that L(ship) = 25*L(model), which then requires V(ship) = V(model)/25 to maintain the same product V*L for both the model and the ship.

The wavemaking resistance of a ship to that of a model is based on other factors than having the same Re. Actual vessels operate at much higher Re than can be simulated with models.