# Fluid Mechanic Dynamic Similarity Question

1. Dec 8, 2013

### 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

2. Dec 8, 2013

### SteamKing

Staff Emeritus
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.