Eli5: How do they effectively test scale models of giant ships in water? Doesn’t the water behave differently in the small vs large scale?

Question

Eli5: How do they effectively test scale models of giant ships in water? Doesn’t the water behave differently in the small vs large scale?

In: Physics

Answer 1

So there is this concept called ‘dimensionless numbers’, and they’re really effective tools to tackle the problem you’re asking about. Essentially, a dimensionless number has no physical dimension like time, distance, temperature, mass, etc. because they denote ratios of certain things. Let’s consider probably the most famous dimensionless number: the Reynolds number.

If you have a fluid flow it can be ordered, what we call laminar flow, or very chaotic, what we call turbulent flow. The Reynolds number tells us something about whether or not a flow will be laminar, turbulent or maybe somewhere inbetween. It can be calculated using a very simple formula:

Re = ρ • U • L / μ

In this equation ρ is the density of the fluid, U is the velocity of the fluid, μ is the viscosity of the fluid (how ‘thick’ the fluid is, syrup for instance has a high viscosity). L is more special, and is called the ‘characteristic length’. If you hold a sphere in a fluid flow L could for instance be the diameter of the sphere.

Say you have two spheres, a big sphere and a small sphere, but you want to have the same flow over the spheres. In that case what you can do is try to match the Reynold numbers of the two cases:

Re_big = Re_small

Because then the flows should be both laminar or turbulent. Say we have control over how fast the fluid flows, in that case we can work out a relation to make sure the Reynold numbers match:

ρ•U_big•L_big / μ = ρ•U_small•L_small / μ

U_small•L_small = U_big•L_big

U_small = U_big•L_big / L_small

So in order for the flow to also have e.g. a turbulent profile with the tiny sphere, the velocity of the flow in the tiny sphere case needs to be L_big/L_small as fast. Because the big sphere has a larger diameter than the small sphere, U_small will be higher than U_big.

There are other dimensionless numbers engineers can match to achieve different similarities between scale and full-sized models in the same way.