Q:

The faster you move through air, increasingly(exponentially?) more power is required to keep accelerating. Because water is near as makes no difference incompressible, does it resist movement more faster you move like air does?

- Jukka Arvila (age 27)

Finland

- Jukka Arvila (age 27)

Finland

A:

First, a slight correction to the description in your question. In these fluids you need more power just to keep moving at a fixed rate through the fluid. Extra power is needed to accelerate, but it's not especially dependent on how fast you're moving.

At low speeds, the power required to keep moving just grows linearly with the speed. For a given speed, the power needed is much bigger in water than in air. That's described by saying that the "viscosity" of water is much bigger than of air. At higher speeds, the drag becomes quadratic in the speed. Once again, the drag is much bigger for water than for air, in this case because the density of the water is much bigger than the density of the air. The compressibility in itself is not directly very important for either of these types of drag.

Here's a way to start thinking of both of these ranges. At low speeds the moving object bumbs into particles of the fluid, giving them some of its momentum. The more momentum the object has, the more that gets transferred on each such collision. This momentum diffuses away in the fluid, going randomly from one particle to the next. The key factor is how rapidly momentum diffuses away in the fluid, described by the viscosity.

At higher speeds, the effect looks more like the object forcing the fluid it collides with to move with it. The amount of material encountered is linearly proportional to the speed, and so is the velocity imparted to that material. So the momentum loss per time (drag force) is proportional to the square of the speed. The key fluid property then is the mass of that region of the fluid, which depends on the density.

There's a Wikipedia article that discusses these effects in greater detail, although perhaps not in a way that's easy to follow: .

Mike W.

*(published on 05/30/2015)*