terminal speed

[newton1]

how to know the fluid resistance is depend on v or v^2 ??

[turin]

Are you asking why fluid resistance is velocity dependent? Or are you asking how to determine whether the dependence goes linear or whether it goes quadratic with velocity?

[Bob3141592]

Originally posted by newton1
how to know the fluid resistance is depend on v or v^2 ??

Well, you could look it up. Or you could run some experiments. A simple experiment might use a tub or water and a submerged block of wood, with a spring or rubber band providing a measurable force to move the block, and a stopwatch.

Experiments in the tub are always fun.

[Chen]

I'm going to guess it depends on v^1... let us know when you find out. [:)]

[JohnDubYa]

It is almost certainly a power series expansion in powers of velocity, with the linear term being the most important contributor. In other words:

F(v) = a v + bv^2 + cv^4 + ...

It would be a fun experiment to determine a, b, c,...

[kuengb]

The v^2 in the formula for turbulent current is an energy thing: the kinetic energy of the fluid whirls goes with v^2, and energy equals force times deplacement.