Is fluid resistance proportional to velocity or velocity squared?

[newton1]

fluid resistance

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.