Velocity - Viscosity/density? WHAAA?

[hasnoidea]

Hi forum,
This is my first post on this site, so please go easy on me :D
I'm a year 12 physics student doing an investigation.
We are given the freedom of choosing any field of physics to investigate.
I don't know what came over me as I chose a field I have never came across before: Fluid mechanics. Just the very simple aspects of fluids, but I am not sure where I stand in this uncharted field. So any help would be appreciated :D

My investigation involves me dropping a marble into a tall measuring cylinder filled with different types of oils and recording the marble's terminal velocity in each drop.
Initially, I have selected to investigate the relationship of Velocity and the Viscosity of each liquid. Hypothesising that the higher the viscosity, the lower the terminal velocity.

But the I found this thing called Stokes Law, it looks something like this...

Velocity = 2/9 * (density of object - density of fluid)/dynamic viscosity * acceleration due to gravity * radius of object squared

I noticed that the equation consists of both the density and viscosity, and density and viscosity is not related and is different for each each liquid (to my knowledge)
So now I cannot draw a relationship between the velocity and viscosity anymore, because following the equation, density will affect it.

I just want to know if I'm in the right track or if I have been derailed and am heading for a cliff...
I'd also like to know what I should do in regards to drawing some sort of relationship between the descent velocity and...SOMETHING!

Thanks for any help! :D

 

[SteamKing]

You are over-thinking this problem. You have a relationship between the velocity of an object dropped into a fluid, whose density and dynamic viscosity are known. The terminal velocity of the object is still directly proportional to the dynamic viscosity of the fluid. The density of the fluid is included in the relationship because the amount of fluid displaced by the dropped object affects the net force causing the object to sink (Net force = buoyant force due to displaced fluid - weight of object).

If you were going to test a fluid with unknown viscosity, you could use the results of a test with a fluid of known viscosity to find out the unknown viscosity. You would have to measure the density of the fluid in a separate task.

 

[boneh3ad]

In addition, Stokes flow only occurs at very low Reynolds numbers, so it won't apply to, say, a marble falling through water but may apply to a marble falling through corn syrup.

 

[hasnoidea]

You are over-thinking this problem. You have a relationship between the velocity of an object dropped into a fluid, whose density and dynamic viscosity are known. The terminal velocity of the object is still directly proportional to the dynamic viscosity of the fluid. The density of the fluid is included in the relationship because the amount of fluid displaced by the dropped object affects the net force causing the object to sink (Net force = buoyant force due to displaced fluid - weight of object).

If you were going to test a fluid with unknown viscosity, you could use the results of a test with a fluid of known viscosity to find out the unknown viscosity. You would have to measure the density of the fluid in a separate task.

Right, so it is fine to say that as the viscosity increases, the velocity decreases?

 

[hasnoidea]

In addition, Stokes flow only occurs at very low Reynolds numbers, so it won't apply to, say, a marble falling through water but may apply to a marble falling through corn syrup.

Yep, I also needed some clarification as to where Stokes Law could be used.
In my test, I'm dropping it in motor oil, so I hope it's enough to have the law applied into it...
Thanks!

 

[boneh3ad]

I don't remember the range of Reynolds numbers it is valid for (single digits if I recall correctly) but it would be easy to calculate your Re for the oil.

 

[hasnoidea]

Hi boneh3ad,

Thank you for your replies.
I was just wondering, as I am really quite ignorant to this fluid mechanics business, if you could briefly explain the concept of Reynolds number in my case.
I know it's got something to do with laminar flow and turbulent.

Thanks you!

 

[boneh3ad]

The Reynolds number is a non-dimensional measure of the ratio of inertial forces to viscous forces. It just tells you the relative importance of the different forces in the fluid. It is defined as
\mathrm{Re} = \frac{\rho V D}{\mu}

Where \rho is the fluid density (you may be able to find this and if not you could measure it with, say, a hydrometer), V is the fluid velocity (in this case the terminal velocity of the ball), D is some characteristic length in the flow (in your case the diameter of the ball) and \mu is the viscosity (which you should be able to find for common motor oil). If you find that number, you can see if Stokes' Law applies or not. Stokes Law is relevant for \mathrm{Re} \ll 1.

 

[DickL]

The above info you've been given is all good; use it. There is another possible consideration, the diameter of the ball you're dropping compared with the diameter of the cylinder you're using. If they are somewhat close to each other (my guess is 3:1 or closer) then you will also encounter flow restriction as the ball drops. The flow restriction will slow the ball's descent as well as the viscosity's resistance. This is the same phenomenon as the damping provided by a shock absorber. Of course this effect can also be calculated and made part of your experiment, but that would be getting you into another level of complexity.

 

[boneh3ad]

I seem to remember that there is a fairly simple correction for wall diameter for an approximate solution though. I can't remember off the top of my head. Do some Googling.

 

[hasnoidea]

Hi everyone,
Thanks so much for your help.
It has helped me to clarify some of the things I was not too sure of.
Also, I believe, the curriculum does not require me to do overly complex calculations.

Once again, thank you!

 

[hasnoidea]

Ahh, I've ran into another question.
I am also testing the velocity of the drop in an oil with different temperatures.
I know that as the temperature increases, the velocity also increase. This trend is apparent in my results.
I know (I think) that this happens because as the liquid is heated, the molecules' velocity increases, causing them to have less contact with each other, hence make it easier for the call to cut through them.
Can anyone verify that please?

Also, is there an equation or a law or something to prove this mathematically?

Thanks a lot!