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I'm trying to find the viscosity of three fluids for a lab. We measured how fast a metal ball will fall through each fluid. we were given:

mass of ball = 8.5g, radius of ball - 5.94mm

from this I found a density of 9682.13kg/m^3

One of the fluids used was water. The experimental density of water was found to be 990 kg/m^3

the time it took the ball to fall 10cm in the water was 3.12sec, making the velocity 0.032m/s

We calculated viscocity using the formula : $$\mu =\frac{2g\,r_{ball}^2(\rho_{ball} - \rho_{fluid})}{(9\,v_{ball})}$$

when I did this I got 20.877 Pas. The accepted viscosity of water should be around 0.001Pas, so I'm just wondering what I'm doing wrong here.

I also rearranged the viscosity equation to find velocity using 0.001Pa*s for viscosity, and I got a velocity of 668.58m/s which seems way too fast. Any help would be greatly appreciated.

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  • $\begingroup$ Check for unit consistency. $\endgroup$ Mar 9, 2021 at 16:07
  • $\begingroup$ Do you notice anything wrong with the units? I've gone through it a couple times and I thought I had everything converted correctly. $\endgroup$
    – catman
    Mar 9, 2021 at 16:21
  • $\begingroup$ If you are using Stokes Law then do check the formula.. you seem to have a lot of extra factors $\endgroup$ Mar 9, 2021 at 16:22
  • $\begingroup$ Hi and welcome to physics.SE! Please do not post formulae as plain text, but use MathJax instead. $\endgroup$
    – ACuriousMind
    Mar 9, 2021 at 16:28
  • $\begingroup$ I accidentally typed the formula in wrong. It should be fixed now. This is the formula the professor told us to use. $\endgroup$
    – catman
    Mar 9, 2021 at 16:51

1 Answer 1

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Assuming that there is nothing wrong in calculation (I haven't verified this), what might be going wrong is the fact that Stokes Law relates viscosity with the terminal velocity. So, $3 cm$ distance is not enough for the object to attain terminal velocity.

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  • $\begingroup$ That's what I was thinking too, but would that account for such a big difference? Also, let me know if I'm understand this wrong but would that then make the terminal velocity of the ball in water 668.58m/s? $\endgroup$
    – catman
    Mar 9, 2021 at 16:49
  • $\begingroup$ No to both questions actually. I find the density very strange. I don't think any metal element thats commonly used has that high density. So that would mean either the mass measurement has a large error or there is an error with radius measurement $\endgroup$ Mar 9, 2021 at 17:12
  • $\begingroup$ Ok thank you so much for the feedback. The mass and radius of the ball were given to us by the professor, so I'm assuming she just made them up and didn't really think about it too much. $\endgroup$
    – catman
    Mar 9, 2021 at 17:21
  • $\begingroup$ Ahh.. that explains the weirdness. Just to give an eg Iron only has a density of $7800\,Kg/m^3$. Your density seems to be pretty high for ordinary materials. $\endgroup$ Mar 9, 2021 at 17:25

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