# Viscosity and velocity

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.

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

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.
• 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. Mar 9, 2021 at 17:25