Question

STOKES law.. driving me nuts
Is stokes law really that useless? doesn't work with anything :X :X

http://www.youtube.com/watch?v=K389Fw2U5sk

i took this video.. and using the video i carefully calculated the terminal speed
then i used stokes law to find out the terminal speed.. i get insane answers

here is the data

Answer 1

density of ball = 7.8 g per cm cube
density of syrup = 6.1 g per cm cube
viscosity = 200 mili Pawsuwee

stokes law gives

\[v_{term} = \frac{2}{9 \eta}(\rho_0-\rho)gR^2 = 0.066(R_{mm})^2\]

so i did the calculation.. if u just plug in R value in milimeter u get the value

From video for 3/32 (1.19mm) inch ball i get v = 0.67 cm/s
but if i plug in the value in my formula i get 9 cm/s

can someone help? :(

Answer 2

"density of syrup = 6.1 g per cm cube" = that is by mistake its 1.6 g/cm^3.. igav the subtracted value!

Answer 3

@chmvijay

Answer 4

Stokes's law is very useful for small particle behavior (aerosols, sprays, dispersions). The Reynolds number (Re = rho v d / mu) must be very small, <<1, so that viscosity is the primary resisting force,
F = 3 pi mu v d for a sphere of diameter d moving with relative velocity v in a medium of viscosity mu. As you know, the force of gravity is reduced by the buoyancy. F= (rho - rhom) V g, the difference in densities times the volume times gravitational acceleration'

Answer 5

thanks douglas .. so basically the spheres here are too big?
so its something like less than 0.05 mm ? anything about that and stokes law is invalid huh?
is there any video where i can use stoke's law?

Answer 6

You are welcome. Whether or not to use Stokes does depend on the particle size and density and the density and viscosity of the fluid. In air, Stokes's law for gravitational settling would generally need correction for particles larger than 0.05mm which is 50 micrometer, microns. One would start with Stokes, calculate a velocity, compare the particle Reynolds number against Re<<1 and refine Stokes or go to another expression if the Re is not <<1. Sorry not to know a video to recommend.

Answer 7

thank you .. :) :) :).. thanks a lot

but atleast the r^2 relationship holds good.. thank god for that.. something works :D

Answer 8

Glad to help.

Answer 9

hey.. actually i took viscosity wrong.. i took viscosity as 2800 mPl.. which is usually the case for honey

(2000 to 3000) then i got proper values :D