Question

The termina lvelocity of a copper ball of radius 2mm falling through a tank of oil at 20C is 6.5cm/s. Compute the viscosity of oil at 20C.

Answer 1

Given,

$V_T=6.5\times {10}^{-2}m/s$

$g=9.8m/s^2$

$r=2mm=2\times {10}^{-3}m$

${\rho }_{co}=8.9\times {10}^{3}kg/m^3$

${\rho }_{oil}=1.5\times {10}^{k}g/m^3$

The terminal velocity is given by

$V_T=\frac{2r^2({\rho }_{co}-{\rho }_{oil})}{9\eta }g$

Viscosity of oil at ${20}^0$

$\eta =\frac{2r^2({\rho }_{co}-{\rho }_{oil})}{9V_T}g$

$\eta =\frac{2(2\times {10}^{-3}{)}^2(8.9\times {10}^3-1.5\times {10}^3)}{9\times 6.5\times {10}^{-2}}\times 9.8$

$\eta =0.9925Ns/m^2$