Fluid Mechanics Viscosity Question 306
Question: If a ball of steel (density$ \rho =7.8g,c{{m}^{-3}} $ ) attains a terminal velocity of $ 10cm{{s}^{-1}} $ when falling in a tank of water (coefficient of viscosity $ {\eta_{water}}=8.5\times {{10}^{-4}}Pa-s $ ) then its terminal velocity in glycerin($ \rho =12gc{{m}^{-3}},,\eta =13.2Pa-s $ ) would be nearly
Options:
A) $ 1.6\times {{10}^{-5}}cm{{s}^{-1}} $
B) $ 6.25\times {{10}^{-4}}cm{{s}^{-1}} $
C) $ 6.45\times {{10}^{-4}}cm{{s}^{-1}} $
D) $ 1.5\times {{10}^{-5}}cm{{s}^{-1}} $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] $ v\propto \frac{\rho -{\rho_{0}}}{\eta } $ $ \therefore ,,,\frac{v_{2}}{v_{1}}=\frac{\rho -{\rho_{02}}}{\rho -{\rho_{01}}}\times \frac{{\eta_{1}}}{{\eta_{2}}}=\frac{7.8-1.2}{7.8-1}\times \frac{8.5\times {{10}^{-4}}\times 10}{13.2} $ $ =6.25\times {{10}^{-4}}cm{{s}^{-1}} $
BETA
