How can the coefficient of viscosity of a highly viscous fluid be determined by stokes method?

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Solution

$S t o k e s l a w s t a t e s t h a t v i s c o u s f o r c e F = 6 π η r v w h e r e η, r a n d v a r e c o e f f i c i e n t o f v i s \cos i t y, r a d i u s o f t h e s p h e r i c a l b o d y f a l l i n g i n t h e v i s c o u s m e d i u m a n d t e r m i n a l v e l o c i t y r e s p e c t i v e l y . L e t t h e d e n s i t y o f t h e b o d y a n d t h e m e d i u m b e ρ a n d σ . T h e w i e g h t o f t h e b o d y W = \frac{4}{3} π r^{3} ρ g a n d t h e b u y a n t f o r c e a c t i n g o n t h e w h e n m o v i n g w i t h t e r m i n a l v e l o c i t y v i n t h e l i q u i d W' = \frac{4}{3} π r^{3} σ g T h e r e f o r e n e t f o r c e a c t i n g d o w n w a r d s = \frac{4}{3} π r^{3} (ρ - σ) g B u t t h i s d o w n w a r d f o r c e i s b a l a n c e d b y t h e v i s c o u s f o r c e a c t i n g o n t h e b o d y i . e . 6 π η r v = \frac{4}{3} π r^{3} (ρ - σ) g o r η = \frac{2}{9 v} {r^{2}}^{3} (ρ - σ) g T h i s i s t h e r e q u i r e d m e t h o d .$

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