When a sphere of radius `r_(1)=1.2` mm moves in glycerine, the laminar flow is observed if the velocity of the sphere does not exceed `v_(1)=23(cm)/(s)`. At what minimum velocity `v_(2)` of a sphere of radius `r_(2)=5.5cm` will the flow in water become turbulent? The viscosities of glycerine and water are equal to `eta_(1)=13.9` and `eta_(2)=0.011P` respectively. (in `(mum)/(s)`)

Answer

5

Explanation

We know that for laminar flow
`(R_(e))_(l)=(rhovD)/(eta)=(2rho_(1)v_(1)r_(1))/(eta_(i))` for glycerine and
`(R_(e))_(t)=(2rho_(2)v_(2)r_(2))/(eta_(2))` for water from strocks law,
`impliesv=(2)/(9eta)r^(2)g(rho-sigma)` by equating above equation we can get D as 5 mm