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A lead sphere is steadily is steadily si...

A lead sphere is steadily is steadily sinking in glycerine whose viscosity is equal to `eta=13.9` P.What is the maximum diameter of the sphere at which the flow around that sphere still remains laminar? It is known that the transition to the turbulent flow correspond to reynolds number `R_(e)=0.5`. (here the charactrstic length is taken to be the sphere diameter). (in mm)

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We have `R=(vrho_0d)/(eta)` and `v` is given by
`6pietarv=(4pi)/(3)r^2(rho-rho_0)g`
(`rho=` density of lead, `rho_0=` density of glycerine.)
`v=(2)/(9eta)(rho-rho_0)gr^2-(1)/(18eta)(rho-rho_0)gd^2`
Thus `1/2=(1)/(18eta^2)(rho-rho_o)grho_0d^3`
and `d=[9eta^2//rho_0(rho-rho_0)g]^(1//3)=5*2mm` on putting the values.
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