A lead sphere is steadily sinking in glycerin whose viscosity is equal to $η = 13.9 P$ . 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 corresponds to Reynolds number $R e = 0.5$ . (Here the characteristic length is taken to be the sphere diameter.)

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A lead sphere is steadily sinking in glycerin whose viscosity is equal to

η = 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 corresponds to Reynolds number

R e = 0.5

. (Here the characteristic length is taken to be the sphere diameter.)

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Text solutionVerified

W e ha v e R = v ρ_{0} d / η an d v i s g i v e n b y 6 π ηr v = \frac{4 π}{3} r^{2} (ρ - ρ_{0}) g (ρ = d e n s i t y o f l e a d, ρ_{0} = d e n s i t y o f g l ycer in e .) v = \frac{2}{9 η} r^{2} (ρ - ρ_{0}) g = \frac{1}{18 η} d^{2} (ρ - ρ_{0}) g T h u s \frac{1}{2} = \frac{1}{18 η} d^{3} (ρ - ρ_{0}) ρ_{0} g an d d = (\frac{9 η}{( ρ - ρ _{0} ) ρ _{0} g})^{1/3} = 5.2 mm

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Question Text	A lead sphere is steadily sinking in glycerin whose viscosity is equal to $η = 13.9 P$ . 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 corresponds to Reynolds number $R e = 0.5$ . (Here the characteristic length is taken to be the sphere diameter.)
Answer Type	Text solution:1
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Text solutionVerified

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