An air bubble of radius 1 mm is allowed to rise through a long cylindrical column of a viscous liquid of radius 5 cm and travels at a steady rate of 2.1 cm per sec. if the density of the liquid is `1.47(g)/(c c)`. Its viscosity is nearly `(n)/(2)` poise. Then find the value of n. Assume `g=980(cm)/(sec^(2))` and neglect the density of air.
Text Solution
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Force of buoyancy on the bubble is much greater than the weight of the air bubble . So the bubble will move up resulting the viscous force acting downward .So in dynamic equilibrium force on buoyancy `F_(B)` = voscous force `F_(0)` `4/3 pir^(3) rho g = 6 pi eta rv_(tau)` ` :. eta = 2/g. (rhor^(2)g)/(v_(r)) = (2xx1.47 xx(0.1)^(2) xx980)/(9 xx 2.1 ) ` ` = 1.524 ` poise
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