Problem 2.61 - Problem 2.61 Given Data on the viscometer...

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Problem 2.61 [Difficulty: 3] Given: Data on the viscometer Find: Time for viscometer to lose 99% of speed Solution: The given data is R5 0 m m = H8 0 m m = a 0.20 mm = I 0.0273 kg m 2 = μ 0.1 Ns m 2 = The equation of motion for the slowing viscometer is I α Torque = τ A R = where α is the angular acceleration and τ is the viscous stress, and A is the surface area of the viscometer The stress is given by τμ du dy = μ V0 a = μ V a = μ R ω a = where V and ω are the instantaneous linear and angular velocities. Hence I α I d ω dt = μ R ω a A R = μ R 2 A a ω = Separating variables d ω ω μ R 2 A aI dt = Integrating and using IC
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