The viscosity of liquids can be measured through the use ofa rotating cylinder

Chapter 1, Problem 1.87

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The viscosity of liquids can be measured through the use ofa rotating cylinder viscometer of the type illustrated in Fig. P1.87.In this device the outer cylinder is fixed and the inner cylinderis rotated with an angular velocity, . The torque required todevelop is measured and the viscosity is calculated from thesetwo measurements. (a) Develop an equation relating , , , , Ro,and Ri. Neglect end effects and assume the velocity distribution inthe gap is linear. (b) The following torque-angular velocity datawere obtained with a rotating cylinder viscometer of the type discussedin part (a).Torque (ft lb) 13.1 26.0 39.5 52.7 64.9 78.6Angular velocity (rads) 1.0 2.0 3.0 4.0 5.0 6.0For this viscometer Ro = 2.50 in., Ri = 2.45 in., and = 5.00 in.Make use of these data and a standard curve-fitting program todetermine the viscosity of the liquid contained in the viscometer.