The viscosity of liquids can be measured through the use of a rotating cylinder viscometer of the type illustrated in Fig. P1.87. In this device the outer cylinder is fixed and the inner cylinder is rotated with an angular velocity, \(\omega\). The torque \(\mathscr{T}\) required to develop \(\omega\) is measured and the viscosity is calculated from these two measurements.

(a) Develop an equation relating \(\mu, \omega, \mathcal{T}, \ell, R_{o}\), and \(R_{i}\). Neglect end effects and assume the velocity distribution in the gap is linear.

(b) The following torque-angular velocity data were obtained with a rotating cylinder viscometer of the type discussed in part (a).

For this viscometer \(R_{o}=2.50\) in., \(R_{i}=2.45\) in., and \(\ell=5.00 \mathrm{in}\). Make use of these data and a standard curve-fitting program to determine the viscosity of the liquid contained in the viscometer.

Figure P1.87

Transcribed Image Text:

Torque (ft. lb) Angular 13.1 26.0 39.5 52.7 64.9 78.6 velocity (rad/s) 1.0 2.0 3.0 4.0 5.0 6.0