The viscosity of liquids can be measured through the use of rotating-cylinder viscosimeter of
the type shown in Figure 2. In this device, the outer cylinder is fixed and the inner cylinder
is rotated with an angular frequency, ω. The torque, T, required to maintain a constant
ω is measured and the dynamic viscosity, µ, is calculated from these two measurements.
By neglecting end effects and assuming the velocity distribution in the gap to be linear, an
equation relating µ, ω, T, l, R0, and Ri may be written as
2πRi
3lω T = µ. R0 − Ri
a) Derive this equation and show that it is dimensionally correct.
The following torque-angular velocity data were obtained with a rotating-cylinder viscosimeter with R0 = 6.0 cm, Ri = 5.9 cm, and l = 25.0 cm:
Torque (N m· ) 0.178 0.353 0.536 0.715 0.880 1.066
Angular velocity 1.0 2.0 3.0 4.0 5.0 6.0
(rad/s)
b) Give your best estimate of the viscosity, µ.
c) Indicate the accuracy of this estimate.
d) Using Appendix B in Young et al.’s book, what fluid do you think was used if the temperature of the fluid was 15oC.