Question 2.5: Determining the Viscosity of a Fluid The viscosity of a flui...
Determining the Viscosity of a Fluid
The viscosity of a fluid is to be measured by a viscometer constructed of two 40-cm-long concentric cylinders (Fig. 2–30). The outer diameter of the inner cylinder is 12 cm, and the gap between the two cylinders is 0.15 cm. The inner cylinder is rotated at 300 rpm, and the torque is measured to be 1.8 N⋅m. Determine the viscosity of the fluid.
The torque and the rpm of a double cylinder viscometer are given.
The viscosity of the fluid is to be determined.
Assumptions 1 The inner cylinder is completely submerged in the fluid.
2 The viscous effects on the two ends of the inner cylinder are negligible.
Analysis The velocity profile is linear only when the curvature effects are negligible, and the profile can be approximated as being linear in this case since ℓ/R = 0.025 << 1. Solving Eq. 2–38 for viscosity and substituting the given values, the viscosity of the fluid is determined to be
T = FR = \mu \frac{2\pi R^3 \omega L}{ℓ} = \mu \frac{4\pi ^2 R^3 \dot{n}L }{ℓ} (2.38)
\mu = \frac{Tℓ}{4\pi ^2 R^3\dot{n}L } = \frac{(1.8 N.m)(0.0015 m)}{4\pi ^2 (0.06 m)^3\left(300 \frac{1}{min} \right)\left(\frac{1 min}{60 s} \right)(0.4 m) } = 0.158 N.s/m^2
Discussion Viscosity is a strong function of temperature, and a viscosity value without a corresponding temperature is of little usefulness. Therefore, the temperature of the fluid should have also been measured during this experiment, and reported with this calculation.