Tutorial Problem #3. As we discussed in lecture, a concentric cylinder viscometer is often used to measure the viscosity (μ) of Newtonian fluids. As shown in the accompanying figure, the outer cylinder (with radius Ro) remains stationary while the inner cylinder (with radius R₁) rotates at an angular velocity of w (rev/min) and the torque (T) required to rotate the inner cylinder is measured. Outer Cylinder Fluid Inner Cylinder T Ro a. Starting from Newton's law of viscosity, derive the correct equation that is used to calculate u in μ terms of w, T, Ro, R₁ and (the height of the fluid in the gap between the two cylinders). Because the radial distance between the cylinders (i.e Ro-R₁) is quite small, you can assume that the velocity profile of the fluid varies linearly with respect to distance between the cylinders. HINT #1: Torque is the required force multiplied by the moment arm (which is R¡ in this case) HINT #2: Multiply the angular velocity by the circumference of the inner cylinder to get the linear velocity. b. For a viscometer with Rj = 12 cm, Ro = 12.15 cm, and = 40 cm, determine the viscosity (Pa*s )of a Newtonian fluid if a torque of 0.036 N-m is required to rotate the inner cylinder at 500 rev/min.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Transcribed Image Text:Tutorial Problem #3. As we discussed in lecture, a concentric cylinder viscometer is often used to measure the viscosity (μ) of Newtonian fluids. As shown in the accompanying figure, the outer cylinder (with radius Ro) remains stationary while the inner cylinder (with radius R₁) rotates at an angular velocity of w (rev/min) and the torque (T) required to rotate the inner cylinder is measured. Outer Cylinder Fluid Inner Cylinder T ω R₁ R a. Starting from Newton's law of viscosity, derive the correct equation that is used to calculate u in μ terms of w, T, Ro, R₁ and € (the height of the fluid in the gap between the two cylinders). Because the radial distance between the cylinders (i.e Ro - R₁) is quite small, you can assume that the velocity profile of the fluid varies linearly with respect to distance between the cylinders. HINT #1: Torque is the required force multiplied by the moment arm (which is R¡ in this case) HINT #2: Multiply the angular velocity by the circumference of the inner cylinder to get the linear velocity. b. For a viscometer with Rj = 12 cm, Ro = 12.15 cm, and € = 40 cm, determine the viscosity (Pa*s )of a Newtonian fluid if a torque of 0.036 N·m is required to rotate the inner cylinder at 500 rev/min.

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