A torque is applied to rotate a cylindrical shaft (diameter D 1 , length L) at a constant angularspeed ω, inside a co-axial, stationary cylinder of the same length and diameter D 2. The gapbetween the bottom surface of the shaft and that of the stationary cylinder is h.(a) Develop a general expression of the torque in terms of the geometric dimensions andthe viscosity μ of an oil filling the gaps between the shaft and the stationary cylinder.Assume linear velocity profiles in all the gaps.(b) Determine the numerical value of the torque in the case of an oil of viscosity of 0.1Pa.s. [D 1=5cm, D 2=5.2cm, L=10cm, ω=50rpm, h=1mm]
A torque is applied to rotate a cylindrical shaft (diameter D 1 , length L) at a constant angularspeed ω, inside a co-axial, stationary cylinder of the same length and diameter D 2. The gapbetween the bottom surface of the shaft and that of the stationary cylinder is h.(a) Develop a general expression of the torque in terms of the geometric dimensions andthe viscosity μ of an oil filling the gaps between the shaft and the stationary cylinder.Assume linear velocity profiles in all the gaps.(b) Determine the numerical value of the torque in the case of an oil of viscosity of 0.1Pa.s. [D 1=5cm, D 2=5.2cm, L=10cm, ω=50rpm, h=1mm]
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
Related questions
Question
A torque is applied to rotate a cylindrical shaft (diameter D 1 , length L) at a constant angular
speed ω, inside a co-axial, stationary cylinder of the same length and diameter D 2. The gap
between the bottom surface of the shaft and that of the stationary cylinder is h.
(a) Develop a general expression of the torque in terms of the geometric dimensions and
the viscosity μ of an oil filling the gaps between the shaft and the stationary cylinder.
Assume linear velocity profiles in all the gaps.
(b) Determine the numerical value of the torque in the case of an oil of viscosity of 0.1
Pa.s. [D 1=5cm, D 2=5.2cm, L=10cm, ω=50rpm, h=1mm]
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