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A massless, circular disk of radius a is initially separated from a flat surface by a thin layer of a viscous fluid by a gap of h, h<< a. Both surfaces are highly polished and smooth. (a) Calculate the pressure distribution and the force required to lift the disk off of the solid surface at a constant velocity V, in terms of µ, V, h, and a. (b) E. 11.. if

A massless, circular disk of radius a is initially separated from a flat surface by a thin layer of a viscous fluid by a gap of h, h<< a. Both surfaces are highly polished and smooth. (a) Calculate the pressure distribution and the force required to lift the disk off of the solid surface at a constant velocity V, in terms of µ, V, h, and a. (b) E. 11.. if

Elements Of Electromagnetics
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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A massless, circular disk of radius a is initially separated from a flat surface by a thin layer of a viscous fluid by a gap of h, h<< a. Both surfaces are highly polished and smooth. (a) Calculate the pressure distribution and the force required to lift the disk off of the solid surface at a constant velocity V, in terms of u, V, h, and a. (b) Evaluate the force numerically if a = 3 cm, V 5 m/s, h 1 mm, and the fluid is water. (Not for credit) What would happen if the gap height were smaller, say 10 um? (c) How would the required force change if the disk were no longer flat, but (i) concave downward or (ii) concave upward? You do not need to provide exact expressions, just give qualitative answers (but justify them!).
Transcribed Image Text:A massless, circular disk of radius a is initially separated from a flat surface by a thin layer of a viscous fluid by a gap of h, h<< a. Both surfaces are highly polished and smooth. (a) Calculate the pressure distribution and the force required to lift the disk off of the solid surface at a constant velocity V, in terms of u, V, h, and a. (b) Evaluate the force numerically if a = 3 cm, V 5 m/s, h 1 mm, and the fluid is water. (Not for credit) What would happen if the gap height were smaller, say 10 um? (c) How would the required force change if the disk were no longer flat, but (i) concave downward or (ii) concave upward? You do not need to provide exact expressions, just give qualitative answers (but justify them!).
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