A solid cylindrical needle of diameter d, length L, and density p may float in liquid of surface tension I. Neglect buoyancy, assume a contact angle of 0 degrees and that the needle is submerged upto the diameter line. (1) Draw the free body diagram indicating the force due to surface tension and the weight of the needle. Given that d << L for a typical needle, can you simplify the surface tension forces? (2) Using the simplification, derive a formula for the maximum diameter dmax such that the cylinder is able to float in the liquid.
A solid cylindrical needle of diameter d, length L, and density p may float in liquid of surface tension I. Neglect buoyancy, assume a contact angle of 0 degrees and that the needle is submerged upto the diameter line. (1) Draw the free body diagram indicating the force due to surface tension and the weight of the needle. Given that d << L for a typical needle, can you simplify the surface tension forces? (2) Using the simplification, derive a formula for the maximum diameter dmax such that the cylinder is able to float in the liquid.
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:A solid cylindrical needle of diameter d, length L, and density p may float in liquid of surface
tension I. Neglect buoyancy, assume a contact angle of 0 degrees and that the needle is submerged
upto the diameter line.
(1) Draw the free body diagram indicating the force due to surface tension and the weight of the
needle. Given that d << L for a typical needle, can you simplify the surface tension forces?
(2) Using the simplification, derive a formula for the maximum diameter dmax such that the
cylinder is able to float in the liquid.
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