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.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter5: Analysis Of Convection Heat Transfer

Section: Chapter Questions

Problem 5.5P: Evaluate the dimensionless groups hcD/k,UD/, and cp/k for water, n-butyl alcohol, mercury, hydrogen,...

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