The Helmholtz free energy of a liquid column that rises, due to surface tension, inside a capillary tube (Figure 1), as a function of the height, h, is given by: F(h) =(ro)gr^2h^2/2 = -2 pi sigma r h cos teta, where r is the radius of the tube, g is the local ac- celaration of gravity, is the surface tension of the liquid, and is the contact angle of the liquid in contact with the wall of the tube. (a) From this expression, obtain the value of h as a function of the other physical parameters at equilibrium.Calculate the height that water will rise in a capil-lary of diameter 0.05mm. Assume that the contactangle between the water and the tube is zero. Thesurface tension of water at experimental conditionsisσ= 7.73×10−2N/m, and the local accelarationof gravity isg= 9.7m/s2.
The Helmholtz free energy of a liquid column that rises, due to surface tension, inside a capillary tube (Figure 1), as a function of the height, h, is given by: F(h) =(ro)gr^2h^2/2 = -2 pi sigma r h cos teta, where r is the radius of the tube, g is the local ac- celaration of gravity, is the surface tension of the liquid, and is the contact angle of the liquid in contact with the wall of the tube. (a) From this expression, obtain the value of h as a function of the other physical parameters at equilibrium.Calculate the height that water will rise in a capil-lary of diameter 0.05mm. Assume that the contactangle between the water and the tube is zero. Thesurface tension of water at experimental conditionsisσ= 7.73×10−2N/m, and the local accelarationof gravity isg= 9.7m/s2.
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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Question
The Helmholtz free energy of a liquid
column that rises, due to surface tension, inside
a capillary tube (Figure 1), as a function of the
height, h, is given by:
F(h) =(ro)gr^2h^2/2 = -2 pi sigma r h cos teta,
where r is the radius of the tube, g is the local ac-
celaration of gravity, is the surface tension of the
liquid, and is the contact angle of the liquid in
contact with the wall of the tube. (a) From this
expression, obtain the value of h as a function of
the other physical parameters at equilibrium.Calculate the height that water will rise in a capil-lary of diameter 0.05mm. Assume that the contactangle between the water and the tube is zero. Thesurface tension of water at experimental conditionsisσ= 7.73×10−2N/m, and the local accelarationof gravity isg= 9.7m/s2.
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