# 3-13 - 3-13. In Figure 3.13 we have illustrated a capillary...

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3-13. In Figure 3.13 we have illustrated a capillary tube that has just been immersed in a pool of water. The water is rising in the capillary so that the height of liquid in the tube is a function of time. Later, in a course on fluid mechanics, you will learn that the average velocity of the liquid, , can be represented by the equation v z ⟨⟩ N o 2 o gravitational capillary force force viscous force 8v 2r z h gh r µ σ−ρ = ±²³ ±´² ´³ (1) in which is the average velocity in the capillary tube. The surface tension σ , capillary radius , and fluid viscosity μ can all be treated as constants in addition to the fluid density ρ and the gravitational constant g. From Eq. 1 it is easy to deduce that the final height of the liquid is given by v z o r o 2 h g r = σρ (2) In this problem you are asked to determine the height h as a function of time for the initial condition given by I.C. h t = = 0 , 0 (3) You may find it convenient to work with a dimensionless height defined by Hh t h = () (4) and you may wish to verify your analysis by doing a simple experiment. This would require that

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## This note was uploaded on 07/15/2010 for the course ECM 051 taught by Professor B.g.higgins during the Winter '10 term at UC Davis.

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3-13 - 3-13. In Figure 3.13 we have illustrated a capillary...

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