Problem 3.36[Difficulty: 3]Given:Water column standin in glass tubeΔh50 mm⋅=D2.5 mm⋅=σ72.8103−×Nm=(From Table A.4, App. A)Find:(a) Column height if surface tension were zero.(b) Column height in 1 mm diameter tubeSolution:We will apply the hydrostatics equations to this system.Governing Equations:dpdhρg⋅=(Hydrostatic Pressure - h is positive downwards)ΔhpΔhcΔh ΔhcπDδθMg= ρgVΣFz0=(Static Equilibrium)Assumptions:(1) Static, incompressible liquid(2) Neglect volume under meniscus(3) Applied pressure remains constant(4) Column height is sum of capillary rise and pressuredifferenceAssumption #4 can be written as:ΔhΔhcΔhp+=Choose a free-body diagram of the capillary rise portion of the column for analysis:ΣFzπD⋅σ⋅cosθ( )⋅π4D2⋅ρ
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