Problem 3.36 [Difficulty: 3] Given: Water column standin in glass tube Δ h5 0 m m ⋅ = D 2.5 mm ⋅ = σ 72.8 10 3 − × N m = (From Table A.4, App. A) Find: (a) Column height if surface tension were zero. (b) Column height in 1 mm diameter tube Solution: We will apply the hydrostatics equations to this system. Governing Equations: dp dh ρ g ⋅ = (Hydrostatic Pressure - h is positive downwards) Δ h p Δ h cΔ h Δ h c π D δ θMg = ρ gV ΣF z 0 = (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 pressure difference Assumption #4 can be written as: Δ h Δ h c Δ h p + = Choose a free-body diagram of the capillary rise portion of the column for analysis: Σ F z π D ⋅ σ ⋅ cos θ () ⋅ π 4 D 2
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