Capillary Rise or Depression
Introduction: Let D be the diameter of the tube and β is the contact angle. The surface tension forces acting around the circumference of the tube = π × D × σ.
This is balanced by the fluid column of height, h, the specific weight of liquid being γ.
Equating, h × γ × A = π × D × σ Cos β, A = πD2/4 and so the vertical component of this force = π × D × σ × Cos β
h = (4π× D× σ× Cos β)/ (γπ D2) = (4 Cos)/ pgD
This equation provides the means for calculating the capillary rise or depression. The sign of Cos β depending on β > 90 or otherwise determines the capillary rise or depression.
Example: Determine the capillary depression of mercury in a 2 mm ID glass tube. Assume
σ = 0.5 N/m and β = 130°.
Specific weight of mercury, γ = 13600 × 9.81 N/m3
Using eqn. h = (4 σ × Cosβ)/ρg/D = (4 × 0.5 × cos130)/ (13600 × 9.81 × 0.002) = – 4.82 × 10–3 m
= – 4.82 mm Ans.